mahd/implementation/SCARA/04_path_planning/path_planning.emx

<?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>C:\users\wouter\My Documents\studie\ma\mahd\implementation\SCARA\04_path_planning\path_planning.emx</LibraryPath>
  <TimeStamp>2020-7-21 13:21:44</TimeStamp>
<AllowLibraryUpdate>True</AllowLibraryUpdate>
 </Description>
 <Attributes>
  <GlobalRelations>parameters
	real A = 0.05 {m};
	real B = 0.05 {m};
variables
	real J0_1_BF1[2];
	real J1_2_BF1[2];
	real J1_2_BF2[2];
	real EE1_BF2[2];
initialequations
	J0_1_BF1 = [A/2;0];
	J1_2_BF1 = [-A/2;0];
	J1_2_BF2 = [B/2;0];
	EE1_BF2 = [-B/2;0];</GlobalRelations>
 </Attributes>
</Information>';
 type Mainmodel
 end;
 implementation bg
  submodels
   C1 640 264
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\3D\C-3.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:12:8</TimeStamp>
</Description>';
    type 'C-3'
     ports
      power in p [3,1];
      signal out state [3,1];
     restrictions
      causality preferred out p;
    end;
    icon bg bottom
     figures
      text 'C' 640 264 color 0 18 bold;
    end;
    implementation eq
parameters
	real c[3,3] = [0.1, 0.0, 0.0; 0.0, 0.1, 0.0; 0.0, 0.0, 0.1] {mN/m};
equations
    state = int(p.f);
    p.e = inverse(c) *state;
implementation_end;
   C2 304 272
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\3D\C-3.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:12:8</TimeStamp>
</Description>';
    type 'C-3'
     ports
      power in p [3,1];
      signal out state [3,1];
     restrictions
      causality preferred out p;
    end;
    icon bg bottom
     figures
      text 'C' 304 272 color 0 18 bold;
    end;
    implementation eq
parameters
	real c[3,3] = [0.1, 0.0, 0.0; 0.0, 0.1, 0.0; 0.0, 0.0, 0.1] {mN/m};
equations
    state = int(p.f);
    p.e = inverse(c) *state;
implementation_end;
   C3 304 224
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\2D\C-2.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:7:27</TimeStamp>
</Description>';
    type 'C-2'
     ports
      power in p [2,1];
      signal out state [2,1];
     restrictions
      causality preferred out p;
    end;
    icon bg bottom
     figures
      text 'C' 304 224 color 0 18 bold;
    end;
    implementation eq
parameters
	real c[2,2] = [0.1, 0.0; 0.0, 0.1]  {mN.m/rad};
equations
    state = int(p.f);
    p.e = inverse(c) *state;
implementation_end;
   C4 640 216
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\2D\C-2.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:7:27</TimeStamp>
</Description>';
    type 'C-2'
     ports
      power in p [2,1];
      signal out state [2,1];
     restrictions
      causality preferred out p;
    end;
    icon bg bottom
     figures
      text 'C' 640 216 color 0 18 bold;
    end;
    implementation eq
parameters
	real c[2,2] = [0.1, 0.0; 0.0, 0.1]  {mN.m/rad};
equations
    state = int(p.f);
    p.e = inverse(c) *state;
implementation_end;
   COM 376 208
    description '<Information><Description><Version>4.8</Version><IsMainModel>1</IsMainModel><LibraryPath>Bond Graph\MR\center_of_mass_v2.emx</LibraryPath><TimeStamp>2020-7-21 12:24:38</TimeStamp></Description><Attributes><GlobalRelations>parameters
	real I [3,1] = [1.6399999999999998e-6; 4.7e-8; 1.61e-6] {N.m.s};
	real m = 0.00455 {kg};</GlobalRelations></Attributes></Information>';
    type Submodel
     ports
      signal in Hin [4,4];
      signal out Hout [4,4];
      power out p [6,1];
    end;
    icon bg bottom
     figures
      rectangle 344 192 408 224 color 0 fill 139;
      text 'COM' 376 208 color 0 'Clear Sans' 16;
     terminals
      Hin 392 192 fixed;
      p 360 192 fixed;
    end;
    implementation bg
     submodels
      AdHi0 544 400
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-9-25 12:3:3</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type MTF
        ports
         power in p1 [6,1];
         power out p2 [6,1];
         signal in H [4,4];
        restrictions
         causality constraint not_equal p1 p2;
       end;
       icon bg left
        figures
         text 'MTF' 544 400 color 0 18 bold;
       end;
       implementation eq
variables
 	real onlyRotH[4,4];
code
	//Only rotations with respect to the inertial system matter!
	onlyRotH = H;
	onlyRotH[1,4] = 0;
	onlyRotH[2,4] = 0;
	onlyRotH[3,4] = 0;
						
	p2.e = transpose(Adjoint(onlyRotH)) * p1.e;
	p1.f = Adjoint(onlyRotH) * p2.f;
implementation_end;
      EJS 616 336
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-10-31 11:43:6</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type MGY
        ports
         power in p1 [6,1];
       end;
       icon bg top
        figures
         text 'MGY' 616 336 color 0 18 bold;
       end;
       implementation eq
//EJS / Gyroscopic effects
parameters
	real global I[3];
	real global m;
variables
	real II[6,6]; //Inertial tensor
	real Q[6,6];
	real QI[6,6];
	real Ia[6];
initialequations
	Ia[1:3] = I;
	Ia[4:6] = m;
	II = diag(Ia);
equations
	Q = transpose(adjoint(p1.f));
	QI = Q*II;
	p1.e = QI*p1.f;implementation_end;
      Gravity 624 400
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-9-25 12:3:26</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type Se
        ports
         power out p [6,1];
        restrictions
         causality fixed out p;
       end;
       icon bg bottom
        figures
         text 'Se' 624 400 color 0 18 bold;
       end;
       implementation eq
parameters
	real global m;
variables
	real effort[6];
equations
	effort = [0;0;0;0;0;-g_n*m];
	p.e = effort;
implementation_end;
      InertialTensor 544 272
       description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\3D\I-3.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:12:14</TimeStamp>
</Description>';
       type 'I-3'
        ports
         power in p [6,1];
         signal out state [6,1];
        restrictions
         causality preferred in p;
       end;
       icon bg bottom
        figures
         text 'I' 544 272 color 0 18 bold;
       end;
       implementation eq
parameters
	real global I[3];
	real global m;
variables
	real II[6,6]; //Inertial tensor
	real Ia[6];
initialequations
	Ia[1:3] = I;
	Ia[4:6] = m;
	II = diag(Ia);
equations
    state = int(p.e); //state = generalized momentum
    p.f = inverse(II)*state;
implementation_end;
      plug Hin 433.4 496;
      plug Hout 691.2 496;
      plug p 439.4 336;
      Splitter1 544 496
       description '<Description><Version>4.0</Version>
   <LibraryPath>Signal\Block Diagram\Splitter.emx</LibraryPath>
  <TimeStamp>2008-01-17 11:28:29</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
</Description>';
       knot Splitter
        ports
         signal knot duplicatable out output [4,4];
         signal knot in input [4,4];
       end;
       icon bg ellipse
        figures
         ellipse 540.8 492.8 547.2 499.2 color -1 fill 0;
         ellipse 539.7 491.7 548.3 500.3 color -1;
        terminals
         input 544 496 fixed;
       end;
       implementation eq
equations
    collect (output) = input;
implementation_end;
      Ta0j 544 336
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
 <TimeStamp>2007-9-27 9:51:18</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
   <Description></Description>
</Description>';
       knot OneJunction
        ports
         power knot duplicatable none p [6,1];
         signal knot out flow [6,1];
        restrictions
         causality constraint one_out p;
       end;
       icon bg bottom
        figures
         text '1' 544 336 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
      ZeroJunction1 504 336
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\ZeroJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:45:16</TimeStamp>
</Description>
</Information>';
       knot ZeroJunction
        ports
         power knot duplicatable none p [6,1];
         signal knot out effort [6,1];
        restrictions
         causality constraint one_in p;
       end;
       icon bg
        figures
         text '0' 504 336 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.f)) = 0;
	equal (collect (p.e));
	effort = first (p.e);
implementation_end;
     end;
     connections
      AdHi0\p2 => Ta0j\p;
      Gravity\p => AdHi0\p1;
      Hin -> Splitter1\input;
      Splitter1\output -> AdHi0\H;
      Splitter1\output -> Hout;
      Ta0j\p => EJS\p1;
      Ta0j\p => InertialTensor\p;
      ZeroJunction1\p => p;
      ZeroJunction1\p => Ta0j\p;
     end;
    implementation_end;
   COM1 720 200
    description '<Information><Description><Version>4.8</Version><IsMainModel>1</IsMainModel><LibraryPath>Bond Graph\MR\center_of_mass_v2.emx</LibraryPath><TimeStamp>2020-7-21 12:24:38</TimeStamp></Description><Attributes><GlobalRelations>parameters
	real I [3,1] = [7.583333333333335e-7; 3.645833333333334e-8; 7.364583333333335e-7] {N.m.s};
	real m = 0.0035 {kg};</GlobalRelations></Attributes></Information>';
    type Submodel
     ports
      signal in Hin [4,4];
      signal out Hout [4,4];
      power out p [6,1];
    end;
    icon bg bottom
     figures
      rectangle 688 184 752 216 color 0 fill 139;
      text 'COM' 720 200 color 0 'Clear Sans' 16;
     terminals
      Hin 736 184 fixed;
      p 704 184 fixed;
    end;
    implementation bg
     submodels
      AdHi0 544 400
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-9-25 12:3:3</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type MTF
        ports
         power in p1 [6,1];
         power out p2 [6,1];
         signal in H [4,4];
        restrictions
         causality constraint not_equal p1 p2;
       end;
       icon bg left
        figures
         text 'MTF' 544 400 color 0 18 bold;
       end;
       implementation eq
variables
 	real onlyRotH[4,4];
code
	//Only rotations with respect to the inertial system matter!
