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   <text:h text:style-name="Heading_20_1" text:outline-level="1">Joints</text:h>
   <text:h text:style-name="Heading_20_2" text:outline-level="2">Simple Joint</text:h>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Constant Velocity Joint</text:h>
   <text:p text:style-name="equation">It is like a rubber tube which transmits angular velocity from one end to the other.</text:p>
   <text:p text:style-name="equation">Note that there is a singularity when the z axes are parallel. The constraint is identically satisfied.</text:p>
   <text:p text:style-name="equation">Therefore the joint works only when there is a bend. Even an infinitesimal amount helps.</text:p>
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     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Cylindrical Joint</text:h>
   <text:p text:style-name="equation">Je remains on z axis of Ie.</text:p>
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          <mi>G</mi>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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            <mrow>
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             <mi>,</mi>
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              <mi mathvariant="normal">s</mi>
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          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
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            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
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          <mo stretchy="false">=</mo>
          <mn>0</mn>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAANIJAACnAQAAAQAAAD0AUwEA
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       AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKgsAAKcBAAABAHKhAAAAAAD//wEAcgCMAAEA
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       AAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQA
       AAAAAAAAcgACACkAAAD9CwAAEQIAAAcASWVKZUllMeECAAAAAP//BwBJAGUASgBlAEkAZQAx
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       AP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
       hgABAAQAAAAAAAAAcgACABoAAADiDgAApwEAAAEAAAA9AFMBAAAAAP//AQA9AIwAAQAAAAAA
       iwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAACnAQAAAAAAAAAABQAA
       AAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAA
       AAByAAIAFwAAAFQQAACnAQAAAQAw1AAAAAAA//8BADAAjAABAAAAAACVAAEABAAAAAAAAACW
       AAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object3" text:anchor-type="as-char" svg:width="1.7693in" svg:height="0.2299in" draw:z-index="3"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
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           <mn>2</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>2</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe2}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe2}
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object5" text:anchor-type="as-char" svg:width="2.4917in" svg:height="0.2437in" draw:z-index="4"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
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            <mn>2</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Fixed Joint</text:h>
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       <semantics>
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         <msub>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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            <mrow>
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              <mi mathvariant="normal">q</mi>
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             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
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             <mi>,</mi>
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          <mo stretchy="false">=</mo>
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           <mi>r</mi>
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          <mo stretchy="false">=</mo>
          <mn>0</mn>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
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       <semantics>
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           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeO1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeO1}
=
0</annotation>
       </semantics>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeO3}
=
0</annotation>
       </semantics>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">No relative rotation from Ie to Je.</text:p>
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       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
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           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
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             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
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           </mstyle>
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           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
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            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
       </semantics>
      </math>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
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           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
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           </mstyle>
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          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>1</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
       </semantics>
      </math>
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         <mrow>
          <mrow>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic j}_JeO
=
A_Ie1Je2
=
0</annotation>
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Hooke Joint</text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
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       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">IeJeIe</mi>
           <mn>1</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
      </math>
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     </draw:image>
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       <semantics>
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         <msub>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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            <mrow>
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             <mi>,</mi>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
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            <mi mathvariant="italic">IeJeO</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeO1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeO1}
=
0</annotation>
       </semantics>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">x axis of Ie is perpendicular to y axis of Je.</text:p>
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       <semantics>
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         <msub>
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         <mrow>
          <mrow>
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             <mi>,</mi>
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             <mi>t</mi>
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           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
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          <msub>
           <mi>A</mi>
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           </mrow>
          </msub>
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          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho jJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic j}_JeO
=
A_Ie1Je2
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA/ggAAMIBAAABAHR3AAAAAAD//wEAdACM
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       AQAEAAAAAAAAAHIAAgAaAAAAtwkAAMIBAAABAAAAn+BmAAAAAAD//wEAn+CMAAEAAAAAAIsA
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       AAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAA
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       AAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAB5
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       hwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA/QsAAO4AAAABAFSQAAAAAAD//wEA
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       AP//AQA9AIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAA
       AACnAQAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA
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     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Planar Joint</text:h>
   <text:p text:style-name="equation">Je remains in xy plane of Ie.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object12" text:anchor-type="as-char" svg:width="2.2272in" svg:height="0.2299in" draw:z-index="13"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">IeJeIe</mi>
           <mn>3</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mrow>
           <msub>
            <mi>r</mi>
            <mrow>
             <mi mathvariant="italic">IeJeIe</mi>
             <mn>3</mn>
            </mrow>
           </msub>
           <mo stretchy="false">−</mo>
           <mi>f</mi>
          </mrow>
         </mrow>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
           <mrow>
            <mi>t</mi>
           </mrow>
           <mo fence="true" form="postfix" stretchy="false">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
- f(t) =
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAEABAAAAAAAAAByAAIAFwAAAGoAAACnAQAAAQBHMQEAAAAA//8BAEcAjAABAAAAAACLAAEA
       AgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAAC
       AP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIA
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       AAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA
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       iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAIMGAACnAQAAAQAs
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAIgcAAKcBAAABAHOhAAAAAAD//wEAcwCM
       AAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAA
       AAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgAB
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       AQAAAJ/gZgAAAAAA//8BAJ/gjAABAAAAAACLAAEAAgAAAB8AigABADoAAAACADQAAAAKAFN0
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       AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAANIJAACnAQAAAQAAAD0AUwEA
       AAAA//8BAD0AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAA
       AAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUA
       AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKgsAAKcBAAABAHKhAAAAAAD//wEAcgCMAAEA
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       AP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
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       AAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAA
       AAByAAIAFwAAAKQQAACnAQAAAQBmfwAAAAAA//8BAGYAjAABAAAAAACLAAEAAgAAAB8AigAB
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       AAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAKwR
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       AAAJAFRob3JuZGFsZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACI
       AAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAASxIAAKcBAAABAHR3
       AAAAAAD//wEAdACMAAEAAAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJv
       bAAAAAAAAKcBAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwAB
       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAABBMAAKcBAAABAAAAn+CHAAAAAAD//wEA
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       AAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////
       AIYAAQAEAAAAAAAAAHIAAgAaAAAAiRMAAKcBAAABAAAAPQBTAQAAAAD//wEAPQCMAAEAAAAA
       AIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAAAAAAAAUA
       AAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAA
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object14" text:anchor-type="as-char" svg:width="2.4917in" svg:height="0.2437in" draw:z-index="14"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">jIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
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           </mrow>
          </msub>
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         </mrow>
        </mrow>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
       </semantics>
      </math>
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    </draw:frame></text:p>
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       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
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           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>1</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Rack and Pinion Joint</text:h>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je.</text:p>
   <text:p text:style-name="equation">x axis of Ie start <text:s/>parallel to x axis of Je.</text:p>
   <text:p text:style-name="equation">Pinion should be on the positive xy plane of Ie.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object15" text:anchor-type="as-char" svg:width="0.3709in" svg:height="0.2165in" draw:z-index="16"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <msub>
         <mi>r</mi>
         <mi mathvariant="italic">pitch</mi>
        </msub>
        <annotation encoding="StarMath 5.0">r_pitch</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
      <office:binary-data>VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAa4DAAAn
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       AgAjAAAAWAEAAPcBAAAFAHBpdGNo9AEAAAAA//8FAHAAaQB0AGMAaACMAAEAAAAAAJUAAQAE
       AAAAAAAAAJYAAQACAAAAAACMAAEAAAAAAA==
      </office:binary-data>
     </draw:image>
    </draw:frame>is pitch radius.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object16" text:anchor-type="as-char" svg:width="2.5783in" svg:height="0.2299in" draw:z-index="17"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mi mathvariant="italic">rack</mi>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mstyle mathvariant="bold">
             <mi mathvariant="normal">q</mi>
            </mstyle>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mrow>
           <msub>
            <mi>r</mi>
            <mrow>
             <mi mathvariant="italic">IeJeIe</mi>
             <mn>1</mn>
            </mrow>
           </msub>
           <mo stretchy="false">+</mo>
           <msub>
            <mi>r</mi>
            <mi mathvariant="italic">pitch</mi>
           </msub>
          </mrow>
         </mrow>
         <mrow>
          <msub>
           <mi>θ</mi>
           <mrow>
            <mi mathvariant="italic">IeJe</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">+</mo>
          <mi>f</mi>
         </mrow>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
           <mrow>
            <mi>t</mi>
           </mrow>
           <mo fence="true" form="postfix" stretchy="false">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rack}
left(
{bold nitalic q}
right)
=
r_{IeJeIe1}+ r_pitch %theta_IeJe3
+ f(t) =
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Revolute, Pin Joint</text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
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          <mi>G</mi>
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           <mn>1</mn>
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             </mstyle>
             <mi>,</mi>
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              <mi mathvariant="normal">s</mi>
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             <mi>,</mi>
             <mi>t</mi>
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          <mo stretchy="false">=</mo>
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           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
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          <mo stretchy="false">=</mo>
          <mn>0</mn>
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        </mrow>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAIgcAAKcBAAABAHOhAAAAAAD//wEAcwCM
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       AAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgAB
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       <semantics>
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         <msub>
          <mi>G</mi>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
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            <mi mathvariant="italic">IeJeO</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeO1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeO1}
=
0</annotation>
       </semantics>
      </math>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object137" text:anchor-type="as-char" svg:width="1.7693in" svg:height="0.2299in" draw:z-index="118"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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           <mn>2</mn>
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         </msub>
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          <mrow>
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          <mo stretchy="false">=</mo>
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           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe2}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe2}
=
0</annotation>
       </semantics>
      </math>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeO2}
=
0</annotation>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
       </semantics>
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       <semantics>
        <mrow>
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          <mi>G</mi>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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            <mrow>
             <mstyle mathvariant="bold">
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              <mi mathvariant="normal">s</mi>
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           <mo fence="true" form="postfix" stretchy="true">)</mo>
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           <mi>r</mi>
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            <mi mathvariant="italic">IeJeO</mi>
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           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeO3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeO3}
=
0</annotation>
       </semantics>
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       ////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKgsAAKcBAAABAHKhAAAAAAD//wEAcgCMAAEAAAAA
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       AAAAjAABAAAAAAA=
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object19" text:anchor-type="as-char" svg:width="2.4917in" svg:height="0.2437in" draw:z-index="18"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">jIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>2</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
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          </mrow>
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         <mrow>
          <mrow>
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            <mrow>
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         <mrow>
          <msub>
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          <msub>
           <mi>A</mi>
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            <mn>3</mn>
           </mrow>
          </msub>
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          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
       </semantics>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Screw Joint</text:h>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je.</text:p>
   <text:p text:style-name="equation">x axis of Ie start <text:s/>parallel to x axis of Je.</text:p>
   <text:p text:style-name="equation">Screw uses the right hand rule.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <msub>
         <mi>d</mi>
         <mi mathvariant="italic">pitch</mi>
        </msub>
        <annotation encoding="StarMath 5.0">d_pitch</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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     </draw:image>
    </draw:frame>is pitch of screw.</text:p>
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       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mi mathvariant="italic">screw</mi>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mstyle mathvariant="bold">
             <mi mathvariant="normal">q</mi>
            </mstyle>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mn>2</mn>
         </mrow>
         <mi>π</mi>
         <mrow>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">−</mo>
          <msub>
           <mi>d</mi>
           <mi mathvariant="italic">pitch</mi>
          </msub>
         </mrow>
         <mrow>
          <msub>
           <mi>θ</mi>
           <mrow>
            <mi mathvariant="italic">IeJe</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">+</mo>
          <mi>f</mi>
         </mrow>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
           <mrow>
            <mi>t</mi>
           </mrow>
           <mo fence="true" form="postfix" stretchy="false">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{screw}
left(
{bold nitalic q}
right)
=
2%pi r_{IeJeIe3}- d_pitch %theta_IeJe3
+ f(t) =
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Spherical, Ball Joint</text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
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             <mi>,</mi>
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              <mi mathvariant="normal">s</mi>
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             <mi>t</mi>
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          <mo stretchy="false">=</mo>
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           <mi>r</mi>
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            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
      </math>
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAIgcAAKcBAAABAHOhAAAAAAD//wEAcwCM
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       <semantics>
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          </mrow>
         </msub>
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          <mrow>
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            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeO1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeO1}
=
0</annotation>
       </semantics>
      </math>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object140" text:anchor-type="as-char" svg:width="1.7693in" svg:height="0.2299in" draw:z-index="124"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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           <mn>2</mn>
          </mrow>
         </msub>
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          <mrow>
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          <mo stretchy="false">=</mo>
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            <mi mathvariant="italic">IeJeIe</mi>
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           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe2}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe2}
=
0</annotation>
       </semantics>
      </math>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Translational, Slider Joint</text:h>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
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       <semantics>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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            <mrow>
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           </mrow>
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          <mo stretchy="false">=</mo>
          <mn>0</mn>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe2}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe2}
=
0</annotation>
       </semantics>
