Initial commit R2017b

mathworks · Oct 21, 2019 · 84830b5 · 84830b5
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diff --git a/Optim/obj_sm_four_bar_optim_match_path.m b/Optim/obj_sm_four_bar_optim_match_path.m
@@ -1,5 +1,5 @@
 function F  = obj_sm_four_bar_optim_match_path(mdl,param_v,x_data_des,y_data_des,map_h)
-% Objective function to optimize trajectory of four bar linkage
+% Objective function to optimize trajectory of four-bar linkage
 % Copyright 2017 The MathWorks, Inc.
 
 load_system(mdl);

diff --git a/Optim/sm_four_bar_optim_match_path.m b/Optim/sm_four_bar_optim_match_path.m
@@ -1,4 +1,4 @@
-% Optimization tune four bar linkage to follow a desired trajectory
+% Optimization tune four-bar linkage to follow a desired trajectory
 % Copyright 2017 MathWorks, Inc.
 
 % Set up model

diff --git a/README.txt b/README.txt
@@ -1,9 +1,9 @@
-Four Bar Trajectory Optimization 
+Four-Bar Linkage Optimization 
 Copyright 2017 The MathWorks, Inc.
 
-Models a four bar linkage in Simscape Multibody.  The lengths
+Models a four-bar linkage in Simscape Multibody.  The lengths
 of the links are parameterized using MATLAB variables.  Adjusting
-those lengths enables the tip of the four bar linkage to follow
+those lengths enables the tip of the four-bar linkage to follow
 different trajectories. Using optimization algorithms, the
 lengths can be automatically tuned so that the tip follows a 
 desired trajectory.

diff --git a/Scripts_Data/sm_four_bar_optim_param_sweep_plot.m b/Scripts_Data/sm_four_bar_optim_param_sweep_plot.m
@@ -11,7 +11,7 @@
 figure(h2_sm_four_bar_optim)
 clf(h2_sm_four_bar_optim)
 numSims = length(simOut);
-title([num2str(numSims) ' Possible Trajectories for Four Bar Linkage'])
+title([num2str(numSims) ' Possible Trajectories for Four-Bar Linkage'])
 axis equal
 grid on
 hold on

diff --git a/Scripts_Data/sm_four_bar_optim_param_sweep_run.m b/Scripts_Data/sm_four_bar_optim_param_sweep_run.m
@@ -1,4 +1,4 @@
-% Parameter sweep for four bar linkage to see possible trajectories
+% Parameter sweep for four-bar linkage to see possible trajectories
 % Copyright 2017 MathWorks, Inc.
 
 % Fixed lengths

diff --git a/Scripts_Data/sm_four_bar_optim_plot1path.m b/Scripts_Data/sm_four_bar_optim_plot1path.m
@@ -1,7 +1,7 @@
 % Code to plot simulation results from sm_four_bar_optim
 %% Plot Description:
 %
-% The plot below shows the path of a pointer on the end of a four bar
+% The plot below shows the path of a pointer on the end of a four-bar
 % linkage.  Varying the lengths of the bars will change the trajectory of
 % this point.
 %
@@ -28,7 +28,7 @@
 % Plot results
 plot(xy_pos(:,1),xy_pos(:,2),'LineWidth',1);
 axis equal
-title('Trajectory of Four Bar Linkage');
+title('Trajectory of Four-Bar Linkage');
 grid on
 
 % Remove temporary variables

diff --git a/html/html/sm_four_bar_optim.html b/html/html/sm_four_bar_optim.html
@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>Four Bar Trajectory Optimization</title><meta name="generator" content="MATLAB 9.2"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2017-03-31"><meta name="DC.source" content="sm_four_bar_optim.m"><style type="text/css">
+      --><title>Four-Bar Linkage Optimization</title><meta name="generator" content="MATLAB 9.3"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2017-09-06"><meta name="DC.source" content="sm_four_bar_optim.m"><style type="text/css">
 html,body,div,span,applet,object,iframe,h1,h2,h3,h4,h5,h6,p,blockquote,pre,a,abbr,acronym,address,big,cite,code,del,dfn,em,font,img,ins,kbd,q,s,samp,small,strike,strong,sub,sup,tt,var,b,u,i,center,dl,dt,dd,ol,ul,li,fieldset,form,label,legend,table,caption,tbody,tfoot,thead,tr,th,td{margin:0;padding:0;border:0;outline:0;font-size:100%;vertical-align:baseline;background:transparent}body{line-height:1}ol,ul{list-style:none}blockquote,q{quotes:none}blockquote:before,blockquote:after,q:before,q:after{content:'';content:none}:focus{outine:0}ins{text-decoration:none}del{text-decoration:line-through}table{border-collapse:collapse;border-spacing:0}
 
 html { min-height:100%; margin-bottom:1px; }
@@ -66,49 +66,49 @@
 
 
 