	onlyRotH = H;
	onlyRotH[1,4] = 0;
	onlyRotH[2,4] = 0;
	onlyRotH[3,4] = 0;
						
	p2.e = transpose(Adjoint(onlyRotH)) * p1.e;
	p1.f = Adjoint(onlyRotH) * p2.f;
implementation_end;
      EJS 616 336
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-10-31 11:43:6</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type MGY
        ports
         power in p1 [6,1];
       end;
       icon bg top
        figures
         text 'MGY' 616 336 color 0 18 bold;
       end;
       implementation eq
//EJS / Gyroscopic effects
parameters
	real global I[3];
	real global m;
variables
	real II[6,6]; //Inertial tensor
	real Q[6,6];
	real QI[6,6];
	real Ia[6];
initialequations
	Ia[1:3] = I;
	Ia[4:6] = m;
	II = diag(Ia);
equations
	Q = transpose(adjoint(p1.f));
	QI = Q*II;
	p1.e = QI*p1.f;implementation_end;
      Gravity 624 400
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-9-25 12:3:26</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type Se
        ports
         power out p [6,1];
        restrictions
         causality fixed out p;
       end;
       icon bg bottom
        figures
         text 'Se' 624 400 color 0 18 bold;
       end;
       implementation eq
parameters
	real global m;
variables
	real effort[6];
equations
	effort = [0;0;0;0;0;-g_n*m];
	p.e = effort;
implementation_end;
      InertialTensor 544 272
       description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\3D\I-3.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:12:14</TimeStamp>
</Description>';
       type 'I-3'
        ports
         power in p [6,1];
         signal out state [6,1];
        restrictions
         causality preferred in p;
       end;
       icon bg bottom
        figures
         text 'I' 544 272 color 0 18 bold;
       end;
       implementation eq
parameters
	real global I[3];
	real global m;
variables
	real II[6,6]; //Inertial tensor
	real Ia[6];
initialequations
	Ia[1:3] = I;
	Ia[4:6] = m;
	II = diag(Ia);
equations
    state = int(p.e); //state = generalized momentum
    p.f = inverse(II)*state;
implementation_end;
      plug Hin 433.4 496;
      plug Hout 691.2 496;
      plug p 439.4 336;
      Splitter1 544 496
       description '<Description><Version>4.0</Version>
   <LibraryPath>Signal\Block Diagram\Splitter.emx</LibraryPath>
  <TimeStamp>2008-01-17 11:28:29</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
</Description>';
       knot Splitter
        ports
         signal knot duplicatable out output [4,4];
         signal knot in input [4,4];
       end;
       icon bg ellipse
        figures
         ellipse 540.8 492.8 547.2 499.2 color -1 fill 0;
         ellipse 539.7 491.7 548.3 500.3 color -1;
        terminals
         input 544 496 fixed;
       end;
       implementation eq
equations
    collect (output) = input;
implementation_end;
      Ta0j 544 336
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
 <TimeStamp>2007-9-27 9:51:18</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
   <Description></Description>
</Description>';
       knot OneJunction
        ports
         power knot duplicatable none p [6,1];
         signal knot out flow [6,1];
        restrictions
         causality constraint one_out p;
       end;
       icon bg bottom
        figures
         text '1' 544 336 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
      ZeroJunction1 504 336
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\ZeroJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:45:16</TimeStamp>
</Description>
</Information>';
       knot ZeroJunction
        ports
         power knot duplicatable none p [6,1];
         signal knot out effort [6,1];
        restrictions
         causality constraint one_in p;
       end;
       icon bg
        figures
         text '0' 504 336 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.f)) = 0;
	equal (collect (p.e));
	effort = first (p.e);
implementation_end;
     end;
     connections
      AdHi0\p2 => Ta0j\p;
      Gravity\p => AdHi0\p1;
      Hin -> Splitter1\input;
      Splitter1\output -> AdHi0\H;
      Splitter1\output -> Hout;
      Ta0j\p => EJS\p1;
      Ta0j\p => InertialTensor\p;
      ZeroJunction1\p => p;
      ZeroJunction1\p => Ta0j\p;
     end;
    implementation_end;
   COM2 904 184
    description '<Information><Description><Version>4.8</Version><IsMainModel>1</IsMainModel><LibraryPath>Bond Graph\MR\center_of_mass_v2.emx</LibraryPath><TimeStamp>2020-7-21 12:24:38</TimeStamp></Description><Attributes><GlobalRelations>parameters
	real I [3,1] = [0.018;0.159;0.159] {mN.m.s};
	real m = 0.015 {kg};</GlobalRelations></Attributes></Information>';
    type Submodel
     ports
      signal in Hin [4,4];
      signal out Hout [4,4];
      power out p [6,1];
    end;
    icon bg bottom
     figures
      rectangle 872 168 936 200 color 0 fill 139;
      text 'COM' 904 184 color 0 'Clear Sans' 16;
     terminals
      Hin 920 168 fixed;
      p 888 168 fixed;
    end;
    implementation bg
     submodels
      AdHi0 544 400
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-9-25 12:3:3</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type MTF
        ports
         power in p1 [6,1];
         power out p2 [6,1];
         signal in H [4,4];
        restrictions
         causality constraint not_equal p1 p2;
       end;
       icon bg left
        figures
         text 'MTF' 544 400 color 0 18 bold;
       end;
       implementation eq
variables
 	real onlyRotH[4,4];
code
	//Only rotations with respect to the inertial system matter!
