ModelicaStandardLibrary/ModelicaTest/MultiBody.mo at master · modelscript/ModelicaStandardLibrary · GitHub

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within ModelicaTest;

package MultiBody "Test models for Modelica.Mechanics.MultiBody"

import Modelica.Mechanics.MultiBody;

model PlanarLoopWithMove

"Move block + multi-body system where index reduction can fail"

extends Modelica.Icons.Example;

parameter SI.Length rh1[3]={0.5,0,0} "Position vector from r1 to r4";

parameter SI.Length rv1[3]={0,0.5,0} "Position vector from r1 to r2";

parameter SI.Length rv2[3]={0.1,0.5,0} "Position vector from r4 to r2";

final parameter SI.Length rh2[3]=rv2 + rh1 - rv1

"Position vector from r2 to r3";

inner MultiBody.World world(

axisDiameter=0.6/40,

axisLength=0.8) annotation (Placement(transformation(extent={{-40,-60},{-20,-40}})));

MultiBody.Joints.Revolute r1(useAxisFlange=true)

annotation (Placement(transformation(

origin={0,-10},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Joints.Revolute r2 annotation (Placement(

transformation(extent={{20,30},{40,50}})));

MultiBody.Joints.Revolute r3 annotation (Placement(

transformation(extent={{-10,-10},{10,10}},

rotation=-90,

origin={90,10})));

MultiBody.Joints.RevolutePlanarLoopConstraint r4

annotation (Placement(transformation(extent={{50,-60},{70,-40}})));

MultiBody.Parts.FixedTranslation rod1(r=rv1) annotation (

Placement(transformation(

origin={0,20},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Parts.FixedTranslation rod2(r=rh1) annotation (

Placement(transformation(extent={{20,-60},{40,-40}})));

MultiBody.Parts.BodyShape bodyShape(

m=1,

r=rh2,

r_CM=rh2/2) annotation (Placement(transformation(extent={{50,30},{70,50}})));

MultiBody.Parts.FixedTranslation rod3(r=rv2) annotation (

Placement(transformation(

origin={90,-20},

extent={{-10,-10},{10,10}},

rotation=90)));

Modelica.Blocks.Math.MatrixGain deg2rad1(

K=[2*Modelica.Math.asin(1)/180,0,0;0,2*Modelica.Math.asin(1)/180,0; 0,0,2*Modelica.Math.asin(1)/180])

annotation (Placement(transformation(extent={{-70,-20},{-50,0}})));

Modelica.Blocks.Sources.CombiTimeTable combiTimeTable(

smoothness=Modelica.Blocks.Types.Smoothness.ContinuousDerivative,

table=[0,0,10,0; 1,10,10,0; 2,20,10,0; 3,30,10,0],

extrapolation=Modelica.Blocks.Types.Extrapolation.LastTwoPoints)

annotation (Placement(transformation(extent={{-100,-20},{-80,0}})));

Modelica.Mechanics.Rotational.Sources.Move move

annotation (Placement(transformation(extent={{-40,-20},{-20,0}})));

equation

connect(world.frame_b, r1.frame_a) annotation (Line(

points={{-20,-50},{-6.66134e-16,-50},{-6.66134e-16,-20}},

color={95,95,95},

thickness=0.5));

connect(rod1.frame_a, r1.frame_b) annotation (Line(

points={{-6.66134e-016,10},{-6.66134e-016,6},{-6.66134e-016,0},{4.44089e-016,

0}},

thickness=0.5));

connect(rod2.frame_a, world.frame_b) annotation (Line(

points={{20,-50},{-20,-50}},

color={95,95,95},

thickness=0.5));

connect(rod1.frame_b, r2.frame_a) annotation (Line(

points={{4.44089e-16,30},{4.44089e-16,40},{20,40}},

color={95,95,95},

thickness=0.5));

connect(bodyShape.frame_b, r3.frame_a) annotation (Line(

points={{70,40},{90,40},{90,20}},

color={95,95,95},

thickness=0.5));

