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MultiBody.mo
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MultiBody.mo
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within ModelicaTest;
package MultiBody "Test models for Modelica.Mechanics.MultiBody"
import Modelica.Mechanics.MultiBody;
model PlanarLoopWithMove
"Move block + multi-body system where index reduction can fail"
import SI = Modelica.SIunits;
extends Modelica.Icons.Example;
parameter SI.Length rh1[3]={0.5,0,0} "Position vector from r1 to r4";
parameter SI.Length rv1[3]={0,0.5,0} "Position vector from r1 to r2";
parameter SI.Length rv2[3]={0.1,0.5,0} "Position vector from r4 to r2";
final parameter SI.Length rh2[3]=rv2 + rh1 - rv1
"Position vector from r2 to r3";
inner MultiBody.World world(
axisDiameter=0.6/40,
axisLength=0.8) annotation (Placement(transformation(extent={{-40,-60},{-20,-40}})));
MultiBody.Joints.Revolute r1(useAxisFlange=true)
annotation (Placement(transformation(
origin={0,-10},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Joints.Revolute r2 annotation (Placement(
transformation(extent={{20,30},{40,50}})));
MultiBody.Joints.Revolute r3 annotation (Placement(
transformation(extent={{-10,-10},{10,10}},
rotation=-90,
origin={90,10})));
MultiBody.Joints.RevolutePlanarLoopConstraint r4
annotation (Placement(transformation(extent={{50,-60},{70,-40}})));
MultiBody.Parts.FixedTranslation rod1(r=rv1) annotation (
Placement(transformation(
origin={0,20},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Parts.FixedTranslation rod2(r=rh1) annotation (
Placement(transformation(extent={{20,-60},{40,-40}})));
MultiBody.Parts.BodyShape bodyShape(
m=1,
r=rh2,
r_CM=rh2/2) annotation (Placement(transformation(extent={{50,30},{70,50}})));
MultiBody.Parts.FixedTranslation rod3(r=rv2) annotation (
Placement(transformation(
origin={90,-20},
extent={{-10,-10},{10,10}},
rotation=90)));
Modelica.Blocks.Math.MatrixGain deg2rad1(
K=[2*Modelica.Math.asin(1)/180,0,0;0,2*Modelica.Math.asin(1)/180,0; 0,0,2*Modelica.Math.asin(1)/180])
annotation (Placement(transformation(extent={{-70,-20},{-50,0}})));
Modelica.Blocks.Sources.CombiTimeTable combiTimeTable(
smoothness=Modelica.Blocks.Types.Smoothness.ContinuousDerivative,
table=[0,0,10,0; 1,10,10,0; 2,20,10,0; 3,30,10,0],
extrapolation=Modelica.Blocks.Types.Extrapolation.LastTwoPoints)
annotation (Placement(transformation(extent={{-100,-20},{-80,0}})));
Modelica.Mechanics.Rotational.Sources.Move move
annotation (Placement(transformation(extent={{-40,-20},{-20,0}})));
equation
connect(world.frame_b, r1.frame_a) annotation (Line(
points={{-20,-50},{-6.66134e-16,-50},{-6.66134e-16,-20}},
color={95,95,95},
thickness=0.5));
connect(rod1.frame_a, r1.frame_b) annotation (Line(
points={{-6.66134e-016,10},{-6.66134e-016,6},{-6.66134e-016,0},{4.44089e-016,
0}},
thickness=0.5));
connect(rod2.frame_a, world.frame_b) annotation (Line(
points={{20,-50},{-20,-50}},
color={95,95,95},
thickness=0.5));
connect(rod1.frame_b, r2.frame_a) annotation (Line(
points={{4.44089e-16,30},{4.44089e-16,40},{20,40}},
color={95,95,95},
thickness=0.5));
connect(bodyShape.frame_b, r3.frame_a) annotation (Line(
points={{70,40},{90,40},{90,20}},
color={95,95,95},
thickness=0.5));
connect(rod2.frame_b, r4.frame_a) annotation (Line(
points={{40,-50},{50,-50}},
color={95,95,95},
thickness=0.5));
connect(r4.frame_b, rod3.frame_a) annotation (Line(
points={{70,-50},{90,-50},{90,-30}},
color={95,95,95},
thickness=0.5));
connect(rod3.frame_b, r3.frame_b) annotation (Line(
points={{90,-10},{90,0}},
color={95,95,95},
thickness=0.5));
connect(combiTimeTable.y, deg2rad1.u) annotation (Line(
points={{-79,-10},{-72,-10}}, color={0,0,127}));
connect(move.flange, r1.axis) annotation (Line(
points={{-20,-10},{-10,-10}}));
connect(deg2rad1.y, move.u) annotation (Line(
points={{-49,-10},{-42,-10}}, color={0,0,127}));
connect(r2.frame_b, bodyShape.frame_a) annotation (Line(
points={{40,40},{50,40}},
color={95,95,95},
thickness=0.5));
annotation (experiment(StopTime=3), Documentation(info="<html>
<p>
This model is a combination of a multi-body system with a kinematic loop
and a Move block, where symbolic transformation is difficult:
</p>
<p>
Standard symbolic transformation works in the following way if functions
are present with annotation \"InineAfterIndexReduction = true\".