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       AAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object26" text:anchor-type="as-char" svg:width="2.4917in" svg:height="0.2437in" draw:z-index="24"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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           <mrow>
            <mrow>
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              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
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           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
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           </mstyle>
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          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
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            <mn>2</mn>
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            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object23" text:anchor-type="as-char" svg:width="2.4618in" svg:height="0.2437in" draw:z-index="25"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">iIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>1</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
       </semantics>
      </math>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic j}_JeO
=
A_Ie1Je2
=
0</annotation>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Universal Joint</text:h>
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       <semantics>
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         <msub>
          <mi>G</mi>
          <mrow>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
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           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
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            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
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      </office:binary-data>
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       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
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           <mn>3</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
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             <mi>,</mi>
             <mi>t</mi>
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           <mo fence="true" form="postfix" stretchy="true">)</mo>
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          <mo stretchy="false">=</mo>
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           <mi>r</mi>
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           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeO3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeO3}
=
0</annotation>
       </semantics>
      </math>
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       AAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQA
       AAAAAAAAcgACABcAAAAQCAAApwEAAAEALG4AAAAAAP//AQAsAIwAAQAAAAAAiwABAAIAAAAf
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       AAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAA
       AK8IAACnAQAAAQB0dwAAAAAA//8BAHQAjAABAAAAAACLAAEAAgAAAB8AigABADoAAAACADQA
       AAAKAFN0YXJTeW1ib2wAANwAAAD4AQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAA
       iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAE0JAACnAQAAAQAA
       AJ/gZgAAAAAA//8BAJ/gjAABAAAAAACLAAEAAgAAAB8AigABADoAAAACADQAAAAKAFN0YXJT
       eW1ib2wAAAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAAB
       AIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAANIJAACnAQAAAQAAAD0AUwEAAAAA
       //8BAD0AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAA
       AKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/
       ////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKgsAAKcBAAABAHKhAAAAAAD//wEAcgCMAAEAAAAA
       AIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAA/QAAAAAAAAAAAAUA
       AAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAA
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       AAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z axis of Ie is perpendicular to z axis of Je.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">kIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>3</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{kIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic k}^T_IeO
{bold nitalic k}_JeO
=
A_Ie3Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
      <office:binary-data>VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAREZAABr
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       ZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwAB
       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAMwkAAMIBAAABAHR3AAAAAAD//wEAdACM
       AAEAAAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAA3AAAAPgBAAD/
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       AQAEAAAAAAAAAHIAAgAaAAAA7AkAAMIBAAABAAAAn+BmAAAAAAD//wEAn+CMAAEAAAAAAIsA
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       AAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAACu
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       ZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEA
       hwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAtgwAAO4AAAABAFSQAAAAAAD//wEA
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       AAAAAAAAAAgAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
       hgABAAQAAAAAAAAAcgACABcAAAB4DgAAwgEAAAEAa+UAAAAAAP//AQBrAIwAAQAAAAAAiwAB
       AAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAA
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       AAIAHQAAAJsPAAAsAgAAAwBKZU+WAQAAAAD//wMASgBlAE8AjAABAAAAAACLAAEAAgAAAB8A
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       AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAtRIAAMIBAAAB
       AEEGAQAAAAD//wEAQQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5k
       YWxlAAAAAAAA/QAAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCH
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       AACnAQAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA
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     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_2" text:outline-level="2">Primitive Joint</text:h>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">AtPoint</text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object102" text:anchor-type="as-char" svg:width="1.7661in" svg:height="0.2299in" draw:z-index="136"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">IeJeIe</mi>
           <mn>1</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
      <office:binary-data>VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAYYRAABH
       AgAAaQAAAIsAAQACAAAA//+BAAEAEAAAAAAAAAAAAAAAhREAAEYCAACVAAEABAAAAAAAAACW
       AAEAAgAAAAkAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAACnAQAA
       AAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCG
       AAEABAAAAAAAAAByAAIAFwAAAGoAAACnAQAAAQBHMQEAAAAA//8BAEcAjAABAAAAAACLAAEA
       AgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAAC
       AP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIA
       AgApAAAAwgEAABECAAAHAEllSmVJZTHhAgAAAAD//wcASQBlAEoAZQBJAGUAMQCMAAEAAAAA
       AIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAA3AAAAPgBAAD//wAAAAAF
       AAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAA
       AAAAAHIAAgAaAAAAwQQAAKcBAAABAAAAnuBmAAAAAAD//wEAnuCMAAEAAAAAAIsAAQACAAAA
       HwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAAAAAAAAgAAAAAAAAA/wMA
       AAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA
       AABgBQAApwEAAAEAce0AAAAAAP//AQBxAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAz
       AAAACQBUaG9ybmRhbGUAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAA
       iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAIMGAACnAQAAAQAs
       bgAAAAAA//8BACwAjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFs
       ZQAAAAAAAKcBAAAAAAAAAAAIAAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwAB
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">InLine</text:h>
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     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">InPlane</text:h>
   <text:p text:style-name="equation">Je remains in xy plane of Ie.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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           <mi mathvariant="italic">IeJeIe</mi>
           <mn>3</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
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             <mi>,</mi>
             <mi>t</mi>
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           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mrow>
           <msub>
            <mi>r</mi>
            <mrow>
             <mi mathvariant="italic">IeJeIe</mi>
             <mn>3</mn>
            </mrow>
           </msub>
           <mo stretchy="false">−</mo>
           <mi>f</mi>
          </mrow>
         </mrow>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
           <mrow>
            <mi>t</mi>
           </mrow>
           <mo fence="true" form="postfix" stretchy="false">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
- f(t) 
=
0</annotation>
       </semantics>
      </math>
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       AAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQA
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     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Orientation</text:h>
   <text:p text:style-name="equation">No relative rotation from Ie to Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object35" text:anchor-type="as-char" svg:width="2.4917in" svg:height="0.2437in" draw:z-index="31"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">jIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>2</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object36" text:anchor-type="as-char" svg:width="2.4618in" svg:height="0.2437in" draw:z-index="32"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">iIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>1</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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    </draw:frame></text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
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           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">jJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>1</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>2</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho jJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic j}_JeO
=
A_Ie1Je2
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">ParallelAxes</text:h>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object38" text:anchor-type="as-char" svg:width="2.4917in" svg:height="0.2437in" draw:z-index="34"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">jIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>2</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object37" text:anchor-type="as-char" svg:width="2.4618in" svg:height="0.2437in" draw:z-index="35"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">iIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>1</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAAAQBQAAwgEAAAEAAACe4GYA
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       AAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA
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       AAAACQBUaG9ybmRhbGUAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAA
       iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAF8IAADCAQAAAQAs
       bgAAAAAA//8BACwAjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFs
       ZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwAB
       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA/ggAAMIBAAABAHR3AAAAAAD//wEAdACM
       AAEAAAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAA3AAAAPgBAAD/
       /wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYA
       AQAEAAAAAAAAAHIAAgAaAAAAtwkAAMIBAAABAAAAn+BmAAAAAAD//wEAn+CMAAEAAAAAAIsA
       AQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAAAAAAAKcBAAD//wAAAAAFAAAA
       AAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAA
       AHIAAgAaAAAAIQoAAMIBAAABAAAAPQBTAQAAAAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCK
       AAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAAAAAAAAgAAAAAAAAA/wMAAAAA
       AAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAB5
       CwAAwgEAAAEAaXcAAAAAAP//AQBpAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAA
       CQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAAB
       AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAABgMAAAsAgAAAwBJZU99
       AQAAAAD//wMASQBlAE8AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3Ju
       ZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEA
       hwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAGAwAAO4AAAABAFSQAAAAAAD//wEA
       VACMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEA
       AAAAAAAAAAgAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
       hgABAAQAAAAAAAAAcgACABcAAADZDQAAwgEAAAEAa+UAAAAAAP//AQBrAIwAAQAAAAAAiwAB
       AAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAA
       AgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABy
       AAIAHQAAAOIOAAAsAgAAAwBKZU+WAQAAAAD//wMASgBlAE8AjAABAAAAAACLAAEAAgAAAB8A
       igABADoAAAACADQAAAAKAFN0YXJTeW1ib2wAAAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAA
       AAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAA
       AIkQAADCAQAAAQAAAD0AUwEAAAAA//8BAD0AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAAC
       ADMAAAAJAFRob3JuZGFsZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMA
       AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAFhIAAMIBAAAB
       AEEGAQAAAAD//wEAQQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5k
       YWxlAAAAAAAA/QAAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCH
       AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACACYAAAA5EwAALAIAAAYASWUxSmUznQIAAAAA
       //8GAEkAZQAxAEoAZQAzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA6AAAAAgA0AAAACgBTdGFy
       U3ltYm9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAA
       AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAADPFQAAwgEAAAEAAAA9AFMBAAAA
       AP//AQA9AIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAA
       AACnAQAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA
       /////wCGAAEABAAAAAAAAAByAAIAFwAAAEEXAADCAQAAAQAw1AAAAAAA//8BADAAjAABAAAA
       AACVAAEABAAAAAAAAACWAAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Perpendicular</text:h>
   <text:p text:style-name="equation">z axis of Ie is perpendicular to z axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object39" text:anchor-type="as-char" svg:width="2.5264in" svg:height="0.2437in" draw:z-index="36"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">kIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>3</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{kIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic k}^T_IeO
{bold nitalic k}_JeO
=
A_Ie3Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
      <office:binary-data>VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAREZAABr
       AgAAoQAAAIsAAQACAAAA//+BAAEAEAAAAAAAAAAAAAAAEBkAAGoCAACVAAEABAAAAAAAAACW
       AAEAAgAAAAkAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAACnAQAA
       AAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCG
       AAEABAAAAAAAAAByAAIAFwAAAGoAAADCAQAAAQBHMQEAAAAA//8BAEcAjAABAAAAAACLAAEA
       AgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAAC
       AP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIA
       AgAdAAAAwgEAACwCAAADAGtJZTEBAAAAAP//AwBrAEkAZQCMAAEAAAAAAIsAAQACAAAAHwCK
       AAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAAAAAAAP0AAAD//wAAAAAFAAAAAAAAAP8DAAAA
       AAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA
       /wIAACwCAAABAAAApSKyAAAAAAD//wEApSKMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIA
       MwAAAAkAVGhvcm5kYWxlAAAAAAAA/QAAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAA
       AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAADTAwAALAIAAAMA
       a0plSgEAAAAA//8DAGsASgBlAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA6AAAAAgA0AAAACgBT
       dGFyU3ltYm9sAADcAAAA+AEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQAC
       AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABFBQAAwgEAAAEAAACe4GYA
       AAAAAP//AQCe4IwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUA
       AAAAAACnAQAAAAAAAAAACAAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAF
       AAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAOQFAADCAQAAAQBx7QAAAAAA//8BAHEAjAAB
       AAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAKcBAAAAAAAA
       AAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAE
       AAAAAAAAAHIAAgAXAAAABwcAAMIBAAABACxuAAAAAAD//wEALACMAAEAAAAAAIsAAQACAAAA
       HwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAAAAAAAAgAAAAAAAAA/wMA
       AAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA
       AACmBwAAwgEAAAEAc6EAAAAAAP//AQBzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAz
       AAAACQBUaG9ybmRhbGUAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAA
       iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAJQIAADCAQAAAQAs
       bgAAAAAA//8BACwAjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFs
       ZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwAB
       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAMwkAAMIBAAABAHR3AAAAAAD//wEAdACM
       AAEAAAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAA3AAAAPgBAAD/
       /wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYA
       AQAEAAAAAAAAAHIAAgAaAAAA7AkAAMIBAAABAAAAn+BmAAAAAAD//wEAn+CMAAEAAAAAAIsA
       AQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAAAAAAAKcBAAD//wAAAAAFAAAA
       AAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAA
       AHIAAgAaAAAAVgoAAMIBAAABAAAAPQBTAQAAAAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCK
       AAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAAAAAAAAgAAAAAAAAA/wMAAAAA
       AAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAACu
       CwAAwgEAAAEAa+UAAAAAAP//AQBrAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAA
       CQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAAB
       AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAANEMAAAsAgAAAwBJZU99
       AQAAAAD//wMASQBlAE8AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3Ju
       ZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEA
       hwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAtgwAAO4AAAABAFSQAAAAAAD//wEA
       VACMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEA
       AAAAAAAAAAgAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
       hgABAAQAAAAAAAAAcgACABcAAAB4DgAAwgEAAAEAa+UAAAAAAP//AQBrAIwAAQAAAAAAiwAB
       AAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAA
       AgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABy
       AAIAHQAAAJsPAAAsAgAAAwBKZU+WAQAAAAD//wMASgBlAE8AjAABAAAAAACLAAEAAgAAAB8A
       igABADoAAAACADQAAAAKAFN0YXJTeW1ib2wAAAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAA
       AAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAA
       AEMRAADCAQAAAQAAAD0AUwEAAAAA//8BAD0AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAAC
       ADMAAAAJAFRob3JuZGFsZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMA
       AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAtRIAAMIBAAAB
       AEEGAQAAAAD//wEAQQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5k
       YWxlAAAAAAAA/QAAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCH
       AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACACYAAADYEwAALAIAAAYASWUzSmUznQIAAAAA
       //8GAEkAZQAzAEoAZQAzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA6AAAAAgA0AAAACgBTdGFy
       U3ltYm9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAA
       AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABtFgAAwgEAAAEAAAA9AFMBAAAA
       AP//AQA9AIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAA
       AACnAQAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA
       /////wCGAAEABAAAAAAAAAByAAIAFwAAAOAXAADCAQAAAQAw1AAAAAAA//8BADAAjAABAAAA
       AACVAAEABAAAAAAAAACWAAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_2" text:outline-level="2">Composite Joint</text:h>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Spherical-Spherical Joint</text:h>
   <text:p text:style-name="equation">Distance from Ie to Je is constant.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object40" text:anchor-type="as-char" svg:width="2.7228in" svg:height="0.2299in" draw:z-index="37"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mi mathvariant="italic">IeJe</mi>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
G_{IeJe}
-
f(t)
=
G_{IeJe}
-
d
=
0</annotation>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Cylindrical-Spherical Joint</text:h>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIexy}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
G_{IeJeIexy}
-
f(t)
=
G_{IeJeIexy}
-
d
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Revolute-Spherical Joint</text:h>
   <text:p text:style-name="equation">Distance from Ie to Je is constant.</text:p>
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        <annotation encoding="StarMath 5.0">G_{IeJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
G_{IeJe}
-
f(t)
=
G_{IeJe}
-
d
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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          <mi>G</mi>
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            <mn>3</mn>
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        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
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       AAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgAB
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Parallel Revolute-Revolute Joint</text:h>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
G_{IeJe}
-
f(t)
=
G_{IeJe}
-
d
=
0</annotation>
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       AQAAAAAA
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">Je remains in xy plane of Ie.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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           <mi mathvariant="italic">IeJeIe</mi>
           <mn>3</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAEABAAAAAAAAAByAAIAFwAAAGoAAACnAQAAAQBHMQEAAAAA//8BAEcAjAABAAAAAACLAAEA
       AgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAAC
       AP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIA
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAIgcAAKcBAAABAHOhAAAAAAD//wEAcwCM
       AAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAA
       AAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgAB
       AAQAAAAAAAAAcgACABcAAAAQCAAApwEAAAEALG4AAAAAAP//AQAsAIwAAQAAAAAAiwABAAIA
       AAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/
       AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIA
       FwAAAK8IAACnAQAAAQB0dwAAAAAA//8BAHQAjAABAAAAAACLAAEAAgAAAB8AigABADoAAAAC
       ADQAAAAKAFN0YXJTeW1ib2wAANwAAAD4AQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8D
       AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAGgJAACnAQAA
       AQAAAJ/gZgAAAAAA//8BAJ/gjAABAAAAAACLAAEAAgAAAB8AigABADoAAAACADQAAAAKAFN0
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       AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAANIJAACnAQAAAQAAAD0AUwEA
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       AAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUA
       AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKgsAAKcBAAABAHKhAAAAAAD//wEAcgCMAAEA
       AAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAA/QAAAAAAAAAA
       AAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQA
       AAAAAAAAcgACACkAAAD9CwAAEQIAAAcASWVKZUllM+ECAAAAAP//BwBJAGUASgBlAEkAZQAz
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       AP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
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       AAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object46" text:anchor-type="as-char" svg:width="2.4917in" svg:height="0.2437in" draw:z-index="42"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">jIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>2</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object45" text:anchor-type="as-char" svg:width="2.4618in" svg:height="0.2437in" draw:z-index="43"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">iIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>1</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAEAAAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAA3AAAAPgBAAD/