connect(rod2.frame_b, r4.frame_a) annotation (Line(

points={{40,-50},{50,-50}},

color={95,95,95},

thickness=0.5));

connect(r4.frame_b, rod3.frame_a) annotation (Line(

points={{70,-50},{90,-50},{90,-30}},

color={95,95,95},

thickness=0.5));

connect(rod3.frame_b, r3.frame_b) annotation (Line(

points={{90,-10},{90,0}},

color={95,95,95},

thickness=0.5));

connect(combiTimeTable.y, deg2rad1.u) annotation (Line(

points={{-79,-10},{-72,-10}}, color={0,0,127}));

connect(move.flange, r1.axis) annotation (Line(

points={{-20,-10},{-10,-10}}));

connect(deg2rad1.y, move.u) annotation (Line(

points={{-49,-10},{-42,-10}}, color={0,0,127}));

connect(r2.frame_b, bodyShape.frame_a) annotation (Line(

points={{40,40},{50,40}},

color={95,95,95},

thickness=0.5));

annotation (experiment(StopTime=3), Documentation(info="<html>

This model is a combination of a multi-body system with a kinematic loop

and a Move block, where symbolic transformation is difficult:

Standard symbolic transformation works in the following way if functions

are present with annotation \"InineAfterIndexReduction = true\".

<ol>

<li> These functions are not inlined, the Pantelides algorithm

is applied and the equations are symbolically differentiated.</li>

<li> The functions are inlined and further symbolic transformation

is performed (sorting the equations, dummy derivative method etc..</li>

</ol>

The model contains the following functions that have annotation

\"InineAfterIndexReduction = true\":

<ol>

<li> MultiBody.Frames.resolve1/resolve2(..) functions are used to transform the coordinates

of a vector in another coordinate system. When these functions need to be differentiated

in the Pantelides algorithm, then Euler's differentiation rule is applied with the angular velocity

that is usually a factor of 2-3 more efficient as if direct differentiation

is applied. The drawback is that the sparsity structure is more \"coarse\" and

this lets the Pantelides algorithm fail in this example (this happens usually only

in systems with kinematic loops). This means that the differentiated equation system

is structurally singular, after the functions with annotation \"InineAfterIndexReduction = true\"

are inlined.</li>

<li> The Rotational.Sources.Move block is using internally functions to express that

an input u[2] is the derivative of input u[1]. In order that this is possible, the functions

have the annotation \"InineAfterIndexReduction = true\" so that the differentiation takes place

with the not inlined functions. After the Pantelides algorithm and the differentiation

is applied, the functions are inlined to enhance efficiency.</li>

</ol>

The problem with (1) is that after inlining the functions with

annotation \"InineAfterIndexReduction = true\", the equations are structurally singular, but the

source of the singularity is now known. One remedy is to restart symbolic processing and to

inline all functions with \"InineAfterIndexReduction = true\" before the Pantelides algorithm

is applied. In the model, this approach is in principal successful and the model would

be structurally regular. However, the Move block is no longer working correctly if the Pantelides

algorithm is applied with inlining. For this reason in MSL 3.2.1 build 3, the annotation

\"InineAfterIndexReduction = true\" in the Move block has been replaced by

annotation \"Inline = false\". This results in slightly less efficient code, but is more robust

in the situation at hand.

</html>"));

end PlanarLoopWithMove;

extends Modelica.Icons.ExamplesPackage;

model SphericalDoublePendulum

"Double pendulum with two spherical joints and two bodies"

extends Modelica.Icons.Example;

inner MultiBody.World world annotation (Placement(

transformation(extent={{-88,0},{-68,20}})));

MultiBody.Parts.BodyBox boxBody1(width=0.06, r={0.4,0.0,

-0.3}) annotation (Placement(transformation(extent={{-10,0},{10,20}})));

MultiBody.Parts.BodyBox boxBody2(width=0.06, r={0.3,-0.4,

0}) annotation (Placement(transformation(extent={{74,0},{94,20}})));

