within ; package ObsoleteModelica3 "Library that contains components from Modelica Standard Library 2.2.2 that have been removed from version 3.0" annotation (uses(Modelica(version="3.0")), Documentation(info="

This package contains models and blocks from the Modelica Standard Library version 2.2.2 that are no longer available in version 3.0. The conversion script for version 3.0 changes references in existing user models automatically to the models and blocks of package ObsoleteModelica3. The user should manually replace all references to ObsoleteModelica3 in his/her models to the models that are recommended in the documentation of the respective model.

In most cases, this means that a model with the name \"ObsoleteModelica3.XXX\" should be renamed to \"Modelica.XXX\" (version 3.0) and then a manual adaptation is needed. For example, a reference to ObsoleteModelica3.Mechanics.MultiBody.Sensors.AbsoluteSensor should be replaced by Modelica.Mechanics.MultiBody.Sensors.AbsoluteSensor (version 3.0). Since the design of the component has changed (e.g., several optional connectors, and no longer one connector where all signals are packed together), this requires some changes at the place where the model is used (besides the renaming of the underlying class).

The models in ObsoleteModelica3 are either not according to the Modelica Language version 3.0 and higher, or the model was changed to get a better design. In all cases, an automatic conversion to the new implementation was not feasible, since too complicated.

In order to easily detect obsolete models and blocks, all of them are specially marked in the icon layer with a red box.

Copyright © 2007-2008, Modelica Association.

This Modelica package is free software; it can be redistributed and/or modified under the terms of the Modelica license, see the license conditions and the accompanying disclaimer here.

")); package Blocks "Library of basic input/output control blocks (continuous, discrete, logical, table blocks)" package Interfaces "Library of connectors and partial models for input/output blocks" connector RealSignal = Real "Real port (both input/output possible)" annotation (__Dymola_obsolete="Connector is not valid according to Modelica 3, since input/output prefixes are missing. When using this connector, it is not possible to check for balanced models.", Documentation(info="

Connector with one signal of type Real (no icon, no input/output prefix).

")); connector BooleanSignal = Boolean "Boolean port (both input/output possible)" annotation (__Dymola_obsolete="Connector is not valid according to Modelica 3, since input/output prefixes are missing. When using this connector, it is not possible to check for balanced models.", Documentation(info="

Connector with one signal of type Boolean (no icon, no input/output prefix).

")); connector IntegerSignal = Integer "Integer port (both input/output possible)" annotation (__Dymola_obsolete="Connector is not valid according to Modelica 3, since input/output prefixes are missing. When using this connector, it is not possible to check for balanced models.", Documentation(info="

Connector with one signal of type Icon (no icon, no input/output prefix).

")); package Adaptors "Obsolete package with components to send signals to a bus or receive signals from a bus (only for backward compatibility)" model AdaptorReal "Completely obsolete adaptor between 'old' and 'new' Real signal connectors (only for backward compatibility)" extends ObsoleteModelica3.Icons.ObsoleteBlock; ObsoleteModelica3.Blocks.Interfaces.RealSignal newReal "Connector of Modelica version 2.1" annotation ( Hide=true, Placement(transformation(extent={{100,-10},{120,10}}, rotation=0))); RealPort oldReal(final n=1) "Connector of Modelica version 1.6" annotation (Placement( transformation(extent={{-120,-10},{-100,10}}, rotation=0))); annotation(structurallyIncomplete, __Dymola_obsolete="Model is not balanced, so equation check will not work. This model is no longer needed", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Rectangle( extent={{-100,40},{100,-40}}, lineColor={0,0,255}, fillColor={255,255,255}, fillPattern=FillPattern.Solid), Text( extent={{-144,96},{144,46}}, lineColor={0,0,0}, textString=""), Text( extent={{-88,22},{88,-24}}, lineColor={0,0,255}, fillColor={191,0,0}, fillPattern=FillPattern.Solid, textString="adaptor"), Text( extent={{-216,-58},{36,-80}}, lineColor={0,0,0}, fillColor={255,255,255}, fillPattern=FillPattern.Solid, textString="port.signal")}), Documentation(info="

Completely obsolete adaptor between the Real signal connector of version 1.6 and version ≥ 2.1 of the Modelica Standard Library. This block is only provided for backward compatibility.