</p>
<ol>
<li> These functions are not inlined, the Pantelides algorithm
is applied and the equations are symbolically differentiated.</li>
<li> The functions are inlined and further symbolic transformation
is performed (sorting the equations, dummy derivative method etc..</li>
</ol>
<p>
The model contains the following functions that have annotation
\"InineAfterIndexReduction = true\":
</p>
<ol>
<li> MultiBody.Frames.resolve1/resolve2(..) functions are used to transform the coordinates
of a vector in another coordinate system. When these functions need to be differentiated
in the Pantelides algorithm, then Euler's differentiation rule is applied with the angular velocity
that is usually a factor of 2-3 more efficient as if direct differentiation
is applied. The drawback is that the sparsity structure is more \"coarse\" and
this lets the Pantelides algorithm fail in this example (this happens usually only
in systems with kinematic loops). This means that the differentiated equation system
is structurally singular, after the functions with annotation \"InineAfterIndexReduction = true\"
are inlined.</li>
<li> The Rotational.Sources.Move block is using internally functions to express that
an input u[2] is the derivative of input u[1]. In order that this is possible, the functions
have the annotation \"InineAfterIndexReduction = true\" so that the differentiation takes place
with the not inlined functions. After the Pantelides algorithm and the differentiation
is applied, the functions are inlined to enhance efficiency.</li>
</ol>
<p>
The problem with (1) is that after inlining the functions with
annotation \"InineAfterIndexReduction = true\", the equations are structurally singular, but the
source of the singularity is now known. One remedy is to restart symbolic processing and to
inline all functions with \"InineAfterIndexReduction = true\" before the Pantelides algorithm
is applied. In the model, this approach is in principal successful and the model would
be structurally regular. However, the Move block is no longer working correctly if the Pantelides
algorithm is applied with inlining. For this reason in MSL 3.2.1 build 3, the annotation
\"InineAfterIndexReduction = true\" in the Move block has been replaced by
annotation \"Inline = false\". This results in slightly less efficient code, but is more robust
in the situation at hand.
</p>
</html>"));
end PlanarLoopWithMove;
extends Modelica.Icons.ExamplesPackage;
model SphericalDoublePendulum
"Double pendulum with two spherical joints and two bodies"
extends Modelica.Icons.Example;
inner MultiBody.World world annotation (Placement(
transformation(extent={{-88,0},{-68,20}})));
MultiBody.Parts.BodyBox boxBody1(width=0.06, r={0.4,0.0,
-0.3}) annotation (Placement(transformation(extent={{-10,0},{10,20}})));
MultiBody.Parts.BodyBox boxBody2(width=0.06, r={0.3,-0.4,
0}) annotation (Placement(transformation(extent={{74,0},{94,20}})));
MultiBody.Joints.Spherical Spherical1(
enforceStates=true,
useQuaternions=false,
angles_fixed=true,
w_rel_a_fixed=true,
z_rel_a_fixed=false,
w_rel_a_start={0.05235987755982989,0.03490658503988659,0.0174532925199433})
annotation (Placement(transformation(extent={{-52,0},{-32,20}})));
MultiBody.Joints.Spherical Spherical2(
enforceStates=true,
useQuaternions=false,
angles_fixed=true,
w_rel_a_fixed=true,
z_rel_a_fixed=false) annotation (Placement(transformation(extent={{32,0},
{52,20}})));
MultiBody.Parts.BodyBox boxBody3(width=0.06, r={0.4,0.0,
-0.3}) annotation (Placement(transformation(extent={{-10,-40},{10,-20}})));
MultiBody.Parts.BodyBox boxBody4(width=0.06, r={0.3,-0.4,
0}) annotation (Placement(transformation(extent={{76,-40},{96,-20}})));
MultiBody.Joints.Spherical Spherical3(
enforceStates=true,
angles_fixed=true,
w_rel_a_fixed=true,
z_rel_a_fixed=false,
w_rel_a_start={0.05235987755982989,0.03490658503988659,0.0174532925199433})
annotation (Placement(transformation(extent={{-52,-40},{-32,-20}})));
MultiBody.Joints.Spherical Spherical4(
enforceStates=true,
angles_fixed=true,
w_rel_a_fixed=true,
z_rel_a_fixed=false) annotation (Placement(transformation(extent={{32,-40},
{52,-20}})));
MultiBody.Parts.BodyBox boxBody5(
width=0.06,
r={0.4,0.0,-0.3},
useQuaternions=true) annotation (Placement(transformation(extent={{-10,-80},
{10,-60}})));
MultiBody.Parts.BodyBox boxBody6(
width=0.06,
r={0.3,-0.4,0},
useQuaternions=true) annotation (Placement(transformation(extent={{74,-80},
{94,-60}})));
MultiBody.Joints.Spherical Spherical5(
angles_fixed=true,
w_rel_a_fixed=true,
z_rel_a_fixed=false,
w_rel_a_start={0.05235987755982989,0.03490658503988659,0.0174532925199433})
annotation (Placement(transformation(extent={{-52,-80},{-32,-60}})));
MultiBody.Joints.Spherical Spherical6(
angles_fixed=true,
w_rel_a_fixed=true,
z_rel_a_fixed=false) annotation (Placement(transformation(extent={{32,-80},
{52,-60}})));
equation
connect(boxBody1.frame_b, Spherical2.frame_a) annotation (Line(
points={{10,10},{32,10}},
thickness=0.5));
connect(Spherical2.frame_b, boxBody2.frame_a) annotation (Line(
points={{52,10},{74,10}},
thickness=0.5));
connect(world.frame_b, Spherical1.frame_a) annotation (Line(
points={{-68,10},{-52,10}},
thickness=0.5));
connect(Spherical1.frame_b, boxBody1.frame_a) annotation (Line(
points={{-32,10},{-10,10}},
thickness=0.5));
connect(boxBody3.frame_b, Spherical4.frame_a) annotation (Line(
points={{10,-30},{32,-30}},
thickness=0.5));
connect(Spherical4.frame_b, boxBody4.frame_a) annotation (Line(
points={{52,-30},{76,-30}},
thickness=0.5));
connect(Spherical3.frame_b, boxBody3.frame_a) annotation (Line(
points={{-32,-30},{-10,-30}},
thickness=0.5));
connect(world.frame_b, Spherical3.frame_a) annotation (Line(
points={{-68,10},{-60,10},{-60,-30},{-52,-30}},
thickness=0.5));
connect(boxBody5.frame_b, Spherical6.frame_a) annotation (Line(
points={{10,-70},{32,-70}},
thickness=0.5));
connect(Spherical6.frame_b, boxBody6.frame_a) annotation (Line(
points={{52,-70},{74,-70}},
thickness=0.5));
connect(Spherical5.frame_b, boxBody5.frame_a) annotation (Line(
points={{-32,-70},{-10,-70}},
thickness=0.5));
connect(Spherical5.frame_a, world.frame_b) annotation (Line(
points={{-52,-70},{-60,-70},{-60,10},{-68,10}},
thickness=0.5));
annotation (experiment(StopTime=3), Documentation(info="<html>
<p>
This example demonstrates that by using joint and body
elements animation is automatically available. Also the revolute
joints are animated. Note, that animation of every component
can be switched of by setting the first parameter <strong>animation</strong>
to <strong>false</strong> or by setting <strong>enableAnimation</strong> in the <strong>world</strong>
object to <strong>false</strong> to switch off animation of all components.