MultiBody.Joints.Spherical Spherical1(

enforceStates=true,

useQuaternions=false,

angles_fixed=true,

w_rel_a_fixed=true,

z_rel_a_fixed=false,

w_rel_a_start={0.05235987755982989,0.03490658503988659,0.0174532925199433})

annotation (Placement(transformation(extent={{-52,0},{-32,20}})));

MultiBody.Joints.Spherical Spherical2(

enforceStates=true,

useQuaternions=false,

angles_fixed=true,

w_rel_a_fixed=true,

z_rel_a_fixed=false) annotation (Placement(transformation(extent={{32,0},

{52,20}})));

MultiBody.Parts.BodyBox boxBody3(width=0.06, r={0.4,0.0,

-0.3}) annotation (Placement(transformation(extent={{-10,-40},{10,-20}})));

MultiBody.Parts.BodyBox boxBody4(width=0.06, r={0.3,-0.4,

0}) annotation (Placement(transformation(extent={{76,-40},{96,-20}})));

MultiBody.Joints.Spherical Spherical3(

enforceStates=true,

angles_fixed=true,

w_rel_a_fixed=true,

z_rel_a_fixed=false,

w_rel_a_start={0.05235987755982989,0.03490658503988659,0.0174532925199433})

annotation (Placement(transformation(extent={{-52,-40},{-32,-20}})));

MultiBody.Joints.Spherical Spherical4(

enforceStates=true,

angles_fixed=true,

w_rel_a_fixed=true,

z_rel_a_fixed=false) annotation (Placement(transformation(extent={{32,-40},

{52,-20}})));

MultiBody.Parts.BodyBox boxBody5(

width=0.06,

r={0.4,0.0,-0.3},

useQuaternions=true) annotation (Placement(transformation(extent={{-10,-80},

{10,-60}})));

MultiBody.Parts.BodyBox boxBody6(

width=0.06,

r={0.3,-0.4,0},

useQuaternions=true) annotation (Placement(transformation(extent={{74,-80},

{94,-60}})));

MultiBody.Joints.Spherical Spherical5(

angles_fixed=true,

w_rel_a_fixed=true,

z_rel_a_fixed=false,

w_rel_a_start={0.05235987755982989,0.03490658503988659,0.0174532925199433})

annotation (Placement(transformation(extent={{-52,-80},{-32,-60}})));

MultiBody.Joints.Spherical Spherical6(

angles_fixed=true,

w_rel_a_fixed=true,

z_rel_a_fixed=false) annotation (Placement(transformation(extent={{32,-80},

{52,-60}})));

equation

connect(boxBody1.frame_b, Spherical2.frame_a) annotation (Line(

points={{10,10},{32,10}},

thickness=0.5));

connect(Spherical2.frame_b, boxBody2.frame_a) annotation (Line(

points={{52,10},{74,10}},

thickness=0.5));

connect(world.frame_b, Spherical1.frame_a) annotation (Line(

points={{-68,10},{-52,10}},

thickness=0.5));

connect(Spherical1.frame_b, boxBody1.frame_a) annotation (Line(

points={{-32,10},{-10,10}},

thickness=0.5));

connect(boxBody3.frame_b, Spherical4.frame_a) annotation (Line(

points={{10,-30},{32,-30}},

thickness=0.5));

connect(Spherical4.frame_b, boxBody4.frame_a) annotation (Line(

points={{52,-30},{76,-30}},

thickness=0.5));

connect(Spherical3.frame_b, boxBody3.frame_a) annotation (Line(

points={{-32,-30},{-10,-30}},

thickness=0.5));

connect(world.frame_b, Spherical3.frame_a) annotation (Line(

points={{-68,10},{-60,10},{-60,-30},{-52,-30}},

thickness=0.5));

connect(boxBody5.frame_b, Spherical6.frame_a) annotation (Line(

points={{10,-70},{32,-70}},

thickness=0.5));

connect(Spherical6.frame_b, boxBody6.frame_a) annotation (Line(

points={{52,-70},{74,-70}},

thickness=0.5));

