Add documentation for kinematics model

implementation/SCARA/01_kinematics/implementation.md

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+# Kinematics model
+
+This is a really simple model.
+It has some inverse kinematics and forwards kinematics.
+
+## Inverse model
+
+The setpoint on the board is given as a x,y position.
+We have to convert this point in to angles of the SCARA joints.
+We have the following setup:
+![Geometrics of the scara](geometrics.pdf)
+
+We can resolve this via the *law of cosines* and *pythagoras theorem*.
+We can find the length of **C** with pythagoras.
+Then with the use of a tangent we can find the angle **phi**.
+Then filling in the *law of cosines* with **C** calculated and **A** and **B** as arm lengths, we can calculate the angles **a**, **b** and **c**.
+As a check we sum these angles and they should add up to the value of Pi.
+
+Then we add **phi** and **b** to get the corner of the first joint relative to the world frame.
+And **c** - Pi + **phi** + **b** gives the angle of the second joint relative to the world frame.
+
+
+## Forward model
+The forward model is as follows.
+``` 
+joint1 = A_length*[cos(angle1);sin(angle1)];
+joint2 = B_length*[cos(angle2);sin(angle2)];
+end_effector = joint1 + joint2;
+```
+This is then drawn as two arms in a 3D viewer.
+![3D view of forward model](3D.png)
+It follows the outside of the square.

implementation/SCARA/documentation/implementation.md

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+# SCARA implementation
+
+## Design
+The Scara moves the marker in a small space along the board.
+The Scara has to be quick and precise. Therefore we want to keep it as small and light as possible.
+In the next image we have a general idea of the design.
+
+![Rough design idea](generaldesign.pdf)
+
+## Specifications
+The Scara has as goal to move the end-effector in a area of 50 mm high and 70 mm wide.
+On of the first tests is to be able to travers that square with in a second.
+Therefore it has to achieve an average speed of 240 mm/s.
+Al be it not for very long. Probably up to 500 mm/s maximum velocity.
+
+The marker has to be lifted as well. 
+That will be the task of the end-effector.
+
+## Details
+The levels of detail that we will implement are at least the following steps.
+
+### Kinematics
+A first model is just a kinematics model without any physics.
+If we look at the design it only implements the A and B part of the arms.
+And we can just mathematically calculate the position of the arms.
+This is usefull to check whether we can even reach all the corners of the square.
+
+### Simple Physics.
+Start adding some Mass to the arms and the marker.
+We can learn some basic requirements for the motor that we require.
+The current implementation would require some infinite power as we have some instantanious speed.
+Thus we have to update our path and induce some control.
+
+It is probably to make some pathing block where we can put some set points into. 
+
+### Adding motor physics.
+Start the better motor physics.
+What kind of motor do we need to power the setup.
+
+### Complex arm structure.
+Add the the C, D and E arms.
+All the arms should now also have complete inertia and mass specifications.
+
+### Add parasitics to the arm structure
+This has to be reviewed at the point that we get here.
+
+## Division
+The submodels will be divided as follows.
+However, during the design I will probably run in more blocks than normal.
+
+![Division of models](division.pdf)
+
+The submodels in the division should be compatible with each other.
+To avoid that we have to update all our models all the time.
+We will build every part of the model in a library for 20-sim. This way it is easy for 20-sim to find the updated models.
+
+![Compatibility solution between different versions](compatibility.pdf)
+
+