")); protected connector RealPort "Connector with signals of type Real" parameter Integer n=1 "Dimension of signal vector" annotation (Hide=true); replaceable type SignalType = Real "type of signal"; SignalType signal[n] "Real signals" annotation (Hide=true); end RealPort; equation newReal = oldReal.signal[1]; end AdaptorReal; model AdaptorBoolean "Completely obsolete adaptor between 'old' and 'new' Boolean signal connectors (only for backward compatibility)" extends ObsoleteModelica3.Icons.ObsoleteBlock; ObsoleteModelica3.Blocks.Interfaces.BooleanSignal newBoolean "Connector of Modelica version 2.1" annotation ( Hide=true, Placement( transformation(extent={{100,-10},{120,10}}, rotation=0))); BooleanPort oldBoolean(final n=1) "Connector of Modelica version 1.6" annotation (Placement( transformation(extent={{-120,-10},{-100,10}}, rotation=0))); annotation(structurallyIncomplete, __Dymola_obsolete="Model is not balanced, so equation check will not work. This model is no longer needed", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Rectangle( extent={{-100,40},{100,-40}}, lineColor={255,0,255}, fillColor={255,255,255}, fillPattern=FillPattern.Solid), Text( extent={{-144,96},{144,46}}, lineColor={0,0,0}, textString=""), Text( extent={{-88,22},{88,-24}}, lineColor={255,0,255}, textString="adaptor"), Text( extent={{-216,-58},{36,-80}}, lineColor={0,0,0}, fillColor={255,255,255}, fillPattern=FillPattern.Solid, textString="port.signal")}), Documentation(info="

Completely obsolete adaptor between the Real signal connector of version 1.6 and version ≥ 2.1 of the Modelica Standard Library. This block is only provided for backward compatibility.

")); protected connector BooleanPort "Connector with signals of type Boolean" parameter Integer n=1 "Dimension of signal vector" annotation (Hide=true); replaceable type SignalType = Boolean "type of signal"; SignalType signal[n] "Boolean signals" annotation (Hide=true); end BooleanPort; equation newBoolean = oldBoolean.signal[1]; end AdaptorBoolean; model AdaptorInteger "Completely obsolete adaptor between 'old' and 'new' Integer signal connectors (only for backward compatibility)" extends ObsoleteModelica3.Icons.ObsoleteBlock; ObsoleteModelica3.Blocks.Interfaces.IntegerSignal newInteger "Connector of Modelica version 2.1" annotation ( Hide=true, Placement( transformation(extent={{100,-10},{120,10}}, rotation=0))); IntegerPort oldInteger(final n=1) "Connector of Modelica version 1.6" annotation (Placement( transformation(extent={{-120,-10},{-100,10}}, rotation=0))); annotation(structurallyIncomplete, __Dymola_obsolete="Model is not balanced, so equation check will not work. This model is no longer needed", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Rectangle( extent={{-100,40},{100,-40}}, lineColor={255,127,0}, fillColor={255,255,255}, fillPattern=FillPattern.Solid), Text( extent={{-144,96},{144,46}}, lineColor={0,0,0}, textString=""), Text( extent={{-88,22},{88,-24}}, lineColor={255,127,0}, textString="adaptor"), Text( extent={{-216,-58},{36,-80}}, lineColor={0,0,0}, fillColor={255,255,255}, fillPattern=FillPattern.Solid, textString="port.signal")}), Documentation(info="

Completely obsolete adaptor between the Real signal connector of version 1.6 and version ≥ 2.1 of the Modelica Standard Library. This block is only provided for backward compatibility.

")); protected connector IntegerPort "Connector with signals of type Integer" parameter Integer n=1 "Dimension of signal vector" annotation (Hide=true); replaceable type SignalType = Integer "type of signal"; SignalType signal[n] "Integer signals" annotation (Hide=true); end IntegerPort; equation newInteger = oldInteger.signal[1]; end AdaptorInteger; end Adaptors; end Interfaces; package Math "Library of mathematical functions as input/output blocks" package UnitConversions "Conversion blocks to convert between SI and non-SI unit signals" block ConvertAllUnits "Obsolete block. Use one of Modelica.Blocks.Math.UnitConversions.XXX instead" replaceable block ConversionBlock = Modelica.Blocks.Interfaces.PartialConversionBlock "Conversion block" annotation (choicesAllMatching=true, Documentation(info= "

Internal replaceable block that is used to construct the \"pull down menu\" of the available unit conversions.