connect(Spherical5.frame_b, boxBody5.frame_a) annotation (Line(

points={{-32,-70},{-10,-70}},

thickness=0.5));

connect(Spherical5.frame_a, world.frame_b) annotation (Line(

points={{-52,-70},{-60,-70},{-60,10},{-68,10}},

thickness=0.5));

annotation (experiment(StopTime=3), Documentation(info="<html>

This example demonstrates that by using joint and body

elements animation is automatically available. Also the revolute

joints are animated. Note, that animation of every component

can be switched of by setting the first parameter animation

to false or by setting enableAnimation in the world

object to false to switch off animation of all components.

<div>

<img src=\"modelica://Modelica/Resources/Images/Mechanics/MultiBody/Examples/Elementary/DoublePendulum.png\"

alt=\"model Examples.Elementary.DoublePendulum\">

</div>

</html>"));

end SphericalDoublePendulum;

model WorldGroundVisualization "Demonstrate visualization of world's ground plane"

extends Modelica.Icons.Example;

MultiBody.Visualizers.FixedArrow visGroundAxis(

animation=true,

r_tail={0,0,0},

n=world.groundAxis_u,

length=world.nominalLength/4) "Visualize arrow in direction of world.groundAxis_u" annotation (Placement(transformation(extent={{0,-10},{20,10}})));

inner MultiBody.World world(

groundLength_v=0.2,

animateGround=true,

groundAxis_u={1,0.3,0},

groundColor={0,128,0},

n={-0.2,0.3,-1},

groundLength_u=1,

animateGravity=true,

gravityType=MultiBody.Types.GravityTypes.UniformGravity)

annotation (Placement(transformation(extent={{-40,-10},{-20,10}})));

equation

connect(visGroundAxis.frame_a, world.frame_b) annotation (Line(

points={{0,0},{-20,0}},

color={95,95,95},

thickness=0.5));

annotation (experiment(StopTime=1));

end WorldGroundVisualization;

package FourbarVariants "Test joints and assembly joints with four bar loop"

extends Modelica.Icons.ExamplesPackage;

model SphericalAndUniversal

"One kinematic loop with four bars (with Spherical and Universal joint)"

extends Modelica.Icons.Example;

output SI.Angle j1_phi "angle of revolute joint j1";

output SI.Position j2_s "distance of prismatic joint j2";

output SI.AngularVelocity j1_w "axis speed of revolute joint j1";

output SI.Velocity j2_v "axis velocity of prismatic joint j2";

inner MultiBody.World world annotation (Placement(

transformation(extent={{-80,-80},{-60,-60}})));

MultiBody.Joints.Revolute j1(

n={1,0,0},

stateSelect=StateSelect.always,

a(fixed=false),

phi(fixed=true),

w(fixed=true, start=5.235987755982989)) annotation (Placement(

transformation(extent={{-54,-40},{-34,-20}})));

MultiBody.Joints.Prismatic j2(

n={1,0,0},

boxWidth=0.05) annotation (Placement(transformation(extent={{12,-80},{32,-60}})));

MultiBody.Parts.BodyCylinder b1(r={0,0.5,0.1},

diameter=0.05) annotation (Placement(transformation(

origin={-30,0},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=

0.05) annotation (Placement(transformation(

origin={50,-50},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Parts.FixedTranslation b3(r={1,0,0},

animation=false) annotation (Placement(transformation(extent={{-32,-80},

{-12,-60}})));

MultiBody.Joints.Spherical spherical(animation=false)

annotation (Placement(transformation(extent={{-20,20},{0,40}})));

MultiBody.Parts.FixedTranslation FixedTranslation1(r={

1,-0.3,-0.1}, animation=false) annotation (Placement(transformation(

extent={{12,20},{32,40}})));