	onlyRotH = H;
	onlyRotH[1,4] = 0;
	onlyRotH[2,4] = 0;
	onlyRotH[3,4] = 0;
						
	p2.e = transpose(Adjoint(onlyRotH)) * p1.e;
	p1.f = Adjoint(onlyRotH) * p2.f;
implementation_end;
      EJS 616 336
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-10-31 11:43:6</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type MGY
        ports
         power in p1 [6,1];
       end;
       icon bg top
        figures
         text 'MGY' 616 336 color 0 18 bold;
       end;
       implementation eq
//EJS / Gyroscopic effects
parameters
	real global I[3];
	real global m;
variables
	real II[6,6]; //Inertial tensor
	real Q[6,6];
	real QI[6,6];
	real Ia[6];
initialequations
	Ia[1:3] = I;
	Ia[4:6] = m;
	II = diag(Ia);
equations
	Q = transpose(adjoint(p1.f));
	QI = Q*II;
	p1.e = QI*p1.f;implementation_end;
      Gravity 624 400
       description '<Information><Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues><LibraryPath></LibraryPath><TimeStamp>2007-9-25 12:3:26</TimeStamp><AllowLibraryUpdate>True</AllowLibraryUpdate></Description></Information>';
       type Se
        ports
         power out p [6,1];
        restrictions
         causality fixed out p;
       end;
       icon bg bottom
        figures
         text 'Se' 624 400 color 0 18 bold;
       end;
       implementation eq
parameters
	real global m;
variables
	real effort[6];
equations
	effort = [0;0;0;0;0;-g_n*m];
	p.e = effort;
implementation_end;
      InertialTensor 544 272
       description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\3D\I-3.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:12:14</TimeStamp>
</Description>';
       type 'I-3'
        ports
         power in p [6,1];
         signal out state [6,1];
        restrictions
         causality preferred in p;
       end;
       icon bg bottom
        figures
         text 'I' 544 272 color 0 18 bold;
       end;
       implementation eq
parameters
	real global I[3];
	real global m;
variables
	real II[6,6]; //Inertial tensor
	real Ia[6];
initialequations
	Ia[1:3] = I;
	Ia[4:6] = m;
	II = diag(Ia);
equations
    state = int(p.e); //state = generalized momentum
    p.f = inverse(II)*state;
implementation_end;
      plug Hin 433.4 496;
      plug Hout 691.2 496;
      plug p 424 336;
      Splitter1 544 496
       description '<Description><Version>4.0</Version>
   <LibraryPath>Signal\Block Diagram\Splitter.emx</LibraryPath>
  <TimeStamp>2008-01-17 11:28:29</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
</Description>';
       knot Splitter
        ports
         signal knot duplicatable out output [4,4];
         signal knot in input [4,4];
       end;
       icon bg ellipse
        figures
         ellipse 540.8 492.8 547.2 499.2 color -1 fill 0;
         ellipse 539.7 491.7 548.3 500.3 color -1;
        terminals
         input 544 496 fixed;
       end;
       implementation eq
equations
    collect (output) = input;
implementation_end;
      Ta0j 544 336
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
 <TimeStamp>2007-9-27 9:51:18</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
   <Description></Description>
</Description>';
       knot OneJunction
        ports
         power knot duplicatable none p [6,1];
         signal knot out flow [6,1];
        restrictions
         causality constraint one_out p;
       end;
       icon bg bottom
        figures
         text '1' 544 336 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
      ZeroJunction1 480 336
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\ZeroJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:45:16</TimeStamp>
</Description>
</Information>';
       knot ZeroJunction
        ports
         power knot duplicatable none p [6,1];
         signal knot out effort [6,1];
        restrictions
         causality constraint one_in p;
       end;
       icon bg
        figures
         text '0' 480 336 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.f)) = 0;
	equal (collect (p.e));
	effort = first (p.e);
implementation_end;
     end;
     connections
      AdHi0\p2 => Ta0j\p;
      Gravity\p => AdHi0\p1;
      Hin -> Splitter1\input;
      Splitter1\output -> AdHi0\H;
      Splitter1\output -> Hout;
      Ta0j\p => EJS\p1;
      Ta0j\p => InertialTensor\p;
      ZeroJunction1\p => p;
      ZeroJunction1\p => Ta0j\p;
     end;
    implementation_end;
   Integrate 184 288
    description '<Information>
 <Description>
    <Version>4.3</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Signal\Block Diagram\Integrate.emx</LibraryPath>
  <TimeStamp>2013-3-8 14:47:42</TimeStamp>
</Description>
</Information>';
    type Integrate
     ports
      signal in input;
      signal out output;
    end;
    icon bg bottom
     figures
      rectangle 168 272 200 304 color 0 fill 15132390;
      text '∫' 184 288.3 color 16711680 'Lucida Sans' 21 italic;
    end;
    implementation eq
parameters
	real initial = 0;		// initial value
equations
	output = int (input, initial);
     implementation_end;
   Integrate1 520 360
    description '<Information>
 <Description>
    <Version>4.3</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Signal\Block Diagram\Integrate.emx</LibraryPath>
  <TimeStamp>2013-3-8 14:47:42</TimeStamp>
</Description>
</Information>';
    type Integrate
     ports
      signal in input;
      signal out output;
    end;
    icon bg bottom
     figures
      rectangle 504 344 536 376 color 0 fill 15132390;
      text '∫' 520 360.3 color 16711680 'Lucida Sans' 21 italic;
    end;
    implementation eq
parameters
	real initial = 0;		// initial value
equations
	output = int (input, initial);
     implementation_end;
   inverse_kinematics1 272 552
    description '<Information>
 <Description>
    <Version>4.8</Version>
  <LibraryPath>SCARA\inverse_kinematics_v1.emx</LibraryPath>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <TimeStamp>2020-7-10 12:26:18</TimeStamp>
<AllowLibraryUpdate>False</AllowLibraryUpdate>
 </Description>
</Information>';
    type 'Submodel-Equation'
     ports
      signal in input [2,1] {m} ;
      signal out angle1 {rad} ;
      signal out angle2 {rad} ;
      signal out a {rad} ;
      signal out b {rad} ;
      signal out c {rad} ;
      signal out phi {rad} ;
      signal out abs_angle2;
    end;
    implementation eq
parameters
	real A_length = 0.065 {m}; // length of first arm
	real B_length = 0.05 {m}; // length of second arm
	real to_rad = 1 {rad};
variables
	real x {m}, y {m};
	real C_length {m}; // length to x and y.
equations
	x = input[1];
	y = input[2];
	phi = atan2(y, x);
	C_length = sqrt(x^2 + y^2);	
 	a = arccos ((B_length^2 + C_length^2 - A_length^2) / (2 * B_length * C_length));
	b = arccos ((A_length^2 + C_length^2 - B_length^2) / (2 * A_length * C_length));
	c = arccos ((A_length^2 + B_length^2 - C_length^2) / (2 * A_length * B_length));
	angle1 = b + phi;
	abs_angle2 =  angle1 - pi * to_rad + c;
	angle2 = c - pi * to_rad;
	
	

 implementation_end;
   Joint 192 120
    description '<Information>
 <Description>
    <Version>4.8</Version>
<IsMainModel>1</IsMainModel>
    <LibraryPath>Bond Graph\MR\joint-v3.emx</LibraryPath>
  <TimeStamp>2020-7-21 12:08:53</TimeStamp>
</Description>
</Information>';
    type 'Submodel-v3'
     ports
      power in Pin [6,1];
      power in Pdiff [6,1];
      signal in Hin [4,4];
      signal out Hout [4,4];
      signal out Hdiff [4,4];
      power out Pout [6,1];
    end;
    icon bg bottom
     figures
      rectangle 168 88 216 152 color 0 fill 14745599;
      text 'Joint' 192 120 color 0 'Clear Sans' 16;
     terminals
      Pin 216 104 fixed;
      Hin 168 136 fixed;
      Hout 216 136 fixed;
      Pout 168 104 fixed;
    end;
    implementation bg
     submodels
      AdHji 424 424
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Bond Graph\MTF.emx</LibraryPath>
 <TimeStamp>2007-9-25 12:3:3</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
       type MTF
        ports
         power out p1 [6,1];
         power in p2 [6,1];
         signal in H [4,4];
        restrictions
         causality constraint not_equal p1 p2;
       end;
       icon bg bottom
        figures
         text 'MTF' 424 424 color 0 18 bold;
       end;
       implementation eq
equations					
	p2.e = transpose(Adjoint(H)) * p1.e;
	p1.f = Adjoint(H) * p2.f;implementation_end;
      FlowSensor2 184 311.9
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\FlowSensor.emx</LibraryPath>
  <TimeStamp>2011-11-29 15:50:53</TimeStamp>
</Description>
</Information>';
       knot FlowSensor
        ports
         power knot in p1 [6,1];
         power knot out p2 [6,1];
         signal knot out flow [6,1];
        restrictions
         causality constraint not_equal p1 p2;
       end;
       icon bg ellipse
        figures
         ellipse 177.1 304.8 190.9 319.1 color 0 fill 16777215;
         text 'f' 184 311.2 color 0;
       end;
       implementation eq
equations
	p2.f = p1.f;