implementation/SCARA/spike/motionprofiletest.emx

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+<?xml version="1.0" encoding="UTF-8"?>
+<Document>
+ <Model version="4.8" build="4.8.2.10124">
+  <Sidops><![CDATA[model 128 184
+ description '<Information>
+ <Description>
+    <Version>4.8</Version>
+<IsMainModel>0</IsMainModel>
+  <KeepParameterValues>False</KeepParameterValues>
+    <LibraryPath>Z:\home\wouter\Documents\studie\ma\mahd\implementation\submodel\SCARA\spike\motionprofiletest.emx</LibraryPath>
+  <TimeStamp>2020-7-9 14:43:21</TimeStamp>
+</Description>
+</Information>';
+ type Mainmodel
+ end;
+ implementation bg
+  submodels
+   Submodel1 328 200
+    description '<Description><Version>4.0</Version>
+   <LibraryPath>Template\Submodel-Equation.emx</LibraryPath>
+<IsMainModel>1</IsMainModel>
+ <KeepParameterValues>False</KeepParameterValues>
+   <TimeStamp>2007-11-1 22:32:1</TimeStamp>
+   <AllowLibraryUpdate>False</AllowLibraryUpdate>
+</Description>';
+    type 'Submodel-Equation'
+     ports
+      signal out output;
+    end;
+    implementation eq
+/* Equation Submodel
+Enter your equations here. You can use the Toolbar buttons at the top ( Add , f(x) etc. ).
+*/
+parameters
+	string dllname = 'MotionProfiles.dll';
+variables
+	real x[3];
+	real t;
+equations
+	// start typing here
+	t = time-0.5;
+	x = dll(dllname,'ProfileCycloidal',t);
+	output = x[1];
+ implementation_end;
+  end;
+  connections
+  end;
+ implementation_end;
+]]>
+</Sidops>
+ </Model>
+ <Experiments>
+     <DefaultExperiment><![CDATA[Experiment 1]]>
+</DefaultExperiment>
+  <Experiment>
+    <Name>Experiment 1</Name>
+    <CreatedBy></CreatedBy>
+    <Info></Info>
+<ExpData>
+  <VersionNumber>4.8</VersionNumber>
+  <ModelProperties>
+  </ModelProperties>
+  <Variables>
+   <Parameters>
+   </Parameters>
+  </Variables>
+  <PlotSpecs>
+   <VarNames>
+    <VarName>time</VarName>
+    <VarName>Submodel1\x[1]</VarName>
+    <VarName>Submodel1\x[2]</VarName>
+    <VarName>Submodel1\x[3]</VarName>
+   </VarNames>
+   <Plots>
+    <Plot>
+     <PlotType>GraphPlot</PlotType>
+     <BasePlot>
+       <PlotId>1</PlotId>
+       <UseWindowsBGColor>false</UseWindowsBGColor>
+       <BGColor>16777215</BGColor>
+       <PlotIsVisible>true</PlotIsVisible>
+     </BasePlot>
+     <Grid>
+      <DrawGrid>true</DrawGrid>
+      <GridColor>15780518</GridColor>
+      <GridBorderLineColor>12624260</GridBorderLineColor>
+      <GridZeroLineColor>0</GridZeroLineColor>
+      <XTicks>10</XTicks>
+      <YTicks>10</YTicks>
+      <ZTicks>10</ZTicks>
+      <Use3DLook>false</Use3DLook>
+     </Grid>
+     <PlotBGColor>16777215</PlotBGColor>
+     <ShowPlotTitle>true</ShowPlotTitle>
+     <TitlePosition>1</TitlePosition>
+     <PlotTitle>model</PlotTitle>
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+     <Fonts>
+      <TitleFont>
+       <Name>Arial</Name>
+       <Height>12</Height>
+       <PitchFamily>34</PitchFamily>
+       <Weight>400</Weight>
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+       <Name>Arial</Name>
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+       <Weight>400</Weight>
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+       <UnderLine>0</UnderLine>
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+     <SharedXAxis>true</SharedXAxis>
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+     <SharedZAxis>false</SharedZAxis>
+     <XAxes>
+      <Axis>
+       <Minimum>0.0</Minimum>
+       <Maximum>10.0</Maximum>
+       <Linear>true</Linear>
+       <Scaling>3</Scaling>
+       <Label>time</Label>
+      </Axis>
+     </XAxes>
+     <YAxes>
+      <Axis>
+       <Minimum>-8.0</Minimum>
+       <Maximum>12.0</Maximum>
+       <Linear>true</Linear>
+       <Scaling>2</Scaling>
+       <Label>x[1]</Label>
+      </Axis>
+      <Axis>
+       <Minimum>0.0</Minimum>
+       <Maximum>10.0</Maximum>
+       <Linear>true</Linear>
+       <Scaling>2</Scaling>
+       <Label>x[2]</Label>
+      </Axis>
+      <Axis>
+       <Minimum>0.0</Minimum>
+       <Maximum>10.0</Maximum>