MultiBody.Joints.Universal Universal1(n_b={0,1,0}, n_a=

{0,0,1}) annotation (Placement(transformation(extent={{44,20},{64,40}})));

equation

j1_phi = j1.phi;

j2_s = j2.s;

j1_w = j1.w;

j2_v = j2.v;

connect(j2.frame_b, b2.frame_a) annotation (Line(

points={{32,-70},{50,-70},{50,-60}},

thickness=0.5));

connect(j1.frame_b, b1.frame_a) annotation (Line(

points={{-34,-30},{-30,-30},{-30,-10}},

thickness=0.5));

connect(j1.frame_a, world.frame_b) annotation (Line(

points={{-54,-30},{-60,-30},{-60,-70}},

thickness=0.5));

connect(b3.frame_a, world.frame_b) annotation (Line(

points={{-32,-70},{-60,-70}},

thickness=0.5));

connect(b3.frame_b, j2.frame_a) annotation (Line(

points={{-12,-70},{12,-70}},

thickness=0.5));

connect(b1.frame_b, spherical.frame_a) annotation (Line(

points={{-30,10},{-30,30},{-20,30}},

thickness=0.5));

connect(spherical.frame_b, FixedTranslation1.frame_a) annotation (Line(

points={{0,30},{12,30}},

thickness=0.5));

connect(FixedTranslation1.frame_b, Universal1.frame_a) annotation (Line(

points={{32,30},{44,30}},

thickness=0.5));

connect(b2.frame_b, Universal1.frame_b) annotation (Line(

points={{50,-40},{50,-2},{80,-2},{80,30},{64,30}},

thickness=0.5));

annotation (experiment(StopTime=5), Documentation(info="<html>

This is a second version of the \"four-bar\" mechanism, see figure:

<div>

</div>

In this case

the three revolute joints on the left top-side and the two revolute

joints on the right top side have been replaced by the joint UniversalSpherical

that is a rod connecting a spherical and a universal joint. This joint is defined

by 1 constraint stating that the distance between the two spherical joints is

constant. Using this joint in a kinematic loop reduces the sizes of

non-linear algebraic equations. For this loop, only one non-linear

algebraic system of equations of order 1 remains.

At the UniversalSpherical joint an additional frame_ia fixed to the rod

is present where components can be attached to the connecting rod. In this

example just a coordinate system is attached to visualize frame_ia (coordinate

system on the right in blue color).

Another feature is that the length of the connecting rod can be

automatically calculated during initialization. In order to do this,

another initialization condition has to be given. In this example, the

initial value of the distance of the prismatic joint j2 has been fixed

(via the \"Initialization\" menu) and the rod length of joint

\"UniversalSpherical\" is computed during initialization since parameter

computeLength = true is set in the joint parameter

menu. The main advantage is that during initialization no non-linear

system of equation is solved and therefore initialization always works.

To be precise, the following trivial non-linear equation is actually solved

for rodLength:

rodLength*rodLength = f(angle of revolute joint, distance of prismatic joint)

</pre></blockquote>

</html>"));

end SphericalAndUniversal;

model SphericalSpherical

"One kinematic loop with four bars (with SphericalSpherical joint)"

extends Modelica.Icons.Example;

output SI.Angle j1_phi "angle of revolute joint j1";

output SI.Position j2_s "distance of prismatic joint j2";

output SI.AngularVelocity j1_w "axis speed of revolute joint j1";

output SI.Velocity j2_v "axis velocity of prismatic joint j2";

inner MultiBody.World world annotation (Placement(

transformation(extent={{-80,-80},{-60,-60}})));

MultiBody.Joints.Revolute j1(

n={1,0,0},

stateSelect=StateSelect.always,

a(fixed=false),

phi(fixed=true),

w(fixed=true, start=5.235987755982989)) annotation (Placement(

transformation(extent={{-54,-40},{-34,-20}})));

MultiBody.Joints.Prismatic j2(

n={1,0,0},

a(fixed=false),

s(fixed=true),

v(fixed=false)) annotation (Placement(transformation(extent={{12,-80},{32,-60}})));