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       AQAEAAAAAAAAAHIAAgAaAAAAtwkAAMIBAAABAAAAn+BmAAAAAAD//wEAn+CMAAEAAAAAAIsA
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       AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAADPFQAAwgEAAAEAAAA9AFMBAAAA
       AP//AQA9AIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAA
       AACnAQAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA
       /////wCGAAEABAAAAAAAAAByAAIAFwAAAEEXAADCAQAAAQAw1AAAAAAA//8BADAAjAABAAAA
       AACVAAEABAAAAAAAAACWAAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object113" text:anchor-type="as-char" svg:width="0.402in" svg:height="0.2201in" draw:z-index="44"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <msub>
         <mstyle mathvariant="bold">
          <mi mathvariant="normal">r</mi>
         </mstyle>
         <mi mathvariant="italic">IeJeO</mi>
        </msub>
        <annotation encoding="StarMath 5.0">{bold nitalic r}_IeJeO</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
      <office:binary-data>VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAf0DAAAv
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       AAAAAAAAAJYAAQACAAAAAACMAAEAAAAAAA==
      </office:binary-data>
     </draw:image>
    </draw:frame>is perpendicular to z axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object114" text:anchor-type="as-char" svg:width="2.1409in" svg:height="0.2437in" draw:z-index="45"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">rIeJe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
           <mi mathvariant="italic">IeJeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rIeJe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic r}^T_IeJeO
{bold nitalic k}_JeO
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAABgoAAMIBAAABAHR3AAAAAAD/
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       ////AIYAAQAEAAAAAAAAAHIAAgAaAAAAwAoAAMIBAAABAAAAn+BmAAAAAAD//wEAn+CMAAEA
       AAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAAAAAAAKcBAAD//wAA
       AAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAE
       AAAAAAAAAHIAAgAaAAAAKgsAAMIBAAABAAAAPQBTAQAAAAD//wEAPQCMAAEAAAAAAIsAAQAC
       AAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAAAAAAAAgAAAAAAAAA
       /wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgAC
       ABcAAACBDAAAwgEAAAEAcrIAAAAAAP//AQByAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAA
       AgAzAAAACQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8D
       AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAIwAAAFUNAAAsAgAA
       BQBJZUplT1kCAAAAAP//BQBJAGUASgBlAE8AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAAC
       ADMAAAAJAFRob3JuZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMA
       AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAOw0AAO4AAAAB
       AFSQAAAAAAD//wEAVACMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5k
       YWxlAAAAAAAApwEAAAAAAAAAAAgAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCH
       AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAADrDwAAwgEAAAEAa+UAAAAAAP//AQBr
       AIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAAD9AAAA
       AAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCG
       AAEABAAAAAAAAAByAAIAHQAAAPMQAAAsAgAAAwBKZU+WAQAAAAD//wMASgBlAE8AjAABAAAA
       AACLAAEAAgAAAB8AigABADoAAAACADQAAAAKAFN0YXJTeW1ib2wAAAAAAACnAQAA//8AAAAA
       BQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAA
       AAAAAAByAAIAGgAAAJsSAADCAQAAAQAAAD0AUwEAAAAA//8BAD0AjAABAAAAAACLAAEAAgAA
       AB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAAAAP8D
       AAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAX
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">Only three of the last four constraints are needed.</text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Radial Perpendicular Revolute-Revolute Joint</text:h>
   <text:p text:style-name="equation">Distance from Ie to Je is constant.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object47" text:anchor-type="as-char" svg:width="2.7228in" svg:height="0.2299in" draw:z-index="46"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mi mathvariant="italic">IeJe</mi>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mrow>
           <msub>
            <mi>G</mi>
            <mi mathvariant="italic">IeJe</mi>
           </msub>
           <mo stretchy="false">−</mo>
           <mi>f</mi>
          </mrow>
         </mrow>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
           <mrow>
            <mi>t</mi>
           </mrow>
           <mo fence="true" form="postfix" stretchy="false">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mrow>
           <msub>
            <mi>G</mi>
            <mi mathvariant="italic">IeJe</mi>
           </msub>
           <mo stretchy="false">−</mo>
           <mi>d</mi>
          </mrow>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
G_{IeJe}
-
f(t)
=
G_{IeJe}
-
d
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">Je remains in xy plane of Ie.</text:p>
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          </mrow>
         </msub>
         <mrow>
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           <mrow>
            <mrow>
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           </mrow>
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            <mn>3</mn>
           </mrow>
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          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
       </semantics>
      </math>
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     </draw:image>
    </draw:frame></text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <msub>
         <mstyle mathvariant="bold">
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         </mstyle>
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        </msub>
        <annotation encoding="StarMath 5.0">{bold nitalic r}_IeJeO</annotation>
       </semantics>
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     </draw:object><draw:image>
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      </office:binary-data>
     </draw:image>
    </draw:frame>is parallel to z axis of Je.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">rIeJe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">iJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
           <mi mathvariant="italic">IeJeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rIeJe ortho iJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic r}^T_IeJeO
{bold nitalic i}_JeO
=
0</annotation>
       </semantics>
      </math>
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    </draw:frame></text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
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           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">jJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
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           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
           <mi mathvariant="italic">IeJeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rIeJe ortho jJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic r}^T_IeJeO
{bold nitalic j}_JeO
=
0</annotation>
       </semantics>
      </math>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z of Ie is perpendicular to z axis of Je.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>3</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{kIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic k}^T_IeO
{bold nitalic k}_JeO
=
A_Ie3Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAMwkAAMIBAAABAHR3AAAAAAD//wEAdACM
       AAEAAAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAA3AAAAPgBAAD/
       /wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYA
       AQAEAAAAAAAAAHIAAgAaAAAA7AkAAMIBAAABAAAAn+BmAAAAAAD//wEAn+CMAAEAAAAAAIsA
       AQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAAAAAAAKcBAAD//wAAAAAFAAAA
       AAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAA
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       AAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAACu
       CwAAwgEAAAEAa+UAAAAAAP//AQBrAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAA
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       AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAANEMAAAsAgAAAwBJZU99
       AQAAAAD//wMASQBlAE8AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3Ju
       ZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEA
       hwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAtgwAAO4AAAABAFSQAAAAAAD//wEA
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       AAAAAAAAAAgAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
       hgABAAQAAAAAAAAAcgACABcAAAB4DgAAwgEAAAEAa+UAAAAAAP//AQBrAIwAAQAAAAAAiwAB
       AAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAA
       AgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABy
       AAIAHQAAAJsPAAAsAgAAAwBKZU+WAQAAAAD//wMASgBlAE8AjAABAAAAAACLAAEAAgAAAB8A
       igABADoAAAACADQAAAAKAFN0YXJTeW1ib2wAAAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAA
       AAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAA
       AEMRAADCAQAAAQAAAD0AUwEAAAAA//8BAD0AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAAC
       ADMAAAAJAFRob3JuZGFsZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMA
       AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAtRIAAMIBAAAB
       AEEGAQAAAAD//wEAQQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5k
       YWxlAAAAAAAA/QAAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCH
       AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACACYAAADYEwAALAIAAAYASWUzSmUznQIAAAAA
       //8GAEkAZQAzAEoAZQAzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA6AAAAAgA0AAAACgBTdGFy
       U3ltYm9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAA
       AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABtFgAAwgEAAAEAAAA9AFMBAAAA
       AP//AQA9AIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAA
       AACnAQAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA
       /////wCGAAEABAAAAAAAAAByAAIAFwAAAOAXAADCAQAAAQAw1AAAAAAA//8BADAAjAABAAAA
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">Only three of the last four constraints are needed.</text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Offset Perpendicular Revolute-Revolute Joint</text:h>
   <text:p text:style-name="equation">Distance from Ie to Je is constant.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object103" text:anchor-type="as-char" svg:width="2.7228in" svg:height="0.2299in" draw:z-index="52"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mi mathvariant="italic">IeJe</mi>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mrow>
           <msub>
            <mi>G</mi>
            <mi mathvariant="italic">IeJe</mi>
           </msub>
           <mo stretchy="false">−</mo>
           <mi>f</mi>
          </mrow>
         </mrow>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
           <mrow>
            <mi>t</mi>
           </mrow>
           <mo fence="true" form="postfix" stretchy="false">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mrow>
           <msub>
            <mi>G</mi>
            <mi mathvariant="italic">IeJe</mi>
           </msub>
           <mo stretchy="false">−</mo>
           <mi>d</mi>
          </mrow>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
G_{IeJe}
-
f(t)
=
G_{IeJe}
-
d
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAEAAgAAAAkAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAACnAQAA
       AAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCG
       AAEABAAAAAAAAAByAAIAFwAAAGoAAACnAQAAAQBHMQEAAAAA//8BAEcAjAABAAAAAACLAAEA
       AgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAP0AAAAAAAAAAAAFAAAAAAAC
       AP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIA
       AgAgAAAAwgEAABECAAAEAEllSmWfAQAAAAD//wQASQBlAEoAZQCMAAEAAAAAAIsAAQACAAAA
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       AAAAngMAAKcBAAABAAAAnuBmAAAAAAD//wEAnuCMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAA
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       AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAAiBAAApwEA
       AAEAce0AAAAAAP//AQBxAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9y
       bmRhbGUAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAAB
       AIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAGAFAACnAQAAAQAsbgAAAAAA//8B
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       AQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAAAAAAAAUAAAAA
       AAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAA
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       AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAACoIAACnAQAAAQAAAJ/gZgAA
       AAAA//8BAJ/gjAABAAAAAACLAAEAAgAAAB8AigABADoAAAACADQAAAAKAFN0YXJTeW1ib2wA
       AAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAF
       AAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAJQIAACnAQAAAQAAAD0AUwEAAAAA//8BAD0A
       jAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAKcBAAAA
       AAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYA
       AQAEAAAAAAAAAHIAAgAXAAAA7AkAAKcBAAABAEcxAQAAAAD//wEARwCMAAEAAAAAAIsAAQAC
       AAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAA/QAAAAAAAAAAAAUAAAAAAAIA
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       AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAK0OAACnAQAA
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       AIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAALYPAACnAQAAAQAAAJ7ghwAAAAAA
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       AKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/
       ////AIYAAQAEAAAAAAAAAHIAAgAXAAAAVBAAAKcBAAABAHR3AAAAAAD//wEAdACMAAEAAAAA
       AIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAAAAAAAKcBAAD//wAAAAAF
       AAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAA
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       AAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAApwEAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/
       AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAADqEgAApwEA
       AAEARzEBAAAAAP//AQBHAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9y
       bmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAAB
       AIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAIAAAAEIUAAARAgAABABJZUplnwEAAAAA
       //8EAEkAZQBKAGUAjAABAAAAAACLAAEAAgAAAB8AigABADoAAAACADQAAAAKAFN0YXJTeW1i
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       AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAOkVAACnAQAAAQAAABIiUwEAAAAA//8B
       ABIijAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAAAAAAAKcB
       AAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////
       AIYAAQAEAAAAAAAAAHIAAgAXAAAAXBcAAKcBAAABAGTUAAAAAAD//wEAZACMAAEAAAAAAIsA
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       AAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAADX
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       AQAAAAAA
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">Je remains in xy plane of Ie.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object104" text:anchor-type="as-char" svg:width="1.7661in" svg:height="0.2299in" draw:z-index="53"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">IeJeIe</mi>
           <mn>3</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
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             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
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            </mrow>
           </mrow>
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          <msub>
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            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
       </semantics>
      </math>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object105" text:anchor-type="as-char" svg:width="0.402in" svg:height="0.2201in" draw:z-index="54"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <msub>
         <mstyle mathvariant="bold">
          <mi mathvariant="normal">r</mi>
         </mstyle>
         <mi mathvariant="italic">IeJeO</mi>
        </msub>
        <annotation encoding="StarMath 5.0">{bold nitalic r}_IeJeO</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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     </draw:image>
    </draw:frame>is perpendicular to z axis of Je.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">rIeJe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
           <mi mathvariant="italic">IeJeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rIeJe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic r}^T_IeJeO
{bold nitalic k}_JeO
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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    </draw:frame></text:p>
   <text:p text:style-name="equation">z of Ie is perpendicular to z axis of Je.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">kIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>3</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{kIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic k}^T_IeO
{bold nitalic k}_JeO
=
A_Ie3Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Radial Perpendicular Revolute-Cylindrical Joint</text:h>
   <text:p text:style-name="equation">Je remains in xy plane of Ie.</text:p>
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       <semantics>
        <mrow>
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          <mi>G</mi>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
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             <mi>,</mi>
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              <mi mathvariant="normal">s</mi>
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           <mo fence="true" form="postfix" stretchy="true">)</mo>
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          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAIgcAAKcBAAABAHOhAAAAAAD//wEAcwCM
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object109" text:anchor-type="as-char" svg:width="0.402in" svg:height="0.2201in" draw:z-index="58"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <msub>
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          <mi mathvariant="normal">r</mi>
         </mstyle>
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        </msub>
        <annotation encoding="StarMath 5.0">{bold nitalic r}_IeJeO</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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      </office:binary-data>
     </draw:image>
    </draw:frame>is parallel to z axis of Je.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">rIeJe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">iJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
           <mi mathvariant="italic">IeJeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rIeJe ortho iJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic r}^T_IeJeO
{bold nitalic i}_JeO
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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    </draw:frame></text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">rIeJe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">jJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
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           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
           <mi mathvariant="italic">IeJeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rIeJe ortho jJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic r}^T_IeJeO
{bold nitalic j}_JeO
=
0</annotation>
       </semantics>
      </math>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z of Ie is perpendicular to z axis of Je.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
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           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>3</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{kIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic k}^T_IeO
{bold nitalic k}_JeO
=
A_Ie3Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAMwkAAMIBAAABAHR3AAAAAAD//wEAdACM
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       AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAANEMAAAsAgAAAwBJZU99
       AQAAAAD//wMASQBlAE8AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3Ju
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       AAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAA
       AgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABy
       AAIAHQAAAJsPAAAsAgAAAwBKZU+WAQAAAAD//wMASgBlAE8AjAABAAAAAACLAAEAAgAAAB8A
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       AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAtRIAAMIBAAAB
       AEEGAQAAAAD//wEAQQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5k
       YWxlAAAAAAAA/QAAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCH
       AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACACYAAADYEwAALAIAAAYASWUzSmUznQIAAAAA
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       AP//AQA9AIwAAQAAAAAAiwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAA
       AACnAQAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">Only three of the last four constraints are needed.</text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Revolute-Translational Joint</text:h>
   <text:p text:style-name="equation">z axis of Ie is parallel to x axis of Je.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object54" text:anchor-type="as-char" svg:width="1.9618in" svg:height="0.2437in" draw:z-index="62"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">kIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">jJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{kIe ortho jJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic k}^T_IeO
{bold nitalic j}_JeO
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCG
       AAEABAAAAAAAAAByAAIAFwAAAGoAAADCAQAAAQBHMQEAAAAA//8BAEcAjAABAAAAAACLAAEA
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       AAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA
       /wIAACwCAAABAAAApSKyAAAAAAD//wEApSKMAAEAAAAAAIsAAQACAAAAHwCKAAEAOQAAAAIA
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAMwkAAMIBAAABAHR3AAAAAAD//wEAdACM
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object55" text:anchor-type="as-char" svg:width="1.9965in" svg:height="0.2437in" draw:z-index="63"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">kIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
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             <mi>,</mi>
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         <mrow>
          <msub>
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          <mo stretchy="false">=</mo>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{kIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic k}^T_IeO
{bold nitalic k}_JeO
=
0</annotation>
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       </semantics>
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     </draw:image>
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       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">rIeJe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">iJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
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           <mrow>
            <mrow>
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             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
           </mstyle>
           <mi mathvariant="italic">IeJeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
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         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rIeJe ortho iJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic r}^T_IeJeO
{bold nitalic i}_JeO
=
0</annotation>
       </semantics>
      </math>
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         <msub>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">r</mi>
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           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{rIeJe ortho jJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic r}^T_IeJeO
{bold nitalic j}_JeO
=
0</annotation>
       </semantics>