</p>
<p>
<img src=\"modelica://Modelica/Resources/Images/Mechanics/MultiBody/Examples/Elementary/DoublePendulum.png\"
alt=\"model Examples.Elementary.DoublePendulum\">
</p>
</html>"));
end SphericalDoublePendulum;
model WorldGroundVisualization "Demonstrate visualization of world's ground plane"
extends Modelica.Icons.Example;
MultiBody.Visualizers.FixedArrow visGroundAxis(
animation=true,
r_tail={0,0,0},
n=world.groundAxis_u,
length=world.nominalLength/4) "Visualize arrow in direction of world.groundAxis_u" annotation (Placement(transformation(extent={{0,-10},{20,10}})));
inner MultiBody.World world(
groundLength_v=0.2,
animateGround=true,
groundAxis_u={1,0.3,0},
groundColor={0,128,0},
n={-0.2,0.3,-1},
groundLength_u=1,
animateGravity=true,
gravityType=MultiBody.Types.GravityTypes.UniformGravity)
annotation (Placement(transformation(extent={{-40,-10},{-20,10}})));
equation
connect(visGroundAxis.frame_a, world.frame_b) annotation (Line(
points={{0,0},{-20,0}},
color={95,95,95},
thickness=0.5));
annotation (experiment(StopTime=1));
end WorldGroundVisualization;
package FourbarVariants "Test joints and assembly joints with four bar loop"
extends Modelica.Icons.ExamplesPackage;
model SphericalAndUniversal
"One kinematic loop with four bars (with Spherical and Universal joint)"
import SI = Modelica.SIunits;
extends Modelica.Icons.Example;
output SI.Angle j1_phi "angle of revolute joint j1";
output SI.Position j2_s "distance of prismatic joint j2";
output SI.AngularVelocity j1_w "axis speed of revolute joint j1";
output SI.Velocity j2_v "axis velocity of prismatic joint j2";
inner MultiBody.World world annotation (Placement(
transformation(extent={{-80,-80},{-60,-60}})));
MultiBody.Joints.Revolute j1(
n={1,0,0},
stateSelect=StateSelect.always,
a(fixed=false),
phi(fixed=true),
w(fixed=true, start=5.235987755982989)) annotation (Placement(
transformation(extent={{-54,-40},{-34,-20}})));
MultiBody.Joints.Prismatic j2(
n={1,0,0},
boxWidth=0.05) annotation (Placement(transformation(extent={{12,-80},{32,-60}})));
MultiBody.Parts.BodyCylinder b1(r={0,0.5,0.1},
diameter=0.05) annotation (Placement(transformation(
origin={-30,0},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=
0.05) annotation (Placement(transformation(
origin={50,-50},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Parts.FixedTranslation b3(r={1,0,0},
animation=false) annotation (Placement(transformation(extent={{-32,-80},
{-12,-60}})));
MultiBody.Joints.Spherical spherical(animation=false)
annotation (Placement(transformation(extent={{-20,20},{0,40}})));
MultiBody.Parts.FixedTranslation FixedTranslation1(r={
1,-0.3,-0.1}, animation=false) annotation (Placement(transformation(
extent={{12,20},{32,40}})));
MultiBody.Joints.Universal Universal1(n_b={0,1,0}, n_a=
{0,0,1}) annotation (Placement(transformation(extent={{44,20},{64,40}})));
equation
j1_phi = j1.phi;
j2_s = j2.s;
j1_w = j1.w;
j2_v = j2.v;
connect(j2.frame_b, b2.frame_a) annotation (Line(
points={{32,-70},{50,-70},{50,-60}},
thickness=0.5));
connect(j1.frame_b, b1.frame_a) annotation (Line(
points={{-34,-30},{-30,-30},{-30,-10}},
thickness=0.5));
connect(j1.frame_a, world.frame_b) annotation (Line(
points={{-54,-30},{-60,-30},{-60,-70}},
thickness=0.5));
connect(b3.frame_a, world.frame_b) annotation (Line(
points={{-32,-70},{-60,-70}},
thickness=0.5));
connect(b3.frame_b, j2.frame_a) annotation (Line(
points={{-12,-70},{12,-70}},
thickness=0.5));
connect(b1.frame_b, spherical.frame_a) annotation (Line(
points={{-30,10},{-30,30},{-20,30}},
thickness=0.5));
connect(spherical.frame_b, FixedTranslation1.frame_a) annotation (Line(
points={{0,30},{12,30}},
thickness=0.5));
connect(FixedTranslation1.frame_b, Universal1.frame_a) annotation (Line(
points={{32,30},{44,30}},
thickness=0.5));
connect(b2.frame_b, Universal1.frame_b) annotation (Line(
points={{50,-40},{50,-2},{80,-2},{80,30},{64,30}},
thickness=0.5));
annotation (experiment(StopTime=5), Documentation(info="<html>
<p>
This is a second version of the \"four-bar\" mechanism, see figure:
</p>
<p>
<img src=\"modelica://Modelica/Resources/Images/Mechanics/MultiBody/Examples/Loops/Fourbar2.png\" alt=\"model Examples.Loops.Fourbar2\">
</p>
<p>
In this case
the three revolute joints on the left top-side and the two revolute
joints on the right top side have been replaced by the joint <strong>UniversalSpherical</strong>
that is a rod connecting a spherical and a universal joint. This joint is defined
by <strong>1 constraint</strong> stating that the distance between the two spherical joints is
constant. Using this joint in a kinematic loop reduces the sizes of
non-linear algebraic equations. For this loop, only one non-linear
algebraic system of equations of order 1 remains.