-  </style></head><body><div class="content"><h1>Four Bar Trajectory Optimization</h1><!--introduction--><p>This examples shows a four bar linkage modeled in Simscape Multibody that is used for an optimization study.</p><p>Mechanical designers often wish to design a four bar linkage that will enable an end effector to follow a certain path.  The lengths of the links and the position of the end effector influence the trajectory of the end effector in a complex kinematic relationship.  Optimization algorithms can be used to tune those lengths to achieve the desired motion.</p><p>In this example, a parameter sweep is performed to see which trajectories are possible when varying a subset of the lengths.  Then those lengths are tuned using optimization algorithms until the resulting trajectory is within tolerances of the desired trajectory.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Model</a></li><li><a href="#3">Simulation Results from Simscape Logging</a></li><li><a href="#5">Results from Parameter Sweep</a></li><li><a href="#7">Results from Optimization</a></li></ul></div><h2 id="1">Model</h2><img vspace="5" hspace="5" src="sm_four_bar_optim_01.png" style="width:446px;height:369px;" alt=""> <p><img vspace="5" hspace="5" src="sm_four_bar_optim_mechanics_explorer_IMAGE.png" alt=""> </p><h2 id="3">Simulation Results from Simscape Logging</h2><p>The plot below shows the path of a pointer on the end of a four bar linkage.  Varying the lengths of the bars will change the trajectory of this point.</p><img vspace="5" hspace="5" src="sm_four_bar_optim_02.png" style="width:560px;height:420px;" alt=""> <h2 id="5">Results from Parameter Sweep</h2><p>Four-bar linkages can be grouped into various cases based on the lengths of their links.  See <a href="http://en.wikipedia.org/wiki/File:Linkage_four_bar_fixed.svg">http://en.wikipedia.org/wiki/File:Linkage_four_bar_fixed.svg</a> The resulting trajectories vary quite widely.  We will limit the scope of our problem to a crank-rocker mechanism.  This means:</p><div><ol><li>Link a (driven link) is the shortest link     (a &lt;= min(b,c,d))</li><li>Link b (connecting link) is the longest link  (b &gt;= max(a,c,d))</li><li>Link a must be able to rotate 180 degrees     (a+b &lt;= c+d)</li></ol></div><img vspace="5" hspace="5" src="sm_four_bar_optim_03.png" style="width:560px;height:420px;" alt=""> <h2 id="7">Results from Optimization</h2><p>Adhering to the same conditions as in the parameter sweep, optimization algorithms are used to find the lengths of Bar A and Bar B that permit the point on the four bar linkage to follow the desired trajectory.  Note that the trajectories are translated so that the minimum x and y values of the trajectories are 0.  This makes visual inspection of the curves slightly easier.</p><pre class="codeoutput">
+  </style></head><body><div class="content"><h1>Four-Bar Linkage Optimization</h1><!--introduction--><p>This example shows a four-bar linkage modeled in Simscape Multibody that is optimized using MATLAB.</p><p>Mechanical designers often wish to design a four-bar linkage that will enable an end effector to follow a certain path.  The lengths of the links and the position of the end effector influence the trajectory of the end effector in a complex kinematic relationship.  Optimization algorithms can be used to tune those lengths to achieve the desired motion.</p><p>In this example, a parameter sweep is performed to see which trajectories are possible when varying a subset of the lengths.  Then those lengths are tuned using MATLAB optimization algorithms until the resulting trajectory is within tolerances of the desired trajectory.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Model</a></li><li><a href="#3">Simulation Results from Simscape Logging</a></li><li><a href="#5">Results from Parameter Sweep</a></li><li><a href="#7">Results from Optimization</a></li></ul></div><h2 id="1">Model</h2><img vspace="5" hspace="5" src="sm_four_bar_optim_01.png" alt=""> <p><img vspace="5" hspace="5" src="sm_four_bar_optim_mechanics_explorer_IMAGE.png" alt=""> </p><h2 id="3">Simulation Results from Simscape Logging</h2><p>The plot below shows the path of a pointer on the end of a four-bar linkage.  Varying the lengths of the bars will change the trajectory of this point.</p><img vspace="5" hspace="5" src="sm_four_bar_optim_02.png" alt=""> <h2 id="5">Results from Parameter Sweep</h2><p>Four-bar linkages can be grouped into various cases based on the lengths of their links.  See <a href="http://en.wikipedia.org/wiki/File:Linkage_four_bar_fixed.svg">http://en.wikipedia.org/wiki/File:Linkage_four_bar_fixed.svg</a> The resulting trajectories vary quite widely.  We will limit the scope of our problem to a crank-rocker mechanism.  This means:</p><div><ol><li>Link a (driven link) is the shortest link     (a &lt;= min(b,c,d))</li><li>Link b (connecting link) is the longest link  (b &gt;= max(a,c,d))</li><li>Link a must be able to rotate 180 degrees     (a+b &lt;= c+d)</li></ol></div><img vspace="5" hspace="5" src="sm_four_bar_optim_03.png" alt=""> <h2 id="7">Results from Optimization</h2><p>Adhering to the same conditions as in the parameter sweep, optimization algorithms are used to find the lengths of Bar A and Bar B that permit the point on the four-bar linkage to follow the desired trajectory.  Note that the trajectories are translated so that the minimum x and y values of the trajectories are 0.  This makes visual inspection of the curves slightly easier.</p><pre class="codeoutput">
 