MultiBody.Parts.BodyCylinder b1(r={0,0.5,0.1},

diameter=0.05) annotation (Placement(transformation(

origin={-30,0},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=

0.05) annotation (Placement(transformation(

origin={50,-50},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Joints.SphericalSpherical sphericalSpherical(

computeRodLength=true, m=1) annotation (Placement(transformation(

extent={{0,20},{-20,40}})));

MultiBody.Parts.FixedTranslation b3(r={1,0,0},

animation=false) annotation (Placement(transformation(extent={{-32,-80},

{-12,-60}})));

equation

connect(j2.frame_b, b2.frame_a) annotation (Line(

points={{32,-70},{50,-70},{50,-60}},

thickness=0.5));

connect(j1.frame_b, b1.frame_a) annotation (Line(

points={{-34,-30},{-30,-30},{-30,-10}},

thickness=0.5));

connect(j1.frame_a, world.frame_b) annotation (Line(

points={{-54,-30},{-60,-30},{-60,-70}},

thickness=0.5));

connect(b1.frame_b, sphericalSpherical.frame_b) annotation (Line(

points={{-30,10},{-30,30},{-20,30}},

thickness=0.5));

connect(sphericalSpherical.frame_a, b2.frame_b) annotation (Line(

points={{0,30},{50,30},{50,-40}},

thickness=0.5));

j1_phi = j1.phi;

j2_s = j2.s;

j1_w = j1.w;

j2_v = j2.v;

connect(b3.frame_a, world.frame_b) annotation (Line(

points={{-32,-70},{-60,-70}},

thickness=0.5));

connect(b3.frame_b, j2.frame_a) annotation (Line(

points={{-12,-70},{12,-70}},

thickness=0.5));

annotation (experiment(StopTime=5), Documentation(info="<html>

This is a third version of the \"four-bar\" mechanism. In this case

the three revolute joints on the left top-side and the two revolute

joints on the right top side have been replaced by the joint SphericalSpherical

that is a rod with two spherical joints on each side. This joint is defined

by 1 constraint stating that the distance between the two spherical joints is

constant. Using this joint in a kinematic loop reduces the sizes of

non-linear algebraic equations. For this loop, only one non-linear

algebraic system of equations of order 1 remains.

The SphericalSpherical joint may be massless or may have a point mass in

the middle of the rod to approximate in an convenient way the rod

mass properties.

Another nice feature is that the length of the connecting rod can be

automatically calculated during initialization. In order to do this,

another initialization condition has to be given. In this example, the

initial value of the distance of the prismatic joint j2 has been fixed

(via the \"Initialization\" menu) and the length parameter of joint

\"SphericalSpherical\" is computed during initialization since parameter

computeLength = true is set in the joint parameter

menu (this sets \"fixed=false\" on parameter \"length\").

</html>"));

end SphericalSpherical;

model UniversalSpherical

"One kinematic loop with four bars (with UniversalSpherical joint)"

extends Modelica.Icons.Example;

output SI.Angle j1_phi "angle of revolute joint j1";

output SI.Position j2_s "distance of prismatic joint j2";

output SI.AngularVelocity j1_w "axis speed of revolute joint j1";

output SI.Velocity j2_v "axis velocity of prismatic joint j2";

inner MultiBody.World world annotation (Placement(

transformation(extent={{-80,-80},{-60,-60}})));

MultiBody.Joints.Revolute j1(

n={1,0,0},

stateSelect=StateSelect.always,

a(fixed=false),

phi(fixed=true),

w(fixed=true, start=5.235987755982989)) annotation (Placement(

transformation(extent={{-54,-40},{-34,-20}})));

MultiBody.Joints.Prismatic j2(

n={1,0,0},

boxWidth=0.01,

a(fixed=false),

s(fixed=false),

v(fixed=false)) annotation (Placement(transformation(extent={{12,-80},{32,-60}})));

MultiBody.Parts.BodyCylinder b1(r={0,0.5,0.1},

diameter=0.05) annotation (Placement(transformation(

origin={-30,0},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=

0.05) annotation (Placement(transformation(

origin={50,-50},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Joints.UniversalSpherical universalSpherical(

rRod_ia={-1,0.3,0.1}, n1_a={0,1,0.1}) annotation (Placement(

transformation(extent={{0,20},{-20,40}})));