</p>
<p>
At the UniversalSpherical joint an additional frame_ia fixed to the rod
is present where components can be attached to the connecting rod. In this
example just a coordinate system is attached to visualize frame_ia (coordinate
system on the right in blue color).
</p>
<p>
Another feature is that the length of the connecting rod can be
automatically calculated during <strong>initialization</strong>. In order to do this,
another initialization condition has to be given. In this example, the
initial value of the distance of the prismatic joint j2 has been fixed
(via the \"Initialization\" menu) and the rod length of joint
\"UniversalSpherical\" is computed during initialization since parameter
<strong>computeLength</strong> = <strong>true</strong> is set in the joint parameter
menu. The main advantage is that during initialization no non-linear
system of equation is solved and therefore initialization always works.
To be precise, the following trivial non-linear equation is actually solved
for rodLength:
</p>
<blockquote><pre>
rodLength*rodLength = f(angle of revolute joint, distance of prismatic joint)
</pre></blockquote>
</html>"));
end SphericalAndUniversal;
model SphericalSpherical
"One kinematic loop with four bars (with SphericalSpherical joint)"
import SI = Modelica.SIunits;
extends Modelica.Icons.Example;
output SI.Angle j1_phi "angle of revolute joint j1";
output SI.Position j2_s "distance of prismatic joint j2";
output SI.AngularVelocity j1_w "axis speed of revolute joint j1";
output SI.Velocity j2_v "axis velocity of prismatic joint j2";
inner MultiBody.World world annotation (Placement(
transformation(extent={{-80,-80},{-60,-60}})));
MultiBody.Joints.Revolute j1(
n={1,0,0},
stateSelect=StateSelect.always,
a(fixed=false),
phi(fixed=true),
w(fixed=true, start=5.235987755982989)) annotation (Placement(
transformation(extent={{-54,-40},{-34,-20}})));
MultiBody.Joints.Prismatic j2(
n={1,0,0},
a(fixed=false),
s(fixed=true),
v(fixed=false)) annotation (Placement(transformation(extent={{12,-80},{32,-60}})));
MultiBody.Parts.BodyCylinder b1(r={0,0.5,0.1},
diameter=0.05) annotation (Placement(transformation(
origin={-30,0},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=
0.05) annotation (Placement(transformation(
origin={50,-50},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Joints.SphericalSpherical sphericalSpherical(
computeRodLength=true, m=1) annotation (Placement(transformation(
extent={{0,20},{-20,40}})));
MultiBody.Parts.FixedTranslation b3(r={1,0,0},
animation=false) annotation (Placement(transformation(extent={{-32,-80},
{-12,-60}})));
equation
connect(j2.frame_b, b2.frame_a) annotation (Line(
points={{32,-70},{50,-70},{50,-60}},
thickness=0.5));
connect(j1.frame_b, b1.frame_a) annotation (Line(
points={{-34,-30},{-30,-30},{-30,-10}},
thickness=0.5));
connect(j1.frame_a, world.frame_b) annotation (Line(
points={{-54,-30},{-60,-30},{-60,-70}},
thickness=0.5));
connect(b1.frame_b, sphericalSpherical.frame_b) annotation (Line(
points={{-30,10},{-30,30},{-20,30}},
thickness=0.5));
connect(sphericalSpherical.frame_a, b2.frame_b) annotation (Line(
points={{0,30},{50,30},{50,-40}},
thickness=0.5));
j1_phi = j1.phi;
j2_s = j2.s;
j1_w = j1.w;
j2_v = j2.v;
connect(b3.frame_a, world.frame_b) annotation (Line(
points={{-32,-70},{-60,-70}},
thickness=0.5));
connect(b3.frame_b, j2.frame_a) annotation (Line(
points={{-12,-70},{12,-70}},
thickness=0.5));
annotation (experiment(StopTime=5), Documentation(info="<html>
<p>
This is a third version of the \"four-bar\" mechanism. In this case
the three revolute joints on the left top-side and the two revolute
joints on the right top side have been replaced by the joint <strong>SphericalSpherical</strong>
that is a rod with two spherical joints on each side. This joint is defined
by <strong>1 constraint</strong> stating that the distance between the two spherical joints is
constant. Using this joint in a kinematic loop reduces the sizes of
non-linear algebraic equations. For this loop, only one non-linear
algebraic system of equations of order 1 remains.