 Iter     Func-count       f(x)      MeshSize     Method
     0           1       0.383738         0.215      
     1           1       0.383738       0.05375     Refine Mesh
     2           2     0.00661577        0.1075     Successful Poll
-    3           2     0.00661577       0.02688     Refine Mesh
+    3           2     0.00661577       0.02687     Refine Mesh
     4           5     0.00272638       0.05375     Successful Poll
     5           9    0.000112722        0.1075     Successful Poll
-    6          11    0.000112722       0.02688     Refine Mesh
+    6          11    0.000112722       0.02687     Refine Mesh
     7          15     2.0582e-05       0.05375     Successful Poll
     8          19     2.0582e-05       0.01344     Refine Mesh
-    9          23    1.67334e-06       0.02688     Successful Poll
+    9          23    1.67334e-06       0.02687     Successful Poll
    10          27    1.67334e-06      0.006719     Refine Mesh
    11          31    1.47731e-07       0.01344     Successful Poll
    12          35    1.47731e-07      0.003359     Refine Mesh
    13          39    1.47731e-07     0.0008398     Refine Mesh
 Optimization terminated: mesh size less than options.MeshTolerance.
-Elapsed Time = 24.3466
+Elapsed Time = 25.6766
     Link    Initial      Final  
     ____    ________    ________
 
     'a'     '0.1800'    '0.1195'
     'b'     '0.2500'    '0.2651'
 
-</pre><img vspace="5" hspace="5" src="sm_four_bar_optim_04.png" style="width:560px;height:420px;" alt=""> <img vspace="5" hspace="5" src="sm_four_bar_optim_05.png" style="width:560px;height:420px;" alt=""> <img vspace="5" hspace="5" src="sm_four_bar_optim_06.png" style="width:560px;height:420px;" alt=""> <p class="footer">Copyright 2017 The MathWorks, Inc.<br><a href="http://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2017a</a><br></p></div><!--
+</pre><img vspace="5" hspace="5" src="sm_four_bar_optim_04.png" alt=""> <img vspace="5" hspace="5" src="sm_four_bar_optim_05.png" alt=""> <img vspace="5" hspace="5" src="sm_four_bar_optim_06.png" alt=""> <p class="footer">Copyright 2017 The MathWorks, Inc.<br><a href="http://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2017b</a><br></p></div><!--
 ##### SOURCE BEGIN #####
-%% Four Bar Trajectory Optimization
+%% Four-Bar Linkage Optimization
 %
-% This examples shows a four bar linkage modeled in Simscape Multibody that
-% is used for an optimization study. 
+% This example shows a four-bar linkage modeled in Simscape Multibody that
+% is optimized using MATLAB. 
 %
-% Mechanical designers often wish to design a four bar linkage that will
+% Mechanical designers often wish to design a four-bar linkage that will
 % enable an end effector to follow a certain path.  The lengths of the
 % links and the position of the end effector influence the trajectory of
 % the end effector in a complex kinematic relationship.  Optimization
 % algorithms can be used to tune those lengths to achieve the desired
 % motion.
 %
 % In this example, a parameter sweep is performed to see which trajectories
-% are possible when varying a subset of the lengths.  Then those lengths are
-% tuned using optimization algorithms until the resulting trajectory is
-% within tolerances of the desired trajectory.
+% are possible when varying a subset of the lengths.  Then those lengths
+% are tuned using MATLAB optimization algorithms until the resulting
+% trajectory is within tolerances of the desired trajectory.
 % 
 % Copyright 2017 The MathWorks, Inc.
 