	p1.e = p2.e;
	flow = p1.f;
implementation_end;
      Hmatrix 256 312
       description '<Information><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></Information>';
       type 'Submodel-Equation'
        ports
         signal in flow [6,1];
         signal out H [4,4];
       end;
       icon bg
        figures
         rectangle 224 296 288 328 color 0 fill 15132390;
         text 'name' 256 312 color 0 'Clear Sans' 16;
       end;
       implementation eq
parameters
	real init[4] = [1;0;0;0];
variables
	real q[4];		//quaternions
	real W[3,4];	//Quaternion Rates Matrix
	real R[3,3];	//Rotation Matrix
	real p[3];		//Position Vector
	real dq[4];
	real Wb[3,4];
equations
	dq = transpose(Wb) * flow[1:3] ./ 2;
	q = int(dq,init);
	p = int(flow[4:6]);
	W = [-q[2],	q[1],	-q[4],	q[3];
		 -q[3],	q[4],	q[1],	-q[2];
		 -q[4],	-q[3],	q[2],	q[1]];
	Wb = [	-q[2],  q[1],  q[4], -q[3];
	   		-q[3], -q[4],  q[1],  q[2];
	   		-q[4],  q[3], -q[2],  q[1]];
 	R = [q[1]^2+q[2]^2-q[3]^2-q[4]^2, 2*(q[2]*q[3]+q[1]*q[4]), 2*(q[2]*q[4]-q[1]*q[3]);
		  2*(q[2]*q[3]-q[1]*q[4]), q[1]^2-q[2]^2+q[3]^2-q[4]^2, 2*(q[3]*q[4]+q[1]*q[2]);
		  2*(q[2]*q[4]+q[1]*q[3]), 2*(q[3]*q[4]-q[1]*q[2]), q[1]^2-q[2]^2-q[3]^2+q[4]^2];
	H = homogeneous(R,p);
	implementation_end;
      MatrixMul 320 576
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Signal\Block Diagram\Gain.emx</LibraryPath>
 <TimeStamp>2007-9-26 12:15:12</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
       type Gain
        ports
         signal in input1 [4,4];
         signal out output [4,4];
         signal in input2 [4,4];
       end;
       icon bg bottom
        figures
         rectangle 304.1 560 335.9 592 color 0 fill 15132390;
         text 'X' 320 576 color 16711680 16 bold;
       end;
       implementation eq
equations
	output = input2*input1;    implementation_end;
      plug Pin 492.1 424;
      plug Pdiff 184 225;
      plug Hin 130.8 576;
      plug Hout 478.4 576;
      plug Hdiff 320 222;
      plug Pout 134.7 424;
      Splitter2 320 312
       description '<Description><Version>4.0</Version>
   <LibraryPath>Signal\Block Diagram\Splitter.emx</LibraryPath>
  <TimeStamp>2008-01-17 11:28:29</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
</Description>';
       knot Splitter
        ports
         signal knot duplicatable out output [4,4];
         signal knot in input [4,4];
       end;
       icon bg ellipse
        figures
         ellipse 316.8 308.8 323.2 315.2 color -1 fill 0;
         ellipse 315.7 307.7 324.3 316.3 color -1;
        terminals
         input 320 312 fixed;
       end;
       implementation eq
equations
    collect (output) = input;
implementation_end;
      Wbai 184 424
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Bond Graph\ZeroJunction.emx</LibraryPath>
 <TimeStamp>2007-9-27 9:51:43</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
       knot ZeroJunction
        ports
         power knot duplicatable none p [6,1];
         signal knot out effort [6,1];
        restrictions
         causality constraint one_in p;
       end;
       icon bg bottom
        figures
         text '0' 184 424 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.f)) = 0;
	equal (collect (p.e));
	effort = first (p.e);
implementation_end;
     end;
     connections
      FlowSensor2\flow -> Hmatrix\flow;
      FlowSensor2\p2 => Wbai\p;
      Hin -> MatrixMul\input2;
      Hmatrix\H -> Splitter2\input;
      MatrixMul\output -> Hout;
      Pdiff => FlowSensor2\p1;
      Pin => AdHji\p2;
      Splitter2\output -> AdHji\H 424 312;
      Splitter2\output -> Hdiff;
      Splitter2\output -> MatrixMul\input1;
      Wbai\p <= AdHji\p1;
      Wbai\p => Pout;
     end;
    implementation_end;
   Joint1 536 120
    description '<Information>
 <Description>
    <Version>4.8</Version>
<IsMainModel>1</IsMainModel>
    <LibraryPath>Bond Graph\MR\joint-v3.emx</LibraryPath>
  <TimeStamp>2020-7-21 12:08:53</TimeStamp>
</Description>
</Information>';
    type 'Submodel-v3'
     ports
      power in Pin [6,1];
      power in Pdiff [6,1];
      signal in Hin [4,4];
      signal out Hout [4,4];
      signal out Hdiff [4,4];
      power out Pout [6,1];
    end;
    icon bg bottom
     figures
      rectangle 512 88 560 152 color 0 fill 14745599;
      text 'Joint' 536 120 color 0 'Clear Sans' 16;
     terminals
      Pin 560 104 fixed;
      Hin 512 136 fixed;
      Hout 560 136 fixed;
      Pout 512 104 fixed;
    end;
    implementation bg
     submodels
      AdHji 424 424
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Bond Graph\MTF.emx</LibraryPath>
 <TimeStamp>2007-9-25 12:3:3</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
       type MTF
        ports
         power out p1 [6,1];
         power in p2 [6,1];
         signal in H [4,4];
        restrictions
         causality constraint not_equal p1 p2;
       end;
       icon bg bottom
        figures
         text 'MTF' 424 424 color 0 18 bold;
       end;
       implementation eq
equations					
	p2.e = transpose(Adjoint(H)) * p1.e;
	p1.f = Adjoint(H) * p2.f;implementation_end;
      FlowSensor2 184 311.9
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\FlowSensor.emx</LibraryPath>
  <TimeStamp>2011-11-29 15:50:53</TimeStamp>
</Description>
</Information>';
       knot FlowSensor
        ports
         power knot in p1 [6,1];
         power knot out p2 [6,1];
         signal knot out flow [6,1];
        restrictions
         causality constraint not_equal p1 p2;
       end;
       icon bg ellipse
        figures
         ellipse 177.1 304.8 190.9 319.1 color 0 fill 16777215;
         text 'f' 184 311.2 color 0;
       end;
       implementation eq
equations
	p2.f = p1.f;
	p1.e = p2.e;
	flow = p1.f;
implementation_end;
      Hmatrix 256 312
       description '<Information><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></Information>';
       type 'Submodel-Equation'
        ports
         signal in flow [6,1];
         signal out H [4,4];
       end;
       icon bg
        figures
         rectangle 224 296 288 328 color 0 fill 15132390;
         text 'name' 256 312 color 0 'Clear Sans' 16;
       end;
       implementation eq
parameters
	real init[4] = [1;0;0;0];
variables
	real q[4];		//quaternions
	real W[3,4];	//Quaternion Rates Matrix
	real R[3,3];	//Rotation Matrix
	real p[3];		//Position Vector
	real dq[4];
	real Wb[3,4];
equations
	dq = transpose(Wb) * flow[1:3] ./ 2;
	q = int(dq,init);
	p = int(flow[4:6]);
	W = [-q[2],	q[1],	-q[4],	q[3];
		 -q[3],	q[4],	q[1],	-q[2];
		 -q[4],	-q[3],	q[2],	q[1]];
	Wb = [	-q[2],  q[1],  q[4], -q[3];
	   		-q[3], -q[4],  q[1],  q[2];
	   		-q[4],  q[3], -q[2],  q[1]];
 	R = [q[1]^2+q[2]^2-q[3]^2-q[4]^2, 2*(q[2]*q[3]+q[1]*q[4]), 2*(q[2]*q[4]-q[1]*q[3]);
		  2*(q[2]*q[3]-q[1]*q[4]), q[1]^2-q[2]^2+q[3]^2-q[4]^2, 2*(q[3]*q[4]+q[1]*q[2]);
		  2*(q[2]*q[4]+q[1]*q[3]), 2*(q[3]*q[4]-q[1]*q[2]), q[1]^2-q[2]^2-q[3]^2+q[4]^2];
	H = homogeneous(R,p);
	implementation_end;
      MatrixMul 320 576
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Signal\Block Diagram\Gain.emx</LibraryPath>
 <TimeStamp>2007-9-26 12:15:12</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
       type Gain
        ports
         signal in input1 [4,4];
         signal out output [4,4];
         signal in input2 [4,4];
       end;
       icon bg bottom
        figures
         rectangle 304.1 560 335.9 592 color 0 fill 15132390;
         text 'X' 320 576 color 16711680 16 bold;
       end;
       implementation eq
equations
	output = input2*input1;    implementation_end;
      plug Pin 492.1 424;
      plug Pdiff 184 225;
      plug Hin 130.8 576;
      plug Hout 478.4 576;
      plug Hdiff 320 222;
      plug Pout 134.7 424;
      Splitter2 320 312
       description '<Description><Version>4.0</Version>
   <LibraryPath>Signal\Block Diagram\Splitter.emx</LibraryPath>
  <TimeStamp>2008-01-17 11:28:29</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
</Description>';
       knot Splitter
        ports
         signal knot duplicatable out output [4,4];
         signal knot in input [4,4];
       end;
       icon bg ellipse
        figures
         ellipse 316.8 308.8 323.2 315.2 color -1 fill 0;
         ellipse 315.7 307.7 324.3 316.3 color -1;
        terminals
         input 320 312 fixed;
       end;
       implementation eq
equations
    collect (output) = input;
implementation_end;
      Wbai 184 424
       description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <LibraryPath>Bond Graph\ZeroJunction.emx</LibraryPath>
 <TimeStamp>2007-9-27 9:51:43</TimeStamp>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
       knot ZeroJunction
        ports
         power knot duplicatable none p [6,1];
         signal knot out effort [6,1];
        restrictions
         causality constraint one_in p;
       end;
       icon bg bottom
        figures
         text '0' 184 424 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.f)) = 0;