</p>
<p>
The SphericalSpherical joint may be massless or may have a point mass in
the middle of the rod to approximate in an convenient way the rod
mass properties.
</p>
<p>
Another nice feature is that the <strong>length</strong> of the connecting rod can be
automatically calculated during <strong>initialization</strong>. In order to do this,
another initialization condition has to be given. In this example, the
initial value of the distance of the prismatic joint j2 has been fixed
(via the \"Initialization\" menu) and the length parameter of joint
\"SphericalSpherical\" is computed during initialization since parameter
<strong>computeLength</strong> = <strong>true</strong> is set in the joint parameter
menu (this sets \"fixed=false\" on parameter \"length\").
</p>
</html>"));
end SphericalSpherical;
model UniversalSpherical
"One kinematic loop with four bars (with UniversalSpherical joint)"
import SI = Modelica.SIunits;
extends Modelica.Icons.Example;
output SI.Angle j1_phi "angle of revolute joint j1";
output SI.Position j2_s "distance of prismatic joint j2";
output SI.AngularVelocity j1_w "axis speed of revolute joint j1";
output SI.Velocity j2_v "axis velocity of prismatic joint j2";
inner MultiBody.World world annotation (Placement(
transformation(extent={{-80,-80},{-60,-60}})));
MultiBody.Joints.Revolute j1(
n={1,0,0},
stateSelect=StateSelect.always,
a(fixed=false),
phi(fixed=true),
w(fixed=true, start=5.235987755982989)) annotation (Placement(
transformation(extent={{-54,-40},{-34,-20}})));
MultiBody.Joints.Prismatic j2(
n={1,0,0},
boxWidth=0.01,
a(fixed=false),
s(fixed=false),
v(fixed=false)) annotation (Placement(transformation(extent={{12,-80},{32,-60}})));
MultiBody.Parts.BodyCylinder b1(r={0,0.5,0.1},
diameter=0.05) annotation (Placement(transformation(
origin={-30,0},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=
0.05) annotation (Placement(transformation(
origin={50,-50},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Joints.UniversalSpherical universalSpherical(
rRod_ia={-1,0.3,0.1}, n1_a={0,1,0.1}) annotation (Placement(
transformation(extent={{0,20},{-20,40}})));
MultiBody.Parts.FixedTranslation b3(animation=false, r=
{0.8,0,0}) annotation (Placement(transformation(extent={{-32,-80},{-12,
-60}})));
MultiBody.Visualizers.FixedFrame fixedFrame4
annotation (Placement(transformation(
origin={-10,70},
extent={{-10,-10},{10,10}},
rotation=90)));
equation
j1_phi = j1.phi;
j2_s = j2.s;
j1_w = j1.w;
j2_v = j2.v;
connect(j2.frame_b, b2.frame_a) annotation (Line(
points={{32,-70},{50,-70},{50,-60}},
thickness=0.5));
connect(j1.frame_b, b1.frame_a) annotation (Line(
points={{-34,-30},{-30,-30},{-30,-10}},
thickness=0.5));
connect(j1.frame_a, world.frame_b) annotation (Line(
points={{-54,-30},{-60,-30},{-60,-70}},
thickness=0.5));
connect(b1.frame_b, universalSpherical.frame_b) annotation (Line(
points={{-30,10},{-30,30},{-20,30}},
thickness=0.5));
connect(universalSpherical.frame_a, b2.frame_b) annotation (Line(
points={{0,30},{50,30},{50,-40}},
thickness=0.5));
connect(b3.frame_a, world.frame_b) annotation (Line(
points={{-32,-70},{-60,-70}},
thickness=0.5));
connect(b3.frame_b, j2.frame_a) annotation (Line(
points={{-12,-70},{12,-70}},
thickness=0.5));
connect(fixedFrame4.frame_a, universalSpherical.frame_ia) annotation (
Line(
points={{-10,60},{-10,50},{-6,50},{-6,40}},
thickness=0.5));
annotation (experiment(StopTime=5), Documentation(info="<html>
<p>
This is a fourth version of the \"four-bar\" mechanism. In this case
the three revolute joints on the left top-side and the two revolute
joints on the right top side have been replaced by the joint <strong>UniversalSpherical</strong>
that is a rod with a spherical and a universal joint on two sides. This joint is defined
by <strong>1 constraint</strong> stating that the distance between the two spherical joints is
constant. Using this joint in a kinematic loop reduces the sizes of
non-linear algebraic equations. For this loop, only one non-linear
algebraic system of equations of order 1 remains.
</p>
<p>
The essential difference to joint SphericalSpherical is that the
orientation of the rod can be computed by removing one degree of freedom
of one of the spherical joints (i.e., replacing it by a universal joint).
Usually, the eigenrotation of the connecting rod is of no technical
interest and by this approximation it is constrained to move in a
somewhat arbitrary way. This allows to have an additional connector,
<strong>frame_ia</strong>, to be fixed on the rod, where other objects can be attached.
In this example, the coordinate system of frame_ia is visualized.
</p>
<p>
Another nice feature is that the <strong>length</strong> of the connecting rod can be
automatically calculated during <strong>initialization</strong>. In order to do this,
another initialization condition has to be given. In this example, the
initial value of the distance of the prismatic joint j2 has been fixed
(via the \"Initialization\" menu) and the length parameter of joint
\"UniversalSpherical\" is computed during initialization since parameter
<strong>computeLength</strong> = <strong>true</strong> is set in the joint parameter
menu (this sets \"fixed=false\" on parameter \"length\").