+       <Linear>true</Linear>
+       <Scaling>2</Scaling>
+       <Label>x[3]</Label>
+      </Axis>
+     </YAxes>
+     <ZAxes>
+     </ZAxes>
+     <Curves>
+      <Curve>
+       <LineColor>3355111</LineColor>
+       <LineStyle>1</LineStyle>
+       <TickColor>3355111</TickColor>
+       <TickStyle>0</TickStyle>
+       <CurveVisible>true</CurveVisible>
+       <PixelThresshold>1</PixelThresshold>
+       <LineThickness>2</LineThickness>
+       <LineOrder>1</LineOrder>
+       <ShowYValues>true</ShowYValues>
+       <XCurveData>
+        <ShowUnit>true</ShowUnit>
+        <VarName>time</VarName>
+       </XCurveData>
+       <YCurveData>
+        <ShowUnit>true</ShowUnit>
+        <VarName>Submodel1\x[1]</VarName>
+       </YCurveData>
+      </Curve>
+      <Curve>
+       <LineColor>6076255</LineColor>
+       <LineStyle>1</LineStyle>
+       <TickColor>6076255</TickColor>
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+       <PixelThresshold>1</PixelThresshold>
+       <LineThickness>2</LineThickness>
+       <LineOrder>1</LineOrder>
+       <ShowYValues>true</ShowYValues>
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+        <ShowUnit>true</ShowUnit>
+        <VarName>time</VarName>
+       </XCurveData>
+       <YCurveData>
+        <ShowUnit>true</ShowUnit>
+        <VarName>Submodel1\x[2]</VarName>
+       </YCurveData>
+      </Curve>
+      <Curve>
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+       <LineStyle>1</LineStyle>
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+       <ShowYValues>true</ShowYValues>
+       <XCurveData>
+        <ShowUnit>true</ShowUnit>
+        <VarName>time</VarName>
+       </XCurveData>
+       <YCurveData>
+        <ShowUnit>true</ShowUnit>
+        <VarName>Submodel1\x[3]</VarName>
+       </YCurveData>
+      </Curve>
+     </Curves>
+     <Legenda>
+      <ShowLegenda>true</ShowLegenda>
+      <BorderPenColor>0</BorderPenColor>
+      <BackgroundColor>16777215</BackgroundColor>
+     </Legenda>
+    </Plot>
+   </Plots>
+   <PlotPanels>
+    <PlotPanel>
+     <PlotPanelId>1</PlotPanelId>
+     <PlotPanelVisible>true</PlotPanelVisible>
+     <Name>Window 1</Name>
+     <Tiling>0</Tiling>
+     <PlotIds>
+       <PlotId>1</PlotId>
+     </PlotIds>
+     <ToggleState>Base</ToggleState>
+    </PlotPanel>
+   </PlotPanels>
+   <WindowRectangles virtualDesktopWidth="1920" virtualDesktopHeight="1080">
+     <WindowRectangle monitor="0" left="0" top="0" right="1920" bottom="1080" plotpanelid="1">
+0.146354 0.222222 0.856771 1.01296
+     </WindowRectangle>
+   </WindowRectangles>
+  </PlotSpecs>
+  <RunSpecs>
+   <SimulatorSettings>
+    <StartTime>0.0</StartTime>
+    <FinishTime>10.0</FinishTime>
+    <AllowPassFinishTime>false</AllowPassFinishTime>
+    <Warp>false</Warp>
+    <FPGonio>false</FPGonio>
+    <UseOutputAfterEach>false</UseOutputAfterEach>
+    <OutputAfterEach>0.1</OutputAfterEach>
+    <EventEpsilon>1.0e-6</EventEpsilon>
+    <AlgebraicTolerance>1.0e-7</AlgebraicTolerance>
+    <SteadyStateAnalysis>false</SteadyStateAnalysis>
+    <UpdateHoldInstructions>true</UpdateHoldInstructions>
+   </SimulatorSettings>
+   <IntegrationMethods>
+    <IntegrationMethod>
+     <Name>Euler</Name>
+     <StepSize>0.01</StepSize>
+     <AutoStepSize>false</AutoStepSize>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>BackwardEuler</Name>
+     <AbsoluteTolerance>1.0e-5</AbsoluteTolerance>
+     <RelativeTolerance>1.0e-5</RelativeTolerance>
+     <AlgebraicAbsoluteTolerance>1.0e-5</AlgebraicAbsoluteTolerance>
+     <AlgebraicRelativeTolerance>1.0e-5</AlgebraicRelativeTolerance>
+     <StepSize>0.01</StepSize>
+     <Alpha>1.0</Alpha>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>AdamsBashforth</Name>
+     <StepSize>0.01</StepSize>
+     <AutoStepSize>false</AutoStepSize>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>RungeKutta2</Name>
+     <StepSize>0.01</StepSize>
+     <AutoStepSize>false</AutoStepSize>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>RungeKutta4</Name>