")); extends ConversionBlock; extends ObsoleteModelica3.Icons.ObsoleteBlock; annotation ( __Dymola_obsolete="Model is not according to Modelica Language 3.0 since replaceable base class present. " + "Use instead one of Modelica.Blocks.Math.UnitConversions.XXX", defaultComponentName="convert", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={Line(points={{-90,0},{30,0}}, color= {191,0,0}), Polygon( points={{90,0},{30,20},{30,-20},{90,0}}, lineColor={191,0,0}, fillColor={191,0,0}, fillPattern=FillPattern.Solid)}), Documentation(info="

This block implements the Modelica.SIunits.Conversions functions as a fixed causality block to simplify their use. The block contains a replaceable block class ConversionBlock that can be changed to be any of the blocks defined in Modelica.Blocks.Math.UnitConversions, and more generally, any blocks that extend from Modelica.Blocks.Interfaces.PartialConversionBlock.

")); end ConvertAllUnits; end UnitConversions; block TwoInputs "Obsolete block. Use instead Modelica.Blocks.Math.InverseBlockConstraints" extends Modelica.Blocks.Interfaces.BlockIcon; extends ObsoleteModelica3.Icons.ObsoleteBlock; annotation(structurallyIncomplete, __Dymola_obsolete="Model is not balanced, i.e., not according to Modelica Language 3.0. Use instead Modelica.Blocks.Math.InverseBlockConstraints", Window( x=0.15, y=0.21, width=0.6, height=0.6), Documentation(info="

This block is used to enable asignment of values to variables preliminary defined as outputs (e.g. useful for inverse model generation).

"), Icon(coordinateSystem( preserveAspectRatio=false, extent={{-100,-100},{100,100}}, grid={2,2}), graphics={Text( extent={{-95,50},{95,-50}}, lineColor={0,0,127}, textString="=")})); Modelica.Blocks.Interfaces.RealInput u1 "Connector of first Real input signal" annotation ( layer="icon", Placement(transformation(extent={{-139.742,-19.0044},{-100,20}}, rotation=0))); Modelica.Blocks.Interfaces.RealInput u2 "Connector of second Real input signal (u1=u2)" annotation ( layer="icon", Placement(transformation( origin={120,0}, extent={{-20,-20},{20,20}}, rotation=180))); equation u1 = u2; end TwoInputs; block TwoOutputs "Obsolete block. Use instead Modelica.Blocks.Math.InverseBlockConstraints" extends Modelica.Blocks.Interfaces.BlockIcon; extends ObsoleteModelica3.Icons.ObsoleteBlock; annotation(structurallyIncomplete, __Dymola_obsolete="Model is not balanced, i.e., not according to Modelica Language 3.0. Use instead Modelica.Blocks.Math.InverseBlockConstraints", Window( x=0.21, y=0.28, width=0.6, height=0.6), Documentation(info="

This block is used to enable calculation of values preliminary defined as inputs. (e.g. useful for inverse model generation).