</p>
</html>"));
end UniversalSpherical;
model JointUSR "One kinematic loop with four bars (using JointUSR joint)"
import SI = Modelica.SIunits;
extends Modelica.Icons.Example;
output SI.Angle j1_phi "angle of revolute joint j1";
output SI.Position j2_s "distance of prismatic joint j2";
output SI.AngularVelocity j1_w "axis speed of revolute joint j1";
output SI.Velocity j2_v "axis velocity of prismatic joint j2";
inner MultiBody.World world annotation (Placement(
transformation(extent={{-80,-80},{-60,-60}})));
MultiBody.Joints.Prismatic j2(
n={1,0,0},
stateSelect=StateSelect.always,
a(fixed=false),
s(fixed=true),
v(fixed=true, start=-0.4)) annotation (Placement(transformation(extent={{10,-80},{30,-60}})));
MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=
0.05) annotation (Placement(transformation(
origin={40,-30},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Parts.FixedTranslation b3(animation=false, r=
{1,0,0}) annotation (Placement(transformation(extent={{-30,-80},{-10,-60}})));
MultiBody.Visualizers.FixedFrame fixedFrame
annotation (Placement(transformation(
origin={30,30},
extent={{-10,-10},{10,10}})));
MultiBody.Joints.Assemblies.JointUSR jointUSR(
n1_a={0,1,0},
n_b={1,0,0},
rRod2_ib={0,0.5,0.1},
checkTotalPower=true,
rRod1_ia={-1,0.3,-0.1}) annotation (Placement(transformation(extent={{0,
0},{-20,20}})));
MultiBody.Parts.Body Body1(
m=1,
I_11=0.1,
I_22=0.1,
I_33=0.1,
r_CM={0.01,0,0}) annotation (Placement(transformation(extent={{-30,30},
{-50,50}})));
MultiBody.Parts.Body Body2(
m=1,
I_11=0.1,
I_22=0.1,
I_33=0.1,
r_CM=jointUSR.eRod1_ia/2) annotation (Placement(transformation(extent={
{20,50},{40,70}})));
MultiBody.Parts.Body Body3(
m=1,
I_11=0.1,
I_22=0.1,
I_33=0.1,
r_CM={0,0,0}) annotation (Placement(transformation(
extent={{-10,-10},{10,10}},
rotation=90,
origin={-10,70})));
Modelica.Mechanics.Rotational.Components.Damper damper(d=0.1) annotation (
Placement(transformation(
origin={-60,10},
extent={{-10,-10},{10,10}},
rotation=90)));
equation
j1_phi = jointUSR.revolute.phi;
j2_s = j2.s;
j1_w = der(jointUSR.revolute.phi);
j2_v = j2.v;
connect(j2.frame_b, b2.frame_a) annotation (Line(
points={{30,-70},{40,-70},{40,-40}},
thickness=0.5));
connect(b3.frame_a, world.frame_b) annotation (Line(
points={{-30,-70},{-60,-70}},
thickness=0.5));
connect(b3.frame_b, j2.frame_a) annotation (Line(
points={{-10,-70},{10,-70}},
thickness=0.5));
connect(world.frame_b, jointUSR.frame_b) annotation (Line(
points={{-60,-70},{-40,-70},{-40,10},{-20,10}},
thickness=0.5));
connect(jointUSR.frame_a, b2.frame_b) annotation (Line(
points={{0,10},{40,10},{40,-20}},
thickness=0.5));
connect(damper.flange_b, jointUSR.axis) annotation (Line(
points={{-60,20},{-50,20},{-50,18},{-20,18}}));
connect(damper.flange_a, jointUSR.bearing) annotation (Line(
points={{-60,0},{-50,0},{-50,14},{-20,14}}));
connect(Body1.frame_a, jointUSR.frame_ib) annotation (Line(
points={{-30,40},{-18,40},{-18,20}},
color={95,95,95},
thickness=0.5));
connect(Body2.frame_a, jointUSR.frame_ia) annotation (Line(
points={{20,60},{10,60},{10,30},{-2,30},{-2,20}},
color={95,95,95},
thickness=0.5));
connect(Body3.frame_a, jointUSR.frame_im) annotation (Line(
points={{-10,60},{-10,20},{-10,20}},
color={95,95,95},
thickness=0.5));
connect(fixedFrame.frame_a, jointUSR.frame_ia) annotation (Line(
points={{20,30},{-2,30},{-2,20}},
color={95,95,95},
thickness=0.5));
annotation (experiment(StopTime=2), Documentation(info="<html>
<p>
This is a fourth version of the \"four-bar\" mechanism. In this case
the three revolute joints on the left top-side and the two revolute
joints on the right top side have been replaced by the joint <strong>UniversalSpherical</strong>
that is a rod with a spherical and a universal joint on two sides. This joint is defined
by <strong>1 constraint</strong> stating that the distance between the two spherical joints is
constant. Using this joint in a kinematic loop reduces the sizes of
non-linear algebraic equations. For this loop, only one non-linear
algebraic system of equations of order 1 remains.
</p>
<p>
The essential difference to joint SphericalSpherical is that the
orientation of the rod can be computed by removing one degree of freedom
of one of the spherical joints (i.e., replacing it by a universal joint).
Usually, the eigenrotation of the connecting rod is of no technical
interest and by this approximation it is constrained to move in a
somewhat arbitrary way. This allows to have an additional connector,
<strong>frame_ia</strong>, to be fixed on the rod, where other objects can be attached.
In this example, the coordinate system of frame_ia is visualized.
</p>
<p>
Another nice feature is that the <strong>length</strong> of the connecting rod can be
automatically calculated during <strong>initialization</strong>. In order to do this,
another initialization condition has to be given. In this example, the
initial value of the distance of the prismatic joint j2 has been fixed
(via the \"Initialization\" menu) and the length parameter of joint
\"UniversalSpherical\" is computed during initialization since parameter
<strong>computeLength</strong> = <strong>true</strong> is set in the joint parameter
menu (this sets \"fixed=false\" on parameter \"length\").