@@ -128,7 +128,7 @@
 %% Simulation Results from Simscape Logging
 %%
 %
-% The plot below shows the path of a pointer on the end of a four bar
+% The plot below shows the path of a pointer on the end of a four-bar
 % linkage.  Varying the lengths of the bars will change the trajectory of
 % this point.
 %
@@ -156,7 +156,7 @@
 %
 % Adhering to the same conditions as in the parameter sweep, optimization
 % algorithms are used to find the lengths of Bar A and Bar B that permit
-% the point on the four bar linkage to follow the desired trajectory.  Note
+% the point on the four-bar linkage to follow the desired trajectory.  Note
 % that the trajectories are translated so that the minimum x and y values
 % of the trajectories are 0.  This makes visual inspection of the curves
 % slightly easier.

diff --git a/html/html/sm_four_bar_optim.png b/html/html/sm_four_bar_optim.png
diff --git a/html/html/sm_four_bar_optim_01.png b/html/html/sm_four_bar_optim_01.png
diff --git a/html/html/sm_four_bar_optim_02.png b/html/html/sm_four_bar_optim_02.png
diff --git a/html/html/sm_four_bar_optim_03.png b/html/html/sm_four_bar_optim_03.png
diff --git a/html/html/sm_four_bar_optim_04.png b/html/html/sm_four_bar_optim_04.png
diff --git a/html/html/sm_four_bar_optim_05.png b/html/html/sm_four_bar_optim_05.png
diff --git a/html/html/sm_four_bar_optim_06.png b/html/html/sm_four_bar_optim_06.png
diff --git a/html/sm_four_bar_optim.m b/html/sm_four_bar_optim.m
@@ -1,19 +1,19 @@
-%% Four Bar Trajectory Optimization
+%% Four-Bar Linkage Optimization
 %
-% This examples shows a four bar linkage modeled in Simscape Multibody that
-% is used for an optimization study. 
+% This example shows a four-bar linkage modeled in Simscape Multibody that
+% is optimized using MATLAB. 
 %
-% Mechanical designers often wish to design a four bar linkage that will
+% Mechanical designers often wish to design a four-bar linkage that will
 % enable an end effector to follow a certain path.  The lengths of the
 % links and the position of the end effector influence the trajectory of
 % the end effector in a complex kinematic relationship.  Optimization
 % algorithms can be used to tune those lengths to achieve the desired
 % motion.
 %
 % In this example, a parameter sweep is performed to see which trajectories
-% are possible when varying a subset of the lengths.  Then those lengths are
-% tuned using optimization algorithms until the resulting trajectory is
-% within tolerances of the desired trajectory.
+% are possible when varying a subset of the lengths.  Then those lengths
+% are tuned using MATLAB optimization algorithms until the resulting
+% trajectory is within tolerances of the desired trajectory.
 % 
 % Copyright 2017 The MathWorks, Inc.
 
@@ -33,7 +33,7 @@
 %% Simulation Results from Simscape Logging
 %%
 %
-% The plot below shows the path of a pointer on the end of a four bar
+% The plot below shows the path of a pointer on the end of a four-bar
 % linkage.  Varying the lengths of the bars will change the trajectory of
 % this point.
 %
@@ -61,7 +61,7 @@
 %
 % Adhering to the same conditions as in the parameter sweep, optimization
 % algorithms are used to find the lengths of Bar A and Bar B that permit
-% the point on the four bar linkage to follow the desired trajectory.  Note
+% the point on the four-bar linkage to follow the desired trajectory.  Note
 % that the trajectories are translated so that the minimum x and y values
 % of the trajectories are 0.  This makes visual inspection of the curves
 % slightly easier.

diff --git a/sm_four_bar_optim.slx b/sm_four_bar_optim.slx