"), Icon(coordinateSystem( preserveAspectRatio=false, extent={{-100,-100},{100,100}}, grid={2,2}), graphics={Text( extent={{-95,50},{95,-50}}, lineColor={0,0,127}, textString="=")})); output Modelica.Blocks.Interfaces.RealOutput y1 "Connector of first Real output signal" annotation (Placement(transformation(extent={{100,-10},{120,10}}, rotation=0))); output Modelica.Blocks.Interfaces.RealOutput y2 "Connector of second Real output signal (y1=y2)" annotation (Placement( transformation( origin={-110.366,-0.90289}, extent={{-10.0005,-10},{10.0005,10}}, rotation=180))); equation y1 = y2; end TwoOutputs; end Math; end Blocks; package Electrical "Library of electrical models (analog, digital, machines, multi-phase)" package Analog "Library for analog electrical models" package Basic "Basic electrical components such as resistor, capacitor, transformer" model HeatingResistor "Obsolete model. Use Modelica.Electrical.Analog.Basic.HeatingResistor instead" extends Modelica.Electrical.Analog.Interfaces.OnePort; extends ObsoleteModelica3.Icons.ObsoleteModel; parameter Modelica.SIunits.Resistance R_ref=1 "Resistance at temperature T_ref"; parameter Modelica.SIunits.Temperature T_ref=300 "Reference temperature"; parameter Real alpha(unit="1/K") = 0 "Temperature coefficient of resistance"; Modelica.SIunits.Resistance R "Resistance = R_ref*(1 + alpha*(heatPort.T - T_ref));"; annotation ( __Dymola_obsolete="Model equations depend on cardinality(..) which will become obsolete in the Modelica language. Use instead Modelica.Electrical.Analog.Basic.HeatingResistor", Diagram(coordinateSystem(preserveAspectRatio=false, extent={{-100, -100},{100,100}}), graphics={ Line(points={{-110,20},{-85,20}}, color={160,160,164}), Polygon( points={{-95,23},{-85,20},{-95,17},{-95,23}}, lineColor={160,160,164}, fillColor={160,160,164}, fillPattern=FillPattern.Solid), Line(points={{90,20},{115,20}}, color={160,160,164}), Line(points={{-125,0},{-115,0}}, color={160,160,164}), Line(points={{-120,-5},{-120,5}}, color={160,160,164}), Text( extent={{-110,25},{-90,45}}, lineColor={160,160,164}, textString="i"), Polygon( points={{105,23},{115,20},{105,17},{105,23}}, lineColor={160,160,164}, fillColor={160,160,164}, fillPattern=FillPattern.Solid), Line(points={{115,0},{125,0}}, color={160,160,164}), Text( extent={{90,45},{110,25}}, lineColor={160,160,164}, textString="i"), Rectangle(extent={{-70,30},{70,-30}}), Line(points={{-96,0},{-70,0}}), Line(points={{70,0},{96,0}}), Line(points={{0,-30},{0,-90}}, color={191,0,0}), Line(points={{-52,-50},{48,50}}, color={0,0,255}), Polygon( points={{40,52},{50,42},{54,56},{40,52}}, lineColor={0,0,255}, fillColor={0,0,255}, fillPattern=FillPattern.Solid)}), Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Text(extent={{-142,60},{143,118}}, textString="%name"), Line(points={{-90,0},{-70,0}}), Line(points={{70,0},{90,0}}), Rectangle( extent={{-70,30},{70,-30}}, lineColor={0,0,255}, fillColor={255,255,255}, fillPattern=FillPattern.Solid), Line(points={{0,-30},{0,-91}}, color={191,0,0}), Line(points={{-52,-50},{48,50}}, color={0,0,255}), Polygon( points={{40,52},{50,42},{54,56},{40,52}}, lineColor={0,0,255}, fillColor={0,0,255}, fillPattern=FillPattern.Solid)}), Documentation(info="

This is a model for an electrical resistor where the generated heat is dissipated to the environment via connector heatPort and where the resistance R is temperature dependent according to the following equation:

    R = R_ref*(1 + alpha*(heatPort.T - T_ref))

alpha is the temperature coefficient of resistance, which is often abbreviated as TCR. In resistor catalogues, it is usually defined as X [ppm/K] (parts per million, similarly to per centage) meaning X*1.e-6 [1/K]. Resistors are available for 1 .. 7000 ppm/K, i.e., alpha = 1e-6 .. 7e-3 1/K;

When connector heatPort is not connected, the temperature dependent behaviour is switched off by setting heatPort.T = T_ref. Additionally, the equation heatPort.Q_flow = 0 is implicitly present due to a special rule in Modelica that flow variables of not connected connectors are set to zero.