</p>
</html>"));
end JointUSR;
model JointSSR "One kinematic loop with four bars (using JointSSR joint)"
import SI = Modelica.SIunits;
extends Modelica.Icons.Example;
parameter Modelica.SIunits.Distance L=Modelica.Math.Vectors.length({-1,
0.3,0.1});
output SI.Angle j1_phi "angle of revolute joint j1";
output SI.Position j2_s "distance of prismatic joint j2";
output SI.AngularVelocity j1_w "axis speed of revolute joint j1";
output SI.Velocity j2_v "axis velocity of prismatic joint j2";
inner MultiBody.World world annotation (Placement(
transformation(extent={{-80,-80},{-60,-60}})));
MultiBody.Joints.Prismatic j2(
n={1,0,0},
stateSelect=StateSelect.always,
a(fixed=false),
s(fixed=true),
v(fixed=true, start=-0.2)) annotation (Placement(transformation(extent={{10,-80},{30,-60}})));
MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=
0.05) annotation (Placement(transformation(
origin={40,-30},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Parts.FixedTranslation b3(animation=false, r=
{1,0,0}) annotation (Placement(transformation(extent={{-30,-80},{-10,-60}})));
MultiBody.Joints.Assemblies.JointSSR jointSSR(
n_b={1,0,0},
rRod2_ib={0,0.5,0.1},
rod1Length=L,
checkTotalPower=true,
rod1Mass=0.1) annotation (Placement(transformation(extent={{0,0},{-20,20}})));
MultiBody.Visualizers.FixedFrame FixedFrame1
annotation (Placement(transformation(extent={{-30,60},{-50,80}})));
MultiBody.Parts.Body Body1(r_CM=jointSSR.rRod2_ib/2, m=
0.1) annotation (Placement(transformation(extent={{-30,30},{-50,50}})));
MultiBody.Parts.Body Body2(m=0.1, r_CM={0,0,0})
annotation (Placement(transformation(extent={{0,30},{20,50}})));
Modelica.Mechanics.Rotational.Components.Damper damper(d=0.5) annotation (
Placement(transformation(
origin={-60,10},
extent={{-10,-10},{10,10}},
rotation=90)));
equation
j1_phi = jointSSR.revolute.phi;
j2_s = j2.s;
j1_w = der(jointSSR.revolute.phi);
j2_v = j2.v;
connect(jointSSR.axis, damper.flange_b) annotation (Line(points={{-20,18},
{-50,18},{-50,20},{-60,20}}));
connect(jointSSR.bearing, damper.flange_a) annotation (Line(points={{-20,
14},{-50,14},{-50,0},{-60,0}}));
connect(world.frame_b, b3.frame_a) annotation (Line(
points={{-60,-70},{-30,-70}},
color={95,95,95},
thickness=0.5));
connect(world.frame_b, jointSSR.frame_b) annotation (Line(
points={{-60,-70},{-40,-70},{-40,10},{-20,10}},
color={95,95,95},
thickness=0.5));
connect(b3.frame_b, j2.frame_a) annotation (Line(
points={{-10,-70},{10,-70}},
color={95,95,95},
thickness=0.5));
connect(j2.frame_b, b2.frame_a) annotation (Line(
points={{30,-70},{40,-70},{40,-40}},
color={95,95,95},
thickness=0.5));
connect(b2.frame_b, jointSSR.frame_a) annotation (Line(
points={{40,-20},{40,10},{0,10}},
color={95,95,95},
thickness=0.5));
connect(Body1.frame_a, jointSSR.frame_ib) annotation (Line(
points={{-30,40},{-18,40},{-18,20}},
color={95,95,95},
thickness=0.5));
connect(Body2.frame_a, jointSSR.frame_im) annotation (Line(
points={{0,40},{-10,40},{-10,20}},
color={95,95,95},
thickness=0.5));
connect(FixedFrame1.frame_a, jointSSR.frame_ib) annotation (Line(
points={{-30,70},{-18,70},{-18,20}},
color={95,95,95},
thickness=0.5));
annotation (experiment(StopTime=1.1), Documentation(info="<html>
<p>
This is a fourth version of the \"four-bar\" mechanism. In this case
the three revolute joints on the left top-side and the two revolute
joints on the right top side have been replaced by the joint <strong>UniversalSpherical</strong>
that is a rod with a spherical and a universal joint on two sides. This joint is defined
by <strong>1 constraint</strong> stating that the distance between the two spherical joints is
constant. Using this joint in a kinematic loop reduces the sizes of
non-linear algebraic equations. For this loop, only one non-linear
algebraic system of equations of order 1 remains.
</p>
<p>
The essential difference to joint SphericalSpherical is that the
orientation of the rod can be computed by removing one degree of freedom
of one of the spherical joints (i.e., replacing it by a universal joint).
Usually, the eigenrotation of the connecting rod is of no technical
interest and by this approximation it is constrained to move in a
somewhat arbitrary way. This allows to have an additional connector,
<strong>frame_ia</strong>, to be fixed on the rod, where other objects can be attached.
In this example, the coordinate system of frame_ia is visualized.
</p>
<p>
Another nice feature is that the <strong>length</strong> of the connecting rod can be
automatically calculated during <strong>initialization</strong>. In order to do this,
another initialization condition has to be given. In this example, the
initial value of the distance of the prismatic joint j2 has been fixed
(via the \"Initialization\" menu) and the length parameter of joint
\"UniversalSpherical\" is computed during initialization since parameter
<strong>computeLength</strong> = <strong>true</strong> is set in the joint parameter
menu (this sets \"fixed=false\" on parameter \"length\").