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Strut Composite Joint</text:h>
   <text:p text:style-name="equation">Same as inline joint.</text:p>
   <text:h text:style-name="Heading_20_2" text:outline-level="2">Contact</text:h>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">SurfaceI-SurfaceJ Constraint<draw:frame draw:style-name="fr1" draw:name="Object56" text:anchor-type="as-char" svg:width="1.5772in" svg:height="0.2417in" draw:z-index="67"><draw:object>
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         <mrow>
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            <mi>,</mi>
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            <mi>,</mi>
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              <mi mathvariant="normal">s</mi>
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             <mi>I</mi>
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            <mi>,</mi>
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              <mi mathvariant="normal">s</mi>
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left(
{bold nitalic q}_I,
{bold nitalic q}_J,
{bold nitalic s}_I,
{bold nitalic s}_J,
t
right)</annotation>
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    </draw:frame></text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
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             </mstyle>
             <mi>,</mi>
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              <mi mathvariant="normal">s</mi>
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             <mi>,</mi>
             <mi>t</mi>
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          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
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            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
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    </draw:frame></text:p>
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       <semantics>
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        <annotation encoding="StarMath 5.0">G_{IeJeIe2}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe2}
=
0</annotation>
       </semantics>
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       AAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object61" text:anchor-type="as-char" svg:width="1.7661in" svg:height="0.2299in" draw:z-index="70"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">IeJeIe</mi>
           <mn>3</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgAB
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       AAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/
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       FwAAAK8IAACnAQAAAQB0dwAAAAAA//8BAHQAjAABAAAAAACLAAEAAgAAAB8AigABADoAAAAC
       ADQAAAAKAFN0YXJTeW1ib2wAANwAAAD4AQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8D
       AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAGgJAACnAQAA
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       AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAANIJAACnAQAAAQAAAD0AUwEA
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       AAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUA
       AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKgsAAKcBAAABAHKhAAAAAAD//wEAcgCMAAEA
       AAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAA/QAAAAAAAAAA
       AAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQA
       AAAAAAAAcgACACkAAAD9CwAAEQIAAAcASWVKZUllM+ECAAAAAP//BwBJAGUASgBlAEkAZQAz
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       AP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
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       AAByAAIAFwAAAFQQAACnAQAAAQAw1AAAAAAA//8BADAAjAABAAAAAACVAAEABAAAAAAAAACW
       AAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">z axis of Ie is parallel to z axis of Je but opposite in direction.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object63" text:anchor-type="as-char" svg:width="2.4917in" svg:height="0.2437in" draw:z-index="71"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">jIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">j</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>2</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
      <office:binary-data>VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAbkYAABr
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       ZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwAB
       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAMwkAAMIBAAABAHR3AAAAAAD//wEAdACM
       AAEAAAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAA3AAAAPgBAAD/
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       AAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAAD9AAAAAAAAAAAABQAAAAAA
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object62" text:anchor-type="as-char" svg:width="2.4618in" svg:height="0.2437in" draw:z-index="72"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">iIe</mi>
           <mo stretchy="false">⊥</mo>
           <mi mathvariant="italic">kJe</mi>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msubsup>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">i</mi>
           </mstyle>
           <mi mathvariant="italic">IeO</mi>
           <mi>T</mi>
          </msubsup>
         </mrow>
         <mrow>
          <msub>
           <mstyle mathvariant="bold">
            <mi mathvariant="normal">k</mi>
           </mstyle>
           <mi mathvariant="italic">JeO</mi>
          </msub>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>A</mi>
           <mrow>
            <mi mathvariant="italic">Ie</mi>
            <mn>1</mn>
            <mi mathvariant="italic">Je</mi>
            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       ZQAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwAB
       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA/ggAAMIBAAABAHR3AAAAAAD//wEAdACM
       AAEAAAAAAIsAAQACAAAAHwCKAAEAOgAAAAIANAAAAAoAU3RhclN5bWJvbAAA3AAAAPgBAAD/
       /wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYA
       AQAEAAAAAAAAAHIAAgAaAAAAtwkAAMIBAAABAAAAn+BmAAAAAAD//wEAn+CMAAEAAAAAAIsA
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{bold nitalic s}_J,
t
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    </draw:frame></text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
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          </mrow>
         </msub>
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              <mi mathvariant="normal">s</mi>
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           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
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           <mi>r</mi>
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            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
      </math>
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     </draw:image>
    </draw:frame></text:p>
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       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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           <mn>2</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
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              <mi mathvariant="normal">s</mi>
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          </mrow>
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           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe2}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe2}
=
0</annotation>
       </semantics>
      </math>
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     </draw:image>
    </draw:frame></text:p>
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       <semantics>
        <mrow>
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          <mi>G</mi>
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          </mrow>
         </msub>
         <mrow>
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            <mn>3</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
       </semantics>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic k}^T_IeO
{bold nitalic i}_JeO
=
A_Ie3Je1
=
0</annotation>
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   <text:p text:style-name="equation"/>
   <text:p text:style-name="Standard">If no slipping is permitted, add nonholonomic constraint</text:p>
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=
{partial {bold nitalic r}_OJeO}
over
{partial {bold nitalic q}_J}
left[{bold nitalic V}right]_J{bold nitalic v}_J
+
{partial {bold nitalic r}_OJeO}
over
{partial t}
-
left(
{partial {bold nitalic r}_OIeO}
over
{partial {bold nitalic q}_I}
left[{bold nitalic V}right]_I{bold nitalic v}_I
+
{partial {bold nitalic r}_OIeO}
over
{partial t}
right)
=
{bold nitalic 0}</annotation>
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">SurfaceI-PointJ Constraint<draw:frame draw:style-name="fr1" draw:name="Object69" text:anchor-type="as-char" svg:width="1.3571in" svg:height="0.2417in" draw:z-index="80"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mstyle mathvariant="bold">
           <mi mathvariant="normal">G</mi>
          </mstyle>
          <mi mathvariant="italic">IeJeIe</mi>
         </msub>
         <mrow>
          <mo fence="true" form="prefix" stretchy="true">(</mo>
          <mrow>
           <mrow>
            <msub>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>I</mi>
            </msub>
            <mi>,</mi>
            <msub>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>J</mi>
            </msub>
            <mi>,</mi>
            <msub>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>I</mi>
            </msub>
            <mi>,</mi>
            <mi>t</mi>
           </mrow>
          </mrow>
          <mo fence="true" form="postfix" stretchy="true">)</mo>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">{bold nitalic G}_IeJeIe
left(
{bold nitalic q}_I,
{bold nitalic q}_J,
{bold nitalic s}_I,
t
right)</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object71" text:anchor-type="as-char" svg:width="1.7661in" svg:height="0.2299in" draw:z-index="81"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">IeJeIe</mi>
           <mn>1</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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       AAAAAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCG
       AAEABAAAAAAAAAByAAIAFwAAAGoAAACnAQAAAQBHMQEAAAAA//8BAEcAjAABAAAAAACLAAEA
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       AP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIA
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       AAAAAAAAAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAA
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       AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAIgcAAKcBAAABAHOhAAAAAAD//wEAcwCM
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       AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAANIJAACnAQAAAQAAAD0AUwEA
       AAAA//8BAD0AjAABAAAAAACLAAEAAgAAAB8AigABADkAAAACADMAAAAJAFRob3JuZGFsZQAA
       AAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAACIAAEAAgAAAAEAhwABAAUA
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       AAAAAIsAAQACAAAAHwCKAAEAOQAAAAIAMwAAAAkAVGhvcm5kYWxlAAAAAAAA/QAAAAAAAAAA
       AAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQA
       AAAAAAAAcgACACkAAAD9CwAAEQIAAAcASWVKZUllMeECAAAAAP//BwBJAGUASgBlAEkAZQAx
       AIwAAQAAAAAAiwABAAIAAAAfAIoAAQA6AAAAAgA0AAAACgBTdGFyU3ltYm9sAAAAAAAApwEA
       AP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
       hgABAAQAAAAAAAAAcgACABoAAADiDgAApwEAAAEAAAA9AFMBAAAAAP//AQA9AIwAAQAAAAAA
       iwABAAIAAAAfAIoAAQA5AAAAAgAzAAAACQBUaG9ybmRhbGUAAAAAAACnAQAAAAAAAAAABQAA
       AAAAAAD/AwAAAAAAAAAAAP8DAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAA
       AAByAAIAFwAAAFQQAACnAQAAAQAw1AAAAAAA//8BADAAjAABAAAAAACVAAEABAAAAAAAAACW
       AAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object72" text:anchor-type="as-char" svg:width="1.7693in" svg:height="0.2299in" draw:z-index="82"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">IeJeIe</mi>
           <mn>2</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
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left(
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{bold nitalic s},