+     <StepSize>0.01</StepSize>
+     <AutoStepSize>false</AutoStepSize>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>RungeKutta8</Name>
+     <UseInitialStepSize>false</UseInitialStepSize>
+     <InitialStepSize>0.001</InitialStepSize>
+     <UseMaximumStepSize>false</UseMaximumStepSize>
+     <MaximumStepSize>1.0</MaximumStepSize>
+     <AbsoluteTolerance>1.0e-6</AbsoluteTolerance>
+     <RelativeTolerance>1.0e-6</RelativeTolerance>
+     <SafetyFactor>0.9</SafetyFactor>
+     <Factor1>0.33</Factor1>
+     <Factor2>6.0</Factor2>
+     <Beta>0.0</Beta>
+     <UseMaxNrSteps>false</UseMaxNrSteps>
+     <MaxNrSteps>100000</MaxNrSteps>
+     <UseStiffDetection>false</UseStiffDetection>
+     <MaxNrStiffnessSteps>1000</MaxNrStiffnessSteps>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>RungeKuttaFehlberg</Name>
+     <UseInitialStepSize>false</UseInitialStepSize>
+     <InitialStepSize>0.001</InitialStepSize>
+     <UseMaximumStepSize>false</UseMaximumStepSize>
+     <MaximumStepSize>1.0</MaximumStepSize>
+     <AbsoluteTolerance>1.0e-6</AbsoluteTolerance>
+     <RelativeTolerance>1.0e-6</RelativeTolerance>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>VodeAdams</Name>
+     <UseInitialStepSize>false</UseInitialStepSize>
+     <InitialStepSize>0.001</InitialStepSize>
+     <UseMaximumStepSize>false</UseMaximumStepSize>
+     <MaximumStepSize>1.0</MaximumStepSize>
+     <AbsoluteTolerance>1.0e-6</AbsoluteTolerance>
+     <RelativeTolerance>1.0e-6</RelativeTolerance>
+     <VodeUseBDF>true</VodeUseBDF>
+     <VodeUseNewton>true</VodeUseNewton>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>BDFMethod</Name>
+     <AbsoluteTolerance>1.0e-5</AbsoluteTolerance>
+     <RelativeTolerance>1.0e-5</RelativeTolerance>
+     <AlgebraicAbsoluteTolerance>1.0e-5</AlgebraicAbsoluteTolerance>
+     <AlgebraicRelativeTolerance>1.0e-5</AlgebraicRelativeTolerance>
+     <UseInitialStepSize>false</UseInitialStepSize>
+     <InitialStepSize>0.001</InitialStepSize>
+     <UseMaximumStepSize>false</UseMaximumStepSize>
+     <MaximumStepSize>1.0</MaximumStepSize>
+    </IntegrationMethod>
+    <IntegrationMethod>
+     <Name>MeBDFiMethod</Name>
+     <AbsoluteTolerance>1.0e-5</AbsoluteTolerance>
+     <RelativeTolerance>1.0e-5</RelativeTolerance>
+     <AlgebraicAbsoluteTolerance>1.0e-5</AlgebraicAbsoluteTolerance>
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+     <UseInitialStepSize>false</UseInitialStepSize>
+     <InitialStepSize>0.001</InitialStepSize>
+     <UseMaximumStepSize>false</UseMaximumStepSize>
+     <MaximumStepSize>1.0</MaximumStepSize>
+    </IntegrationMethod>
+    <SelectedIntegrationMethod>8</SelectedIntegrationMethod>
+   </IntegrationMethods>
+  </RunSpecs>
+  <MultipleRun>
+   <NrSteps>10</NrSteps>
+   <CopyFromStates>false</CopyFromStates>
+   <JoinParameterVariation>true</JoinParameterVariation>
+   <ClearAfterRun>true</ClearAfterRun>
+   <RedrawAfterRun>false</RedrawAfterRun>
+   <DrawDuringSimulation>true</DrawDuringSimulation>
+   <ActionBeforeOptimization>0</ActionBeforeOptimization>
+   <CompareValue>0.0</CompareValue>
+   <UseCompareValue>true</UseCompareValue>
+   <MultipleRunType>MultipleRun</MultipleRunType>
+   <Minimize>true</Minimize>
+   <OptimizationVariable></OptimizationVariable>
+   <ResulVarUsage>UseEndValue</ResulVarUsage>
+   <Tolerance>0.001</Tolerance>
+   <OptimizationMethod>BroydonFletcherGoldfarbShanno</OptimizationMethod>
+   <MultipleRunVariables>
+   </MultipleRunVariables>
+  </MultipleRun>
+  <ExportData>
+   <WriteAsText>true</WriteAsText>
+   <ReadAsText>true</ReadAsText>
+   <WriteHeader>true</WriteHeader>
+   <ReadHeader>true</ReadHeader>
+   <ReadFilename></ReadFilename>
+   <WriteFilename></WriteFilename>
+   <DoWrite>false</DoWrite>
+   <ExportVariables>
+   </ExportVariables>
+   <ImportVariables>
+   </ImportVariables>
+  </ExportData>
+  <BreakPoints>
+  </BreakPoints>
+  <AnimationPlayback>
+   <PlaybackSpeed>1.0</PlaybackSpeed>
+  </AnimationPlayback>
+</ExpData>
+  </Experiment>
+</Experiments>
+</Document>