", revisions= " "), uses(Modelica(version="2.2.1"))); Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort annotation (Placement( transformation( origin={0,-100}, extent={{10,-10},{-10,10}}, rotation=270))); equation v = R*i; if cardinality(heatPort) > 0 then R = R_ref*(1 + alpha*(heatPort.T - T_ref)); heatPort.Q_flow = -v*i; else /* heatPort is not connected resulting in the implicit equation 'heatPort.Q_flow = 0' */ R = R_ref; heatPort.T = T_ref; end if; end HeatingResistor; end Basic; end Analog; end Electrical; package Icons "Library of icons" partial block ObsoleteBlock "Icon for an obsolete block (use only for this case)" annotation (__Dymola_obsolete="Only used to mark an obsolete block. Do not use otherwise.", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100, -100},{100,100}}), graphics={Rectangle( extent={{-102,102},{102,-102}}, lineColor={255,0,0}, pattern=LinePattern.Dash, lineThickness=0.5)}), Documentation(info="

This partial class is intended to design a default icon for an obsolete class that will be removed from the PowerTrain library later on.

", revisions="            Copyright © 1999-2007, DLR Institute of Robotics and Mechatronics ")); equation end ObsoleteBlock; partial model ObsoleteModel "Icon for an obsolete model (use only for this case)" annotation (__Dymola_obsolete="Only used to mark an obsolete model. Do not use otherwise.", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100, -100},{100,100}}), graphics={Rectangle( extent={{-102,102},{102,-102}}, lineColor={255,0,0}, pattern=LinePattern.Dash, lineThickness=0.5)}), Documentation(info="

This partial class is intended to design a default icon for an obsolete class that will be removed from the PowerTrain library later on.

", revisions="            Copyright © 1999-2007, DLR Institute of Robotics and Mechatronics ")); equation end ObsoleteModel; partial class Enumeration "Obsolete class (icon for an enumeration emulated by a package). Use a real enumeration instead" annotation (__Dymola_obsolete="Icon for an emulated enumeration. Emulated enumerations are no longer used (only real enumerations)", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Text(extent={{-138,164},{138,104}}, textString="%name"), Ellipse( extent={{-100,100},{100,-100}}, lineColor={255,0,127}, fillColor={255,255,255}, fillPattern=FillPattern.Solid), Text( extent={{-100,100},{100,-100}}, lineColor={255,0,127}, fillColor={223,159,191}, fillPattern=FillPattern.Solid, textString="e")}), Documentation(info="

This icon is designed for an enumeration (that is emulated by a package).