	equal (collect (p.e));
	effort = first (p.e);
implementation_end;
     end;
     connections
      FlowSensor2\flow -> Hmatrix\flow;
      FlowSensor2\p2 => Wbai\p;
      Hin -> MatrixMul\input2;
      Hmatrix\H -> Splitter2\input;
      MatrixMul\output -> Hout;
      Pdiff => FlowSensor2\p1;
      Pin => AdHji\p2;
      Splitter2\output -> AdHji\H 424 312;
      Splitter2\output -> Hdiff;
      Splitter2\output -> MatrixMul\input1;
      Wbai\p <= AdHji\p1;
      Wbai\p => Pout;
     end;
    implementation_end;
   Link 288 120
    description '<Information>
 <Description>
    <Version>4.8</Version>
  <LibraryPath>Bond Graph\MR\link-v3.emx</LibraryPath>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <TimeStamp>2020-7-21 11:14:41</TimeStamp>
<AllowLibraryUpdate>False</AllowLibraryUpdate>
 </Description>
</Information>';
    type 'Submodel-Equation'
     ports
      signal in Hin [4,4];
      signal out Hout [4,4];
      power in Pin [6,1];
      power out Pout [6,1];
     restrictions
      causality constraint not_equal Pin Pout;
    end;
    icon bg bottom
     figures
      rectangle 256 96 320 144 color 0 fill 8454041;
      text 'Link' 288 120 color 0 'Clear Sans' 16;
     terminals
      Hin 256 136 fixed;
      Hout 320 136 fixed;
      Pin 320 104 fixed;
      Pout 256 104 fixed;
    end;
    implementation eq
parameters
	real offset[6]= [0;0;0;0;0.0325;0]; //coordinates of joint_1
variables
	real Hab[4,4];
	real AdHab[6,6];
	real R[3,3];
	real omega[3];
initialequations
	omega = offset[1:3];
	R = dll('EulerAngles.dll','RotationMatrixFromEulXYZs',omega);
	Hab = homogeneous(R,offset[4:6]);
	AdHab = Adjoint(Hab);
equations
	Hout = Hin * Hab;
	Pout.e = transpose(AdHab) * Pin.e;
	Pin.f = AdHab * Pout.f;

    implementation_end;
   Link1 456 120
    description '<Information>
 <Description>
    <Version>4.8</Version>
  <LibraryPath>Bond Graph\MR\link-v3.emx</LibraryPath>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <TimeStamp>2020-7-21 11:14:41</TimeStamp>
<AllowLibraryUpdate>False</AllowLibraryUpdate>
 </Description>
</Information>';
    type 'Submodel-Equation'
     ports
      signal in Hin [4,4];
      signal out Hout [4,4];
      power in Pin [6,1];
      power out Pout [6,1];
     restrictions
      causality constraint not_equal Pin Pout;
    end;
    icon bg bottom
     figures
      rectangle 424 96 488 144 color 0 fill 8454041;
      text 'Link' 456 120 color 0 'Clear Sans' 16;
     terminals
      Hin 424 136 fixed;
      Hout 488 136 fixed;
      Pin 488 104 fixed;
      Pout 424 104 fixed;
    end;
    implementation eq
parameters
	real offset[6]= [0;0;0;0;0.0325;0]; //coordinates of joint_1
variables
	real Hab[4,4];
	real AdHab[6,6];
	real R[3,3];
	real omega[3];
initialequations
	omega = offset[1:3];
	R = dll('EulerAngles.dll','RotationMatrixFromEulXYZr',omega);
	Hab = homogeneous(R,offset[4:6]);
	AdHab = Adjoint(Hab);
equations
	Hout = Hin * Hab;
	Pout.e = transpose(AdHab) * Pin.e;
	Pin.f = AdHab * Pout.f;

    implementation_end;
   Link2 624 120
    description '<Information>
 <Description>
    <Version>4.8</Version>
  <LibraryPath>Bond Graph\MR\link-v3.emx</LibraryPath>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <TimeStamp>2020-7-19 15:22:34</TimeStamp>
<AllowLibraryUpdate>False</AllowLibraryUpdate>
 </Description>
</Information>';
    type 'Submodel-Equation'
     ports
      signal in Hin [4,4];
      signal out Hout [4,4];
      power in Pin [6,1];
      power out Pout [6,1];
     restrictions
      causality constraint not_equal Pin Pout;
    end;
    icon bg bottom
     figures
      rectangle 592 96 656 144 color 0 fill 8454041;
      text 'Link' 624 120 color 0 'Clear Sans' 16;
     terminals
      Hin 592 136 fixed;
      Hout 656 136 fixed;
      Pin 656 104 fixed;
      Pout 592 104 fixed;
    end;
    implementation eq
parameters
	real offset[3]= [0;0.025;0]; //coordinates of joint_1 
variables
	real Hab[4,4];
	real AdHab[6,6];
equations
	Hab = homogeneous(eye(3),offset);
	AdHab = Adjoint(eye(3),offset);
	Hout = Hin * Hab;
	Pout.e = transpose(AdHab) * Pin.e;
	Pin.f = AdHab * Pout.f;

    implementation_end;
   Link3 800 120
    description '<Information>
 <Description>
    <Version>4.8</Version>
  <LibraryPath>Bond Graph\MR\link-v3.emx</LibraryPath>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <TimeStamp>2020-7-19 15:22:34</TimeStamp>
<AllowLibraryUpdate>False</AllowLibraryUpdate>
 </Description>
</Information>';
    type 'Submodel-Equation'
     ports
      signal in Hin [4,4];
      signal out Hout [4,4];
      power in Pin [6,1];
      power out Pout [6,1];
     restrictions
      causality constraint not_equal Pin Pout;
    end;
    icon bg bottom
     figures
      rectangle 768 96 832 144 color 0 fill 8454041;
      text 'Link' 800 120 color 0 'Clear Sans' 16;
     terminals
      Hin 768 136 fixed;
      Hout 832 136 fixed;
      Pin 832 104 fixed;
      Pout 768 104 fixed;
    end;
    implementation eq
parameters
	real offset[3]= [0;0.025;0]; //coordinates of joint_1 
variables
	real Hab[4,4];
	real AdHab[6,6];
equations
	Hab = homogeneous(eye(3),offset);
	AdHab = Adjoint(eye(3),offset);
	Hout = Hin * Hab;
	Pout.e = transpose(AdHab) * Pin.e;
	Pin.f = AdHab * Pout.f;

    implementation_end;
   motor_joint1 112 384
    description '<Description>
	<Version>4.8</Version>
	<IsMainModel>1</IsMainModel>
	</Description>';
    type Submodel
     ports
      signal in input;
      power out p2;
    end;
    implementation bg
     submodels
      Gain1 552 88
       description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Block Diagram\Gain.emx</LibraryPath>
  <TimeStamp>2007-9-26 12:15:12</TimeStamp>
</Description>';
       type Gain
        ports
         signal in input;
         signal out output;
       end;
       icon bg bottom
        figures
         rectangle 536.1 72 567.9 104 color 0 fill 15132390;
         text 'K' 552 88 color 16711680 16 bold;
       end;
       implementation eq
parameters
	real K = 12.0;		// gain
equations
	output = K * input;
    implementation_end;
      GY 624 208
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\GY.emx</LibraryPath>
  <TimeStamp>2011-11-29 15:53:45</TimeStamp>
</Description>
</Information>';
       type GY
        ports
         power in p1;
         power out p2;
        restrictions
         causality constraint equal p1 p2;
       end;
       icon bg bottom
        figures
         text 'GY' 624 208 color 0 18 bold;
       end;
       implementation eq
parameters
	real r = 0.127;
equations
	p1.e = r * p2.f;
	p2.e = r * p1.f;
implementation_end;
      MSe 624 88
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\MSe.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:12:33</TimeStamp>
</Description>
</Information>';
       type MSe
        ports
         power out p;
         signal in effort;
        restrictions
         causality fixed out p;
       end;
       icon bg bottom
        figures
         text 'MSe' 624 88 color 0 18 bold;
       end;
       implementation eq
variables
	real flow;
equations
	p.e = effort;
	flow = p.f;
implementation_end;
      plug input 424 88;
      plug p2 624 296;
      OneJunction2 624 136
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
       knot OneJunction
        ports
         power knot duplicatable none p [1];
         signal knot out flow [1];
        restrictions
         causality constraint one_out p;
       end;
       icon bg
        figures
         text '1' 624 136 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
      R 680 136
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\R.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:35:37</TimeStamp>
</Description>
</Information>';
       type R
        ports
         power in p;
       end;
       icon bg bottom
        figures
         text 'R' 680 136 color 0 18 bold;
       end;
       implementation eq
parameters
	real r = 2;
equations
	p.e = r * p.f;
implementation_end;
      SignalLimiter2 488 88
       description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Block Diagram Non-Linear\SignalLimiter-Limit.emx</LibraryPath>
  <TimeStamp>2007-9-26 12:47:40</TimeStamp>
</Description>';
       type 'SignalLimiter-Limit'
        ports
         signal in input;
         signal out output;
       end;
       icon bg bottom
        figures
         group
          rectangle 472 72 504 104 color 0 fill 15132390;
          line 487.9 76.5 487.9 101 color 0 fill 15132390;
          line 475 88.2 500.7 88.2 color 0 fill 15132390;
          spline 481.9 95.1 493.9 81.4 color 16711680 fill 15132390 width 2;
          spline 493.3 82.2 501.9 81.8 color 16711680 fill 15132390 width 2;
          spline 475 95.6 481.9 95.1 color 16711680 fill 15132390 width 2;
         end;
       end;
       implementation eq
parameters
	real maximum = 1;
	real minimum = -1;
equations
	output = limit (input, minimum, maximum);