MultiBody.Parts.FixedTranslation b3(animation=false, r=

{0.8,0,0}) annotation (Placement(transformation(extent={{-32,-80},{-12,

-60}})));

MultiBody.Visualizers.FixedFrame fixedFrame4

annotation (Placement(transformation(

origin={-10,70},

extent={{-10,-10},{10,10}},

rotation=90)));

equation

j1_phi = j1.phi;

j2_s = j2.s;

j1_w = j1.w;

j2_v = j2.v;

connect(j2.frame_b, b2.frame_a) annotation (Line(

points={{32,-70},{50,-70},{50,-60}},

thickness=0.5));

connect(j1.frame_b, b1.frame_a) annotation (Line(

points={{-34,-30},{-30,-30},{-30,-10}},

thickness=0.5));

connect(j1.frame_a, world.frame_b) annotation (Line(

points={{-54,-30},{-60,-30},{-60,-70}},

thickness=0.5));

connect(b1.frame_b, universalSpherical.frame_b) annotation (Line(

points={{-30,10},{-30,30},{-20,30}},

thickness=0.5));

connect(universalSpherical.frame_a, b2.frame_b) annotation (Line(

points={{0,30},{50,30},{50,-40}},

thickness=0.5));

connect(b3.frame_a, world.frame_b) annotation (Line(

points={{-32,-70},{-60,-70}},

thickness=0.5));

connect(b3.frame_b, j2.frame_a) annotation (Line(

points={{-12,-70},{12,-70}},

thickness=0.5));

connect(fixedFrame4.frame_a, universalSpherical.frame_ia) annotation (

Line(

points={{-10,60},{-10,50},{-6,50},{-6,40}},

thickness=0.5));

annotation (experiment(StopTime=5), Documentation(info="<html>

This is a fourth version of the \"four-bar\" mechanism. In this case

the three revolute joints on the left top-side and the two revolute

joints on the right top side have been replaced by the joint UniversalSpherical

that is a rod with a spherical and a universal joint on two sides. This joint is defined

by 1 constraint stating that the distance between the two spherical joints is

constant. Using this joint in a kinematic loop reduces the sizes of

non-linear algebraic equations. For this loop, only one non-linear

algebraic system of equations of order 1 remains.

The essential difference to joint SphericalSpherical is that the

orientation of the rod can be computed by removing one degree of freedom

of one of the spherical joints (i.e., replacing it by a universal joint).

Usually, the eigenrotation of the connecting rod is of no technical

interest and by this approximation it is constrained to move in a

somewhat arbitrary way. This allows to have an additional connector,

frame_ia, to be fixed on the rod, where other objects can be attached.

In this example, the coordinate system of frame_ia is visualized.

Another nice feature is that the length of the connecting rod can be

automatically calculated during initialization. In order to do this,

another initialization condition has to be given. In this example, the

initial value of the distance of the prismatic joint j2 has been fixed

(via the \"Initialization\" menu) and the length parameter of joint

\"UniversalSpherical\" is computed during initialization since parameter

computeLength = true is set in the joint parameter

menu (this sets \"fixed=false\" on parameter \"length\").

</html>"));

end UniversalSpherical;

model JointUSR "One kinematic loop with four bars (using JointUSR joint)"

extends Modelica.Icons.Example;

output SI.Angle j1_phi "angle of revolute joint j1";

output SI.Position j2_s "distance of prismatic joint j2";

output SI.AngularVelocity j1_w "axis speed of revolute joint j1";

output SI.Velocity j2_v "axis velocity of prismatic joint j2";

inner MultiBody.World world annotation (Placement(

transformation(extent={{-80,-80},{-60,-60}})));