</p>
</html>"));
end JointSSR;
model JointUSP "One kinematic loop with four bars (using JointUSP joint)"
import SI = Modelica.SIunits;
extends Modelica.Icons.Example;
output SI.Angle revolute_phi "angle of revolute joint j1";
output SI.Position prismatic_s "distance of prismatic joint j2";
output SI.AngularVelocity revolute_w "axis speed of revolute joint j1";
output SI.Velocity prismatic_v "axis velocity of prismatic joint j2";
inner MultiBody.World world annotation (Placement(
transformation(extent={{-80,-80},{-60,-60}})));
MultiBody.Joints.Revolute revolute(
n={1,0,0},
stateSelect=StateSelect.always,
a(fixed=false),
phi(fixed=true),
w(fixed=true, start=5.235987755982989)) annotation (Placement(
transformation(extent={{-40,-40},{-20,-20}})));
MultiBody.Parts.BodyCylinder body1(r={0,0.5,0.1},
diameter=0.05) annotation (Placement(transformation(
origin={-10,-10},
extent={{-10,-10},{10,10}},
rotation=90)));
MultiBody.Parts.BodyCylinder body3(r={0,0.2,0},
diameter=0.05) annotation (Placement(transformation(
origin={40,60},
extent={{-10,-10},{10,10}})));
MultiBody.Parts.FixedTranslation ground_rod(animation=
false, r={1.2,0,0}) annotation (Placement(transformation(extent={{-32,
-80},{-12,-60}})));
MultiBody.Joints.Assemblies.JointUSP jointUSP(
rRod2_ib={0,0.2,0},
n1_a={0,0,-1},
n_b={-1,0,0},
rod1Diameter=0.04,
boxWidth=0.05,
rRod1_ia={1,-0.3,0.1}) annotation (Placement(transformation(extent={{0,
20},{20,40}})));
MultiBody.Parts.BodyCylinder body2(r={1,-0.3,0.1},
diameter=0.05) annotation (Placement(transformation(extent={{-10,50},
{-30,70}})));
Modelica.Mechanics.Translational.Components.Damper damper(d=50)
annotation (Placement(transformation(
origin={50,30},
extent={{10,-10},{-10,10}},
rotation=270)));
equation
revolute_phi = revolute.phi;
prismatic_s = jointUSP.prismatic.s;
revolute_w = revolute.w;
prismatic_v = der(jointUSP.prismatic.s);
connect(jointUSP.bearing, damper.flange_a) annotation (Line(points={{20,
34},{38,34},{38,18},{50,18},{50,20}}, color={0,191,0}));
connect(jointUSP.axis, damper.flange_b) annotation (Line(points={{20,38},
{38,38},{38,40},{50,40}}, color={0,191,0}));
connect(ground_rod.frame_b, jointUSP.frame_b) annotation (Line(
points={{-12,-70},{30,-70},{30,30},{20,30}},
color={95,95,95},
thickness=0.5));
connect(world.frame_b, ground_rod.frame_a) annotation (Line(
points={{-60,-70},{-32,-70}},
color={95,95,95},
thickness=0.5));
connect(world.frame_b, revolute.frame_a) annotation (Line(
points={{-60,-70},{-50,-70},{-50,-30},{-40,-30}},
color={95,95,95},
thickness=0.5));
connect(revolute.frame_b, body1.frame_a) annotation (Line(
points={{-20,-30},{-10,-30},{-10,-20}},
color={95,95,95},
thickness=0.5));
connect(body1.frame_b, jointUSP.frame_a) annotation (Line(
points={{-10,0},{-10,30},{0,30}},
color={95,95,95},
thickness=0.5));
connect(jointUSP.frame_ia, body2.frame_a) annotation (Line(
points={{2,40},{2,60},{-10,60}},
color={95,95,95},
thickness=0.5));
connect(jointUSP.frame_ib, body3.frame_a) annotation (Line(
points={{18,40},{18,60},{30,60}},
color={95,95,95},
thickness=0.5));
annotation (experiment(StopTime=5), Documentation(info=""));
end JointUSP;
end FourbarVariants;
package Frames "Test functions of package Frames"
extends Modelica.Icons.ExamplesPackage;
model AngularVelocity "Test angular velocity functions"
import SI = Modelica.SIunits;
import Modelica.Mechanics.MultiBody.Frames.{angularVelocity1, angularVelocity2, resolve1};
extends Modelica.Icons.Example;
MultiBody.Frames.Orientation R=body.frame_a.R;
SI.AngularVelocity wa[3]=angularVelocity2(R);
SI.AngularVelocity w1[3]=resolve1(R, wa);
SI.AngularVelocity w2[3]=angularVelocity1(R);
SI.AngularVelocity w_err[3]=w2 - w1;
inner MultiBody.World world annotation (Placement(
transformation(extent={{-80,20},{-60,40}})));
MultiBody.Parts.FixedTranslation bar2(r={0.8,0,0},
animation=false) annotation (Placement(transformation(extent={{-20,20},{0,40}})));
MultiBody.Forces.Spring spring1(
width=0.1,
coilWidth=0.005,
numberOfWindings=5,
c=20,
s_unstretched=0) annotation (Placement(transformation(
origin={-40,0},
extent={{-10,-10},{10,10}},
rotation=270)));
MultiBody.Parts.BodyShape body(
m=1,
I_11=1,
I_22=1,
I_33=1,
r={0.4,0,0},
r_CM={0.2,0,0},
width=0.05,
angles_start={0.174532925199433,0.174532925199433,0.174532925199433},
a_0(each fixed=false),
angles_fixed=true,