  implementation_end;
     end;
     connections
      Gain1\output -> MSe\effort;
      GY\p2 => p2;
      input -> SignalLimiter2\input;
      MSe\p => OneJunction2\p;
      OneJunction2\p => GY\p1;
      R\p <= OneJunction2\p;
      SignalLimiter2\output -> Gain1\input;
     end;
    implementation_end;
   motor_joint2 680 432
    description '<Description>
	<Version>4.8</Version>
	<IsMainModel>1</IsMainModel>
	</Description>';
    type Submodel
     ports
      signal in input;
      power out p2;
    end;
    implementation bg
     submodels
      Gain1 552 88
       description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Block Diagram\Gain.emx</LibraryPath>
  <TimeStamp>2007-9-26 12:15:12</TimeStamp>
</Description>';
       type Gain
        ports
         signal in input;
         signal out output;
       end;
       icon bg bottom
        figures
         rectangle 536.1 72 567.9 104 color 0 fill 15132390;
         text 'K' 552 88 color 16711680 16 bold;
       end;
       implementation eq
parameters
	real K = 12.0;		// gain
equations
	output = K * input;
    implementation_end;
      GY 624 200
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\GY.emx</LibraryPath>
  <TimeStamp>2011-11-29 15:53:45</TimeStamp>
</Description>
</Information>';
       type GY
        ports
         power in p1;
         power out p2;
        restrictions
         causality constraint equal p1 p2;
       end;
       icon bg bottom
        figures
         text 'GY' 624 200 color 0 18 bold;
       end;
       implementation eq
parameters
	real r = 0.127;
equations
	p1.e = r * p2.f;
	p2.e = r * p1.f;
implementation_end;
      MSe 624 88
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\MSe.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:12:33</TimeStamp>
</Description>
</Information>';
       type MSe
        ports
         power out p;
         signal in effort;
        restrictions
         causality fixed out p;
       end;
       icon bg bottom
        figures
         text 'MSe' 624 88 color 0 18 bold;
       end;
       implementation eq
variables
	real flow;
equations
	p.e = effort;
	flow = p.f;
implementation_end;
      plug input 424 88;
      plug p2 624 256;
      OneJunction2 624 136
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
       knot OneJunction
        ports
         power knot duplicatable none p [1];
         signal knot out flow [1];
        restrictions
         causality constraint one_out p;
       end;
       icon bg
        figures
         text '1' 624 136 color 0 18 bold;
       end;
       implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
      R 664 136
       description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\R.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:35:37</TimeStamp>
</Description>
</Information>';
       type R
        ports
         power in p;
       end;
       icon bg bottom
        figures
         text 'R' 664 136 color 0 18 bold;
       end;
       implementation eq
parameters
	real r = 2;
equations
	p.e = r * p.f;
implementation_end;
      SignalLimiter2 488 88
       description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Block Diagram Non-Linear\SignalLimiter-Limit.emx</LibraryPath>
  <TimeStamp>2007-9-26 12:47:40</TimeStamp>
</Description>';
       type 'SignalLimiter-Limit'
        ports
         signal in input;
         signal out output;
       end;
       icon bg bottom
        figures
         group
          rectangle 472 72 504 104 color 0 fill 15132390;
          line 487.9 76.5 487.9 101 color 0 fill 15132390;
          line 475 88.2 500.7 88.2 color 0 fill 15132390;
          spline 481.9 95.1 493.9 81.4 color 16711680 fill 15132390 width 2;
          spline 493.3 82.2 501.9 81.8 color 16711680 fill 15132390 width 2;
          spline 475 95.6 481.9 95.1 color 16711680 fill 15132390 width 2;
         end;
       end;
       implementation eq
parameters
	real maximum = 1;
	real minimum = -1;
equations
	output = limit (input, minimum, maximum);
  implementation_end;
     end;
     connections
      Gain1\output -> MSe\effort;
      GY\p2 => p2;
      input -> SignalLimiter2\input;
      MSe\p => OneJunction2\p;
      OneJunction2\p => GY\p1;
      R\p <= OneJunction2\p;
      SignalLimiter2\output -> Gain1\input;
     end;
    implementation_end;
   Negate1 272 448
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Block Diagram\Negate.emx</LibraryPath>
  <TimeStamp>2007-9-26 12:14:11</TimeStamp>
</Description>';
    type Negate
     ports
      signal in input;
      signal out output;
    end;
    icon bg bottom
     figures
      rectangle 256 432 288 464 color 0 fill 15132390;
      text '-1' 272 448 color 16711680 16 bold;
    end;
    implementation eq
equations
	output = - input;
     implementation_end;
   Negate2 520 552
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Block Diagram\Negate.emx</LibraryPath>
  <TimeStamp>2007-9-26 12:14:11</TimeStamp>
</Description>';
    type Negate
     ports
      signal in input;
      signal out output;
    end;
    icon bg bottom
     figures
      rectangle 504 536 536 568 color 0 fill 15132390;
      text '-1' 520 552 color 16711680 16 bold;
    end;
    implementation eq
equations
	output = - input;
     implementation_end;
   new_joint1 376 280
    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 in input [4,4];
    end;
    implementation eq
variables
	real position[3];
	real rotation[3];
	real R[3,3];
equations
	position = input[1:3,4];
	rotation = dll('EulerAngles.dll','EulXYZsFromHMatrix',input);
	//[input[3,2];input[1,3];input[2,1]];
	R = input[1:3,1:3];implementation_end;
   new_joint2 720 256
    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 in input [4,4];
    end;
    implementation eq
variables
	real position[3];
	real rotation[3];
	real R[3,3];
equations
	// start typing here
	position = input[1:3,4];
	rotation = [input[3,2];input[1,3];input[2,1]];
	R = input[1:3,1:3];implementation_end;
   new_joint3 1016 184
    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 in input [4,4];
    end;
    implementation eq
variables
	real position[3];
	real rotation[3];
	real R[3,3];
equations
	position = input[1:3,4];
	rotation = [input[3,2];input[1,3];input[2,1]];
	R = input[1:3,1:3];implementation_end;
   OneJunction1 360 104
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [6,1];
      signal knot out flow [6,1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 360 104 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   OneJunction12 888 104
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [6,1];
      signal knot out flow [6,1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 888 104 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   OneJunction17 520 288
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [1];
      signal knot out flow [1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 520 288 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   OneJunction2 120 104
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [6,1];
      signal knot out flow [6,1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 120 104 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   OneJunction3 704 104
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [6,1];
      signal knot out flow [6,1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 704 104 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   OneJunction4 593 232
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [2,1];
      signal knot out flow [2,1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 593 232 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   OneJunction5 257 240
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [2,1];
      signal knot out flow [2,1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 257 240 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   OneJunction6 257 256
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [3,1];
      signal knot out flow [3,1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 257 256 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   OneJunction7 593 248
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [3,1];
      signal knot out flow [3,1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 593 248 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   PID1 584 432
    description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Control\PID Control\Continuous\PD.emx</LibraryPath>
  <TimeStamp>2008-1-17 10:49:7</TimeStamp>
</Description>';
    type PD
     ports
      signal in error;
      signal out output;
    end;
    icon bg bottom
     figures
      rectangle 568 416 600 448 color 0 fill 15132390;
      text 'PD' 584.5 432.1 color 16711680 18 bold;
    end;
    implementation eq
parameters
	real kp = 2 {};			// Proportional gain
	real tauD = 0.6 {s};		// Derivative time constant: tauD > 0