implementation/endeffector/gripperbase.stl

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implementation/library/setpoint/rectanglepath.emx

@@ -0,0 +1,17 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Document>
+  <Model version="4.8" build="4.8.2.10124">
+    <Sidops>
+<![CDATA[rectanglepath 112 184
 description '<Information>
+ <Description>
+    <Version>4.8</Version>
+  <LibraryPath>setpoint\rectanglepath.emx</LibraryPath>
+<IsMainModel>1</IsMainModel>
+  <KeepParameterValues>False</KeepParameterValues>
+    <TimeStamp>2020-7-10 12:30:38</TimeStamp>
+<AllowLibraryUpdate>False</AllowLibraryUpdate>
+ </Description>
+</Information>';
 type 'Submodel-Equation'
  ports
   signal out output [2,1];
 end;
 implementation eq
/* 
This will generate coordinates for the box that has to be drawn
*/
parameters
	real w = 0.07{m} ;
	real h = 0.05 {m};
	real t  = 1 {s};
	real origin[2] = [0.05,0.05]{m};
variables
	real v {m/s};
	real t_w {s};
	real t_h {s};
	real period {s};
	real test1, test2, test3;
initialequations
	v = (2*w + 2*h)/t;
	t_w = w / v;
	t_h = h / v;
equations
	period = floor(time / t) * t;
	output[1] = v*(ramp(period+t_h) - ramp(period + t_w+t_h) - ramp(period + t_w + t_h + t_h)) + origin[1];
	output[2] = v*(ramp(period) - ramp(period + t_h) - ramp(period + t_h + t_w) + ramp(period + 2 * t_h + t_w))+ origin[2];
implementation_end;
]]>
+    </Sidops>
+  </Model>
+</Document>