")); end Enumeration; end Icons; package Mechanics "Library of 1-dim. and 3-dim. mechanical components (multi-body, rotational, translational)" package MultiBody "Library to model 3-dimensional mechanical systems" package Forces "Components that exert forces and/or torques between frames" model WorldForceAndTorque "Obsolete model. Use instead Modelica.Mechanics.MultiBody.Forces.WorldForceAndTorque" import SI = Modelica.SIunits; import Modelica.Mechanics.MultiBody.Types; extends Modelica.Mechanics.MultiBody.Interfaces.PartialOneFrame_b; extends ObsoleteModelica3.Icons.ObsoleteModel; Modelica.Blocks.Interfaces.RealInput load[6] "[1:6] = x-, y-, z-coordinates of force and x-, y-, z-coordiantes of torque resolved in world frame" annotation (Placement(transformation(extent={{-140,-20},{-100,20}}, rotation=0))); parameter Boolean animation=true "= true, if animation shall be enabled"; parameter Real N_to_m(unit="N/m") = world.defaultN_to_m " Force arrow scaling (length = force/N_to_m)" annotation (Dialog(group="if animation = true", enable=animation)); parameter Real Nm_to_m(unit="N.m/m") = world.defaultNm_to_m " Torque arrow scaling (length = torque/Nm_to_m)" annotation (Dialog(group="if animation = true", enable=animation)); input SI.Diameter forceDiameter=world.defaultArrowDiameter " Diameter of force arrow" annotation (Dialog(group="if animation = true", enable=animation)); input SI.Diameter torqueDiameter=forceDiameter " Diameter of torque arrow" annotation (Dialog(group="if animation = true", enable=animation)); input Types.Color forceColor=Modelica.Mechanics.MultiBody.Types.Defaults.ForceColor " Color of force arrow" annotation (Dialog(group="if animation = true", enable=animation)); input Types.Color torqueColor=Modelica.Mechanics.MultiBody.Types.Defaults.TorqueColor " Color of torque arrow" annotation (Dialog(group="if animation = true", enable=animation)); input Types.SpecularCoefficient specularCoefficient = world.defaultSpecularCoefficient "Reflection of ambient light (= 0: light is completely absorbed)" annotation (Dialog(group="if animation = true", enable=animation)); annotation ( __Dymola_obsolete="Based on a packed result signal which is not a good design. Use instead Modelica.Mechanics.MultiBody.Forces.WorldForceAndTorque", preferedView="info", Diagram(coordinateSystem(preserveAspectRatio=false, extent={{-100, -100},{100,100}}), graphics={ Polygon( points={{-100,10},{50,10},{50,31},{97,0},{50,-31},{50,-10},{-100, -10},{-100,10}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line( points={{-100,11},{-94,24},{-86,39},{-74,59},{-65,71},{-52,83}, {-35,92},{-22,95},{-8,95},{7,91},{19,84},{32,76},{44,66}, {52,58},{58,51}}, color={0,0,0}, thickness=0.5), Polygon( points={{97,18},{72,77},{38,42},{97,18}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid)}), Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Text( extent={{-74,62},{44,24}}, lineColor={192,192,192}, textString="world"), Polygon( points={{-100,10},{50,10},{50,31},{94,0},{50,-31},{50,-10},{-100, -10},{-100,10}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Text(extent={{-137,-47},{148,-108}}, textString="%name"), Line( points={{-98,14},{-92,27},{-84,42},{-72,62},{-63,74},{-50,86}, {-33,95},{-20,98},{-6,98},{9,94},{21,87},{34,79},{46,69}, {54,61},{60,54}}, color={0,0,0}, thickness=0.5), Polygon( points={{99,21},{74,80},{40,45},{99,21}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid)}), Documentation(info="

The 6 signals of the load connector are interpreted as the x-, y- and z-coordinates of a force and as the x-, y-, and z-coordinates of a torque resolved in the world frame and acting at the frame connector to which this component is attached. The input signals are mapped to the force and torque in the following way: 

   force  = load[1:3]
   torque = load[4:6]

The force and torque are by default visualized as an arrow (force) and as a double arrow (torque) acting at the connector to which they are connected. The diameters and colors of the arrows are fixed and can be defined via parameters forceDiameter, torqueDiameter, forceColor and torqueColor. The arrows point in the directions defined by the inPort.signal signals. The lengths of the arrows are proportional to the length of the force and torque vectors, respectively, using parameters N_to_m and Nm_to_m as scaling factors. For example, if N_to_m = 100 N/m, then a force of 350 N is displayed as an arrow of length 3.5 m.

An example how to use this model is given in the following figure:

This leads to the following animation

")); annotation ( Coordsys( extent=[-100, -100; 100, 100], grid=[1, 1], component=[20, 20]), Window( x=0.18, y=0.01, width=0.8, height=0.82), Documentation(info=" An external force element exerts the inport signal as negative force on the connector frame (the force vector is resolved in the world frame). "), Icon(Text(extent=[-132, 99; 128, 39], string="%name"), Polygon(points=[-100, 10; 49, 10; 49, 31; 100, 0; 49, -31; 49, -10; -100, -10; -100, 10], style( color=0, gradient=0, fillColor=0, fillPattern=1))), Diagram(Polygon(points=[-90, 10; 40, 10; 40, 31; 91, 0; 40, -31; 40, -10; -90, -10; -90, 10], style( color=0, gradient=0, fillColor=0, fillPattern=1)))); protected SI.Position f_in_m[3]=frame_b.f/N_to_m "Force mapped from N to m for animation"; SI.Position t_in_m[3]=frame_b.t/Nm_to_m "Torque mapped from Nm to m for animation"; Modelica.Mechanics.MultiBody.Visualizers.Advanced.Arrow forceArrow( diameter=forceDiameter, color=forceColor, specularCoefficient=specularCoefficient, R=frame_b.R, r=frame_b.r_0, r_tail=f_in_m, r_head=-f_in_m) if world.enableAnimation and animation; Modelica.Mechanics.MultiBody.Visualizers.Advanced.DoubleArrow torqueArrow( diameter=torqueDiameter, color=torqueColor, specularCoefficient=specularCoefficient, R=frame_b.R, r=frame_b.r_0, r_tail=t_in_m, r_head=-t_in_m) if world.enableAnimation and animation; equation frame_b.f = -Modelica.Mechanics.MultiBody.Frames.resolve2(frame_b.R, load[1 :3]); frame_b.t = -Modelica.Mechanics.MultiBody.Frames.resolve2(frame_b.R, load[4 :6]); end WorldForceAndTorque; annotation (uses(Modelica(version="3.0"))); model FrameForceAndTorque "Obsolete model. Use instead Modelica.Mechanics.MultiBody.Forces.ForceAndTorque" import SI = Modelica.SIunits; import Modelica.Mechanics.MultiBody.Types; extends Modelica.Mechanics.MultiBody.Interfaces.PartialOneFrame_b; extends ObsoleteModelica3.Icons.ObsoleteModel; Modelica.Mechanics.MultiBody.Interfaces.Frame_resolve frame_resolve "If connected, the input signals are resolved in this frame" annotation (Placement(transformation( origin={0,100}, extent={{16,-16},{-16,16}}, rotation=270))); Modelica.Blocks.Interfaces.RealInput load[6] "[1:6] = x-, y-, z-coordinates of force and x-, y-, z-coordiantes of torque resolved in frame_b or frame_resolved (if connected)" annotation (Placement(transformation(extent={{-140,-20},{-100,20}}, rotation=0))); parameter Boolean animation=true "= true, if animation shall be enabled"; parameter Real N_to_m(unit="N/m") = world.defaultN_to_m " Force arrow scaling (length = force/N_to_m)" annotation (Dialog(group="if animation = true", enable=animation)); parameter Real Nm_to_m(unit="N.m/m") = world.defaultNm_to_m " Torque arrow scaling (length = torque/Nm_to_m)" annotation (Dialog(group="if animation = true", enable=animation)); input SI.Diameter forceDiameter=world.defaultArrowDiameter " Diameter of force arrow" annotation (Dialog(group="if animation = true", enable=animation)); input SI.Diameter torqueDiameter=forceDiameter " Diameter of torque arrow" annotation (Dialog(group="if animation = true", enable=animation)); input Types.Color forceColor=Modelica.Mechanics.MultiBody.Types.Defaults.ForceColor " Color of force arrow" annotation (Dialog(group="if animation = true", enable=animation)); input Types.Color torqueColor=Modelica.Mechanics.MultiBody.Types.Defaults.TorqueColor " Color of torque arrow" annotation (Dialog(group="if animation = true", enable=animation)); input Types.SpecularCoefficient specularCoefficient = world.defaultSpecularCoefficient "Reflection of ambient light (= 0: light is completely absorbed)" annotation (Dialog(group="if animation = true", enable=animation)); annotation ( __Dymola_obsolete="Based on a packed result signal which is not a good design. Use instead Modelica.Mechanics.MultiBody.Forces.ForceAndTorque", preferedView="info", Diagram(coordinateSystem(preserveAspectRatio=false, extent={{-100, -100},{100,100}}), graphics={ Polygon( points={{-100,10},{50,10},{50,31},{97,0},{50,-31},{50,-10},{-100, -10},{-100,10}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line(points={{-100,11},{-94,24},{-86,39},{-74,59},{-65,71},{-52, 83},{-35,92},{-22,95},{-8,95},{7,91},{19,84},{32,76},{44, 66},{52,58},{58,51}}, color={0,0,0}), Polygon( points={{97,18},{72,77},{38,42},{97,18}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line( points={{0,97},{0,10}}, color={95,95,95}, pattern=LinePattern.Dot)}), Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Text( extent={{-74,62},{44,24}}, lineColor={192,192,192}, textString="resolve"), Polygon( points={{-100,10},{50,10},{50,31},{94,0},{50,-31},{50,-10},{-100, -10},{-100,10}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Text(extent={{-137,-47},{148,-108}}, textString="%name"), Line(points={{-100,10},{-92,26},{-84,42},{-76,52},{-60,68},{-46, 76},{-31,82},{-17,85},{-2,87},{14,86},{26,82},{37,75},{46, 69},{54,61},{60,54}}, color={0,0,0}), Polygon( points={{99,21},{74,80},{40,45},{99,21}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line( points={{0,95},{0,10}}, color={95,95,95}, pattern=LinePattern.Dot)}), Documentation(info="