	real beta = 0.2{};		// Tameness constant: 0 < beta << 1
variables
	real state, rate;
equations
	rate = (kp * error - output) / (beta * tauD);
	state = int (rate);
	output = state + kp * error /  beta;
      implementation_end;
   PID2 200 384
    description '<Description>
 <Version>4.0</Version>
 <IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Control\PID Control\Continuous\PD.emx</LibraryPath>
  <TimeStamp>2008-1-17 10:49:7</TimeStamp>
</Description>';
    type PD
     ports
      signal in error;
      signal out output;
    end;
    icon bg bottom
     figures
      rectangle 184 368 216 400 color 0 fill 15132390;
      text 'PD' 200.5 384.1 color 16711680 18 bold;
    end;
    implementation eq
parameters
	real kp = 2 {};			// Proportional gain
	real tauD = 0.6 {s};		// Derivative time constant: tauD > 0
	real beta = 0.2{};		// Tameness constant: 0 < beta << 1
variables
	real state, rate;
equations
	rate = (kp * error - output) / (beta * tauD);
	state = int (rate);
	output = state + kp * error /  beta;
      implementation_end;
   PlusMinus4 272 384
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Block Diagram\PlusMinus.emx</LibraryPath>
  <TimeStamp>2007-9-27 10:15:13</TimeStamp>
</Description>';
    knot PlusMinus
     ports
      signal knot duplicatable in plus [1];
      signal knot duplicatable in minus [1];
      signal knot out output [1];
    end;
    icon bg ellipse
     figures
      ellipse 264 376 280 392 color 0 fill 16777215;
    end;
    implementation eq
equations
    output = sum (collect (plus)) - sum (collect (minus));
    implementation_end;
   PlusMinus5 520 432
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Signal\Block Diagram\PlusMinus.emx</LibraryPath>
  <TimeStamp>2007-9-27 10:15:13</TimeStamp>
</Description>';
    knot PlusMinus
     ports
      signal knot duplicatable in plus [1];
      signal knot duplicatable in minus [1];
      signal knot out output [1];
    end;
    icon bg ellipse
     figures
      ellipse 512 424 528 440 color 0 fill 16777215;
    end;
    implementation eq
equations
    output = sum (collect (plus)) - sum (collect (minus));
    implementation_end;
   PowerMux 192 214
			specifications active 'rot_x'
				specification 'rot_x'
 description '<Information>
 <Description>
    <Version>4.8</Version>
  <LibraryPath>Bond Graph\MR\PowerMux-Rotation.emx</LibraryPath>
  <TimeStamp>2020-7-20 14:35:23</TimeStamp>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
  <AllowLibraryUpdate>True</AllowLibraryUpdate>
 </Description>
</Information>';
 type 'PowerMux-Rotation'
  ports
   power in input;
   power out output [6,1];
   power in input_rot2 [2,1];
   power in input_pos3 [3,1];
  restrictions
   causality constraint not_equal input output;
   causality constraint not_equal input_rot2 output;
   causality constraint not_equal input_pos3 output;
 end;
 icon bg bottom
  figures
   line 168 216 216 216 color 0 width 2;
   rectangle 168 208 216 220 color -1;
   text '1' 186 211 color 8421504 8;
  terminals
   input 176 216 fixed;
   output 192 216 fixed;
   input_rot2 208 216 fixed;
   input_pos3 192 216 fixed;
 end;
 implementation eq
equations
	output.e[1] = input.e;
	output.e[2:3] = input_rot2.e;
	output.e[4:6] = input_pos3.e;
	output.f[1] = input.f;
	output.f[2:3] = input_rot2.f;
	output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
				specification 'rot_y'
description '<Description>
   <Version>4.1</Version>
  <LibraryPath>Bond Graph\PowerMux.emx</LibraryPath>
  <TimeStamp>2011-3-4 15:12:50</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
 type PowerMux
  ports
   power in input;
   power out output [6,1];
   power in input_rot2 [2,1];
   power in input_pos3 [3,1];
  restrictions
   causality constraint not_equal input output;
 end;
 icon bg bottom
  figures
   line 808 216 808 264 color 0 width 2;
   rectangle 804 216 816 264 color -1;
   text '1' 813 234 color 8421504 8;
  terminals
   input 808 224 fixed;
   output 808 240 fixed;
   input_rot2 808 256 fixed;
   input_pos3 808 240 fixed;
 end;
 implementation eq
equations
	output.e[1] = input_rot2.e[1];
	output.e[2] = input.e;
	output.e[3] = input_rot2.e[2];
	output.e[4:6] = input_pos3.e;
	output.f[1] = input_rot2.f[1];
	output.f[2] = input.f;
	output.f[3] = input_rot2.f[2];
	output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
				specification 'rot_z'
description '<Description>
   <Version>4.1</Version>
  <LibraryPath>Bond Graph\PowerMux.emx</LibraryPath>
  <TimeStamp>2011-3-4 15:12:50</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
 type PowerMux
  ports
   power in input;
   power out output [6,1];
   power in input_rot2 [2,1];
   power in input_pos3 [3,1];
  restrictions
   causality constraint not_equal input output;
 end;
 icon bg bottom
  figures
   line 808 216 808 264 color 0 width 2;
   rectangle 804 216 816 264 color -1;
   text '1' 813 234 color 8421504 8;
  terminals
   input 808 224 fixed;
   output 808 240 fixed;
   input_rot2 808 256 fixed;
   input_pos3 808 240 fixed;
 end;
 implementation eq
equations
	output.e[3] = input.e;
	output.e[1:2] = input_rot2.e;
	output.e[4:6] = input_pos3.e;
	output.f[3] = input.f;
	output.f[1:2] = input_rot2.f;
	output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
			end;
   PowerMux1 536 206
			specifications active 'rot_x'
				specification 'rot_x'
 description '<Information>
 <Description>
    <Version>4.8</Version>
  <LibraryPath>Bond Graph\MR\PowerMux-Rotation.emx</LibraryPath>
  <TimeStamp>2020-7-20 14:35:23</TimeStamp>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
  <AllowLibraryUpdate>True</AllowLibraryUpdate>
 </Description>
</Information>';
 type 'PowerMux-Rotation'
  ports
   power in input;
   power out output [6,1];
   power in input_rot2 [2,1];
   power in input_pos3 [3,1];
  restrictions
   causality constraint not_equal input output;
   causality constraint not_equal input_rot2 output;
   causality constraint not_equal input_pos3 output;
 end;
 icon bg bottom
  figures
   line 512 208 560 208 color 0 width 2;
   rectangle 512 200 560 212 color -1;
   text '1' 530 203 color 8421504 8;
  terminals
   input 520 208 fixed;
   output 536 208 fixed;
   input_rot2 552 208 fixed;
   input_pos3 536 208 fixed;
 end;
 implementation eq
equations
	output.e[1] = input.e;
	output.e[2:3] = input_rot2.e;
	output.e[4:6] = input_pos3.e;
	output.f[1] = input.f;
	output.f[2:3] = input_rot2.f;
	output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
				specification 'rot_y'
description '<Description>
   <Version>4.1</Version>
  <LibraryPath>Bond Graph\PowerMux.emx</LibraryPath>
  <TimeStamp>2011-3-4 15:12:50</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
 type PowerMux
  ports
   power in input;
   power out output [6,1];
   power in input_rot2 [2,1];
   power in input_pos3 [3,1];
  restrictions
   causality constraint not_equal input output;
 end;
 icon bg bottom
  figures
   line 808 216 808 264 color 0 width 2;
   rectangle 804 216 816 264 color -1;
   text '1' 813 234 color 8421504 8;
  terminals
   input 808 224 fixed;
   output 808 240 fixed;
   input_rot2 808 256 fixed;
   input_pos3 808 240 fixed;
 end;
 implementation eq
equations
	output.e[1] = input_rot2.e[1];
	output.e[2] = input.e;
	output.e[3] = input_rot2.e[2];
	output.e[4:6] = input_pos3.e;
	output.f[1] = input_rot2.f[1];
	output.f[2] = input.f;
	output.f[3] = input_rot2.f[2];
	output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
				specification 'rot_z'
description '<Description>
   <Version>4.1</Version>
  <LibraryPath>Bond Graph\PowerMux.emx</LibraryPath>
  <TimeStamp>2011-3-4 15:12:50</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
 <AllowLibraryUpdate>True</AllowLibraryUpdate>
</Description>';
 type PowerMux
  ports
   power in input;
   power out output [6,1];
   power in input_rot2 [2,1];
   power in input_pos3 [3,1];
  restrictions
   causality constraint not_equal input output;
 end;
 icon bg bottom
  figures
   line 808 216 808 264 color 0 width 2;
   rectangle 804 216 816 264 color -1;
   text '1' 813 234 color 8421504 8;
  terminals
   input 808 224 fixed;
   output 808 240 fixed;
   input_rot2 808 256 fixed;
   input_pos3 808 240 fixed;
 end;
 implementation eq
equations
	output.e[3] = input.e;
	output.e[1:2] = input_rot2.e;
	output.e[4:6] = input_pos3.e;
	output.f[3] = input.f;
	output.f[1:2] = input_rot2.f;
	output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
			end;
   R1 472 288
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\R.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:35:37</TimeStamp>
</Description>
</Information>';
    type R
     ports
      power in p;
    end;
    icon bg bottom
     figures
      text 'R' 472 288 color 0 18 bold;
    end;
    implementation eq
parameters
	real r = 0.0001;
equations
	p.e = r * p.f;
implementation_end;
   R2 257 184
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\2D\R-2.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:6:54</TimeStamp>