t
right)
=
r_{IeJeIe2}
=
0</annotation>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">CurveI-CurveJ Constraint<draw:frame draw:style-name="fr1" draw:name="Object74" text:anchor-type="as-char" svg:width="1.5925in" svg:height="0.2417in" draw:z-index="84"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mstyle mathvariant="bold">
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          </mstyle>
          <mi mathvariant="italic">IeJeIe</mi>
         </msub>
         <mrow>
          <mo fence="true" form="prefix" stretchy="true">(</mo>
          <mrow>
           <mrow>
            <msub>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>I</mi>
            </msub>
            <mi>,</mi>
            <msub>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>J</mi>
            </msub>
            <mi>,</mi>
            <msub>
             <mi>s</mi>
             <mi>I</mi>
            </msub>
            <mi>,</mi>
            <msub>
             <mi>s</mi>
             <mi>J</mi>
            </msub>
            <mi>,</mi>
            <mi>t</mi>
           </mrow>
          </mrow>
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         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">{bold nitalic G}_IeJeIe
left(
{bold nitalic q}_I,
{bold nitalic q}_J,
s_I,
s_J,
t
right)</annotation>
       </semantics>
      </math>
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     </draw:image>
    </draw:frame></text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
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           <mn>1</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
      </math>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe2}
=
0</annotation>
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     </draw:image>
    </draw:frame></text:p>
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         <mrow>
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            <mrow>
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             </mstyle>
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             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
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           </mrow>
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          <mo stretchy="false">=</mo>
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        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
=
0</annotation>
       </semantics>
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     </draw:image>
    </draw:frame></text:p>
   <text:p text:style-name="equation">x axis of Ie (tangent) is parallel to x axis of Je (tangent), maybe in opposite direction.</text:p>
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       <semantics>
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         <msub>
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          <mrow>
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           <mrow>
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             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
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          <mo stretchy="false">=</mo>
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          <msub>
           <mstyle mathvariant="bold">
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           </mstyle>
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          </msub>
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           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
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         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{jIe ortho iJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic i}_JeO
=
A_Ie2Je1
=
0</annotation>
       </semantics>
      </math>
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    </draw:frame></text:p>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">CurveI-PointJ Constraint<draw:frame draw:style-name="fr1" draw:name="Object75" text:anchor-type="as-char" svg:width="1.3646in" svg:height="0.2417in" draw:z-index="90"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mstyle mathvariant="bold">
           <mi mathvariant="normal">G</mi>
          </mstyle>
          <mi mathvariant="italic">IeJeIe</mi>
         </msub>
         <mrow>
          <mo fence="true" form="prefix" stretchy="true">(</mo>
          <mrow>
           <mrow>
            <msub>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>I</mi>
            </msub>
            <mi>,</mi>
            <msub>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>J</mi>
            </msub>
            <mi>,</mi>
            <msub>
             <mi>s</mi>
             <mi>I</mi>
            </msub>
            <mi>,</mi>
            <mi>t</mi>
           </mrow>
          </mrow>
          <mo fence="true" form="postfix" stretchy="true">)</mo>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">{bold nitalic G}_IeJeIe
left(
{bold nitalic q}_I,
{bold nitalic q}_J,
s_I,
t
right)</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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      </office:binary-data>
     </draw:image>
    </draw:frame></text:h>
   <text:p text:style-name="equation">Displacement vector from Ie to Je is zero.</text:p>
   <text:p text:style-name="equation"><draw:frame draw:style-name="fr1" draw:name="Object76" text:anchor-type="as-char" svg:width="1.7661in" svg:height="0.2299in" draw:z-index="91"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
          <mi>G</mi>
          <mrow>
           <mi mathvariant="italic">IeJeIe</mi>
           <mn>1</mn>
          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="true">(</mo>
           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
           <mo fence="true" form="postfix" stretchy="true">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <msub>
           <mi>r</mi>
           <mrow>
            <mi mathvariant="italic">IeJeIe</mi>
            <mn>1</mn>
           </mrow>
          </msub>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{IeJeIe1}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe1}
=
0</annotation>
       </semantics>
      </math>
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       AAEAAgAAAAAAjAABAAAAAAA=
      </office:binary-data>
     </draw:image>
    </draw:frame></text:p>
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=
0</annotation>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">PointI-PointJ Constraint<draw:frame draw:style-name="fr1" draw:name="Object79" text:anchor-type="as-char" svg:width="1.1492in" svg:height="0.2417in" draw:z-index="94"><draw:object>
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t
right)</annotation>
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   <text:p text:style-name="equation">Same as Spherical Joint.</text:p>
   <text:p text:style-name="equation"/>
   <text:h text:style-name="Heading_20_2" text:outline-level="2">Motion</text:h>
   <text:h text:style-name="Heading_20_3" text:outline-level="3">Translation</text:h>
   <text:p text:style-name="equation">Applied to translational or cylindrical joints only.</text:p>
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t
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=
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-
f(t)
=
0</annotation>
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Bryant Angle z Rotation</text:h>
   <text:p text:style-name="equation">Applied to revolute or cylindrical joints only.</text:p>
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-
f(t)
=
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   <text:h text:style-name="Heading_20_3" text:outline-level="3">Full Motion</text:h>
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left(
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{bold nitalic s},
t
right)
=
r_{IeJeIe1}
-
f_x(t)
=
0</annotation>
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left(
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{bold nitalic s},
t
right)
=
r_{IeJeIe2}
-
f_y(t)
=
0</annotation>
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         <mrow>
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            </mrow>
           </msub>
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            <mi>z</mi>
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          </mrow>
         </mrow>
         <mrow>
          <mrow>
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           </mrow>
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        <annotation encoding="StarMath 5.0">G_{IeJeIe3}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
r_{IeJeIe3}
-
f_z(t)
=
0</annotation>
       </semantics>
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   <text:p text:style-name="equation">When Bryant Angle<draw:frame draw:style-name="fr2" draw:name="Object124" text:anchor-type="as-char" svg:width="0.9244in" svg:height="0.4217in" draw:z-index="146"><draw:object>
      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
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          <mrow>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
           <mrow>
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           </mrow>
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          </mfrac>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">%theta_IeJe2y
(t)
neq
{%pi over 2 }</annotation>
       </semantics>
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     </draw:image>
    </draw:frame>for the interval of interest, use</text:p>
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      <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
       <semantics>
        <mrow>
         <msub>
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          </mrow>
         </msub>
         <mrow>
          <mrow>
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           <mrow>
            <mrow>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">q</mi>
             </mstyle>
             <mi>,</mi>
             <mstyle mathvariant="bold">
              <mi mathvariant="normal">s</mi>
             </mstyle>
             <mi>,</mi>
             <mi>t</mi>
            </mrow>
           </mrow>
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          </mrow>
          <mo stretchy="false">=</mo>
          <mrow>
           <msub>
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            <mrow>
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             <mn>1</mn>
             <mi>x</mi>
            </mrow>
           </msub>
           <mo stretchy="false">−</mo>
           <msub>
            <mi>f</mi>
            <mrow>
             <mi>θ</mi>
             <mn>1</mn>
             <mi>x</mi>
            </mrow>
           </msub>
          </mrow>
         </mrow>
         <mrow>
          <mrow>
           <mo fence="true" form="prefix" stretchy="false">(</mo>
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            <mi>t</mi>
           </mrow>
           <mo fence="true" form="postfix" stretchy="false">)</mo>
          </mrow>
          <mo stretchy="false">=</mo>
          <mn>0</mn>
         </mrow>
        </mrow>
        <annotation encoding="StarMath 5.0">G_{%theta IeJe1x}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
%theta_{IeJe1x}
-
f_{%theta 1x}(t)
=
0</annotation>
       </semantics>
      </math>
     </draw:object><draw:image>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
%theta_{IeJe2y}
-
f_{%theta 2y}(t)
=
0</annotation>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
%theta_{IeJe3z}
-
f_{%theta 3z}(t)
=
0</annotation>
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r_ImIeImz(t) 
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic j}^T_IeO
{bold nitalic k}_JeO
=
A_Ie2Je3
=
0</annotation>
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        <annotation encoding="StarMath 5.0">G_{iIe ortho kJe}
left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic k}_JeO
=
A_Ie1Je3
=
0</annotation>
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left(
{bold nitalic q},
{bold nitalic s},
t
right)
=
{bold nitalic i}^T_IeO
{bold nitalic j}_JeO
=
A_Ie1Je2
=
0</annotation>
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