MultiBody.Joints.Prismatic j2(

n={1,0,0},

stateSelect=StateSelect.always,

a(fixed=false),

s(fixed=true),

v(fixed=true, start=-0.4)) annotation (Placement(transformation(extent={{10,-80},{30,-60}})));

MultiBody.Parts.BodyCylinder b2(r={0,0.2,0}, diameter=

0.05) annotation (Placement(transformation(

origin={40,-30},

extent={{-10,-10},{10,10}},

rotation=90)));

MultiBody.Parts.FixedTranslation b3(animation=false, r=

{1,0,0}) annotation (Placement(transformation(extent={{-30,-80},{-10,-60}})));

MultiBody.Visualizers.FixedFrame fixedFrame

annotation (Placement(transformation(

origin={30,30},

extent={{-10,-10},{10,10}})));

MultiBody.Joints.Assemblies.JointUSR jointUSR(

n1_a={0,1,0},

n_b={1,0,0},

rRod2_ib={0,0.5,0.1},

checkTotalPower=true,

rRod1_ia={-1,0.3,-0.1}) annotation (Placement(transformation(extent={{0,

0},{-20,20}})));

MultiBody.Parts.Body Body1(

m=1,

I_11=0.1,

I_22=0.1,

I_33=0.1,

r_CM={0.01,0,0}) annotation (Placement(transformation(extent={{-30,30},

{-50,50}})));

MultiBody.Parts.Body Body2(

m=1,

I_11=0.1,

I_22=0.1,

I_33=0.1,

r_CM=jointUSR.eRod1_ia/2) annotation (Placement(transformation(extent={

{20,50},{40,70}})));

MultiBody.Parts.Body Body3(

m=1,

I_11=0.1,

I_22=0.1,

I_33=0.1,

r_CM={0,0,0}) annotation (Placement(transformation(

extent={{-10,-10},{10,10}},

rotation=90,

origin={-10,70})));

Modelica.Mechanics.Rotational.Components.Damper damper(d=0.1) annotation (

Placement(transformation(

origin={-60,10},

extent={{-10,-10},{10,10}},

rotation=90)));

equation

j1_phi = jointUSR.revolute.phi;

j2_s = j2.s;

j1_w = der(jointUSR.revolute.phi);

j2_v = j2.v;

connect(j2.frame_b, b2.frame_a) annotation (Line(

points={{30,-70},{40,-70},{40,-40}},

thickness=0.5));

connect(b3.frame_a, world.frame_b) annotation (Line(

points={{-30,-70},{-60,-70}},

thickness=0.5));

connect(b3.frame_b, j2.frame_a) annotation (Line(

points={{-10,-70},{10,-70}},

thickness=0.5));

connect(world.frame_b, jointUSR.frame_b) annotation (Line(

points={{-60,-70},{-40,-70},{-40,10},{-20,10}},

thickness=0.5));

connect(jointUSR.frame_a, b2.frame_b) annotation (Line(

points={{0,10},{40,10},{40,-20}},

thickness=0.5));

connect(damper.flange_b, jointUSR.axis) annotation (Line(

points={{-60,20},{-50,20},{-50,18},{-20,18}}));

connect(damper.flange_a, jointUSR.bearing) annotation (Line(

points={{-60,0},{-50,0},{-50,14},{-20,14}}));

connect(Body1.frame_a, jointUSR.frame_ib) annotation (Line(

points={{-30,40},{-18,40},{-18,20}},

color={95,95,95},

thickness=0.5));

connect(Body2.frame_a, jointUSR.frame_ia) annotation (Line(

points={{20,60},{10,60},{10,30},{-2,30},{-2,20}},

color={95,95,95},

thickness=0.5));

connect(Body3.frame_a, jointUSR.frame_im) annotation (Line(

points={{-10,60},{-10,20},{-10,20}},

color={95,95,95},

thickness=0.5));

connect(fixedFrame.frame_a, jointUSR.frame_ia) annotation (Line(

points={{20,30},{-2,30},{-2,20}},

color={95,95,95},

thickness=0.5));

annotation (experiment(StopTime=2), Documentation(info="<html>