</Description>';
    type 'R-2'
     ports
      power in p [2,1];
    end;
    icon bg bottom
     figures
      text 'R' 257 184 color 0 18 bold;
    end;
    implementation eq
parameters
	real r[2,2] = [1.0, 0.0; 0.0, 1.0] {kN.m.s/rad};
equations					
	p.e = r * p.f;
implementation_end;
   R3 257 312
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\3D\R-3.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:11:54</TimeStamp>
</Description>';
    type 'R-3'
     ports
      power in p [3,1];
    end;
    icon bg bottom
     figures
      text 'R' 257 312 color 0 18 bold;
    end;
    implementation eq
parameters
	real r[3,3] = [1.0, 0.0, 0.0; 0.0, 1.0, 0.0; 0.0, 0.0, 1.0]  {kN.s/m};
equations					
	p.e = r * p.f;
implementation_end;
   R4 593 176
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\2D\R-2.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:6:54</TimeStamp>
</Description>';
    type 'R-2'
     ports
      power in p [2,1];
    end;
    icon bg bottom
     figures
      text 'R' 593 176 color 0 18 bold;
    end;
    implementation eq
parameters
	real r[2,2] = [1.0, 0.0; 0.0, 1.0] {kN.m.s/rad};
equations					
	p.e = r * p.f;
implementation_end;
   R5 593 304
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\3D\R-3.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:11:54</TimeStamp>
</Description>';
    type 'R-3'
     ports
      power in p [3,1];
    end;
    icon bg bottom
     figures
      text 'R' 593 304 color 0 18 bold;
    end;
    implementation eq
parameters
	real r[3,3] = [1.0, 0.0, 0.0; 0.0, 1.0, 0.0; 0.0, 0.0, 1.0]  {kN.s/m};
equations					
	p.e = r * p.f;
implementation_end;
   R7 56 288
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\R.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:35:37</TimeStamp>
</Description>
</Information>';
    type R
     ports
      power in p;
    end;
    icon bg bottom
     figures
      text 'R' 56 288 color 0 18 bold;
    end;
    implementation eq
parameters
	real r = 0.0001;
equations
	p.e = r * p.f;
implementation_end;
   rectanglepath 104 552
    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  = 0.5 {s};
	real origin[2] = [0.01,0.03]{m};
variables
	real v {m/s};
	real t_w {s};
	real t_h {s};
	real period {s};
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;
   rectanglepath1 272 656
    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;
    icon bg
     figures
      rectangle 216 640 328 672 color 0 fill 15132390;
      text 'name' 272 656 color 0 'Clear Sans' 16;
    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  = 0.5 {s};
	real origin[2] = [0.01,0.03]{m};
variables
	real v {m/s};
	real t_w {s};
	real t_h {s};
	real period {s};
	boolean y;
initialequations
	v = (2*w + 2*h)/t;
	t_w = w / v;
	t_h = h / v;
code
y = frequencyevent (t,0);
period = time - floor(time / t) * t;

if period < t_w or time < 2 then
	output = origin;
else
	if period < t_w + t_h then
		output = origin + [w;0];
	else	
		if period < 2 * t_w + t_h then
			output = origin + [w;h];
		else
			output = origin + [0;h];
		end;
	end;
end;



	//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;
   Sf2 64 104
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
   <LibraryPath>Bond Graph\2D\Sf-2.emx</LibraryPath>
  <TimeStamp>2007-9-25 12:7:5</TimeStamp>
</Description>';
    type 'Sf-2'
     ports
      power out p [6,1];
     restrictions
      causality fixed in p;
    end;
    icon bg bottom
     figures
      text 'Sf' 64 104 color 0 18 bold;
    end;
    implementation eq
parameters
	real flow[6,1] = 	0;
variables
	real effort [6];
equations
	p.f = flow;
	effort = p.e;
implementation_end;
   Splitter1 392 136
    description '<Description><Version>4.0</Version>
   <LibraryPath>Signal\Block Diagram\Splitter.emx</LibraryPath>
  <TimeStamp>2008-01-17 11:28:29</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
</Description>';
    knot Splitter
     ports
      signal knot duplicatable out output [4,4];
      signal knot in input [4,4];
    end;
    icon bg ellipse
     figures
      ellipse 388.8 132.8 395.2 139.2 color -1 fill 0;
      ellipse 387.7 131.7 396.3 140.3 color -1;
     terminals
      input 392 136 fixed;
    end;
    implementation eq
equations
    collect (output) = input;
implementation_end;
   Splitter2 736 136
    description '<Description><Version>4.0</Version>
   <LibraryPath>Signal\Block Diagram\Splitter.emx</LibraryPath>
  <TimeStamp>2008-01-17 11:28:29</TimeStamp>
<IsMainModel>1</IsMainModel>
 <KeepParameterValues>False</KeepParameterValues>
</Description>';
    knot Splitter
     ports
      signal knot duplicatable out output [4,4];
      signal knot in input [4,4];
    end;
    icon bg ellipse
     figures
      ellipse 732.8 132.8 739.2 139.2 color -1 fill 0;
      ellipse 731.7 131.7 740.3 140.3 color -1;
     terminals
      input 736 136 fixed;
    end;
    implementation eq
equations
    collect (output) = input;
implementation_end;
   Zero 112 136
    description '<Description><Version>4.0</Version><IsMainModel>1</IsMainModel><KeepParameterValues>False</KeepParameterValues>
  <LibraryPath>Signal\Sources\Zero.emx</LibraryPath>
  <TimeStamp>2007-9-27 15:54:36</TimeStamp>
</Description>
';
    type Zero
     ports
      signal out output [4,4];
    end;
    icon bg bottom
     figures
      rectangle 96.1 120 127.9 152 color 0 fill 15132390;
      text '0' 112 136 color 16711680 18 bold;
    end;
    implementation eq
equations
	output = eye(4);implementation_end;
   ZeroJunction1 112 328
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [1];
      signal knot out flow [1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 112 328 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   ZeroJunction2 656 368
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [1];
      signal knot out flow [1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 656 368 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
   ZeroJunction7 112 288
    description '<Information>
 <Description>
    <Version>4.2</Version>
<IsMainModel>1</IsMainModel>
  <KeepParameterValues>False</KeepParameterValues>
    <LibraryPath>Bond Graph\OneJunction.emx</LibraryPath>
  <TimeStamp>2011-11-29 16:17:51</TimeStamp>
</Description>
</Information>';
    knot OneJunction
     ports
      power knot duplicatable none p [1];
      signal knot out flow [1];
     restrictions
      causality constraint one_out p;
    end;
    icon bg
     figures
      text '1' 112 288 color 0 18 bold;
    end;
    implementation eq
equations
	sum (direct (p.e)) = 0;
	equal (collect (p.f));
	flow = first (p.f);
implementation_end;
  end;
  connections
   C1\p <= OneJunction7\p;
   C2\p <= OneJunction6\p;
   COM\Hout -> new_joint1\input;
   COM1\Hout -> new_joint2\input;
   COM2\Hin <- Link3\Hout 920 136;
   COM2\Hout -> new_joint3\input;
   COM2\p => OneJunction12\p;
   Integrate\input <- ZeroJunction7\flow;
   Integrate\output -> PlusMinus4\minus;
   Integrate1\output -> PlusMinus5\minus;
   inverse_kinematics1\angle1 -> Negate1\input;
   inverse_kinematics1\angle2 -> Negate2\input;
   Joint\Hout -> Link\Hin;
   Joint\Pdiff <= PowerMux\output;
   Joint\Pin <= Link\Pout;
   Joint\Pout => OneJunction2\p;
   Link\Pin <= OneJunction1\p;
   Link1\Hout -> Joint1\Hin;
   Link1\Pin <= Joint1\Pout;
   Link1\Pout => OneJunction1\p;
   Link2\Hin <- Joint1\Hout;
   Link2\Hout -> Splitter2\input;
   Link2\Pin <= OneJunction3\p;
   Link2\Pout => Joint1\Pin;
   Link3\Pin <= OneJunction12\p;
   Link3\Pout => OneJunction3\p;
   motor_joint1\p2 => ZeroJunction1\p;
   motor_joint2\p2 => ZeroJunction2\p;
   Negate1\output -> PlusMinus4\plus;
   Negate2\output -> PlusMinus5\plus;
   OneJunction1\p <= COM\p;
   OneJunction17\flow -> Integrate1\input;
   OneJunction3\p <= COM1\p;
   OneJunction4\p => C4\p;
   OneJunction4\p => R4\p;
   OneJunction5\p => C3\p;
   OneJunction5\p => R2\p;
   OneJunction6\p => R3\p;
   OneJunction7\p => R5\p;
   PID1\error <- PlusMinus5\output;
   PID1\output -> motor_joint2\input;
   PID2\output -> motor_joint1\input;
   PlusMinus4\output -> PID2\error;
   PowerMux\input_pos3 <= OneJunction6\p;
   PowerMux\input_rot2 <= OneJunction5\p;
   PowerMux1\input <= OneJunction17\p;
   PowerMux1\input_pos3 <= OneJunction7\p;
   PowerMux1\input_rot2 <= OneJunction4\p;
   PowerMux1\output => Joint1\Pdiff;
   R1\p <= OneJunction17\p;
   R7\p <= ZeroJunction7\p;
   rectanglepath1\output -> inverse_kinematics1\input;
   Sf2\p => OneJunction2\p;
   Splitter1\input <- Link\Hout;
   Splitter1\output -> COM\Hin;
   Splitter1\output -> Link1\Hin;
   Splitter2\output -> COM1\Hin;
   Splitter2\output -> Link3\Hin;
   Zero\output -> Joint\Hin;
   ZeroJunction1\p => ZeroJunction7\p;
   ZeroJunction2\p => OneJunction17\p;
   ZeroJunction7\p => PowerMux\input;
  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>
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