The 6 signals of the load connector are interpreted as the x-, y- and z-coordinates of a force and as the x-, y-, and z-coordinates of a torque acting at the frame connector to which this component is attached. If connector frame_resolve is not connected, the force and torque coordinates are with respect to frame_b. If connector frame_resolve is connected, the force and torque coordinates are with respect to frame_resolve. In this case the force and torque in connector frame_resolve are set to zero, i.e., this connector is solely used to provide the information of the coordinate system, in which the force coordinates are defined. The input signals are mapped to the force and torque in the following way: 

   force  = load[1:3]
   torque = load[4:6]

The force and torque are by default visualized as an arrow (force) and as a double arrow (torque) acting at the connector to which they are connected. The diameters and colors of the arrows are fixed and can be defined via parameters forceDiameter, torqueDiameter, forceColor and torqueColor. The arrows point in the directions defined by the inPort.signal signals. The lengths of the arrows are proportional to the length of the force and torque vectors, respectively, using parameters N_to_m and Nm_to_m as scaling factors. For example, if N_to_m = 100 N/m, then a force of 350 N is displayed as an arrow of length 3.5 m.

An example how to use this model is given in the following figure:

This leads to the following animation

")); annotation ( Coordsys( extent=[-100, -100; 100, 100], grid=[1, 1], component=[20, 20]), Window( x=0.18, y=0.01, width=0.8, height=0.82), Documentation(info=" An external force element exerts the inport signal as negative force on the connector frame (the force vector is resolved in the world frame). "), Icon(Text(extent=[-132, 99; 128, 39], string="%name"), Polygon(points=[-100, 10; 49, 10; 49, 31; 100, 0; 49, -31; 49, -10; -100, -10; -100, 10], style( color=0, gradient=0, fillColor=0, fillPattern=1))), Diagram(Polygon(points=[-90, 10; 40, 10; 40, 31; 91, 0; 40, -31; 40, -10; -90, -10; -90, 10], style( color=0, gradient=0, fillColor=0, fillPattern=1)))); protected SI.Position f_in_m[3]=frame_b.f/N_to_m "Force mapped from N to m for animation"; SI.Position t_in_m[3]=frame_b.t/Nm_to_m "Torque mapped from Nm to m for animation"; Modelica.Mechanics.MultiBody.Visualizers.Advanced.Arrow forceArrow( diameter=forceDiameter, color=forceColor, specularCoefficient=specularCoefficient, R=frame_b.R, r=frame_b.r_0, r_tail=f_in_m, r_head=-f_in_m) if world.enableAnimation and animation; Modelica.Mechanics.MultiBody.Visualizers.Advanced.DoubleArrow torqueArrow( diameter=torqueDiameter, color=torqueColor, specularCoefficient=specularCoefficient, R=frame_b.R, r=frame_b.r_0, r_tail=t_in_m, r_head=-t_in_m) if world.enableAnimation and animation; equation if cardinality(frame_resolve) == 0 then frame_b.f = -load[1:3]; frame_b.t = -load[4:6]; frame_resolve.r_0 = zeros(3); frame_resolve.R = Modelica.Mechanics.MultiBody.Frames.nullRotation(); else frame_b.f = -Modelica.Mechanics.MultiBody.Frames.resolveRelative( load[1:3], frame_resolve.R, frame_b.R); frame_b.t = -Modelica.Mechanics.MultiBody.Frames.resolveRelative( load[4:6], frame_resolve.R, frame_b.R); frame_resolve.f = zeros(3); frame_resolve.t = zeros(3); end if; end FrameForceAndTorque; model ForceAndTorque "Obsolete model. Use instead Modelica.Mechanics.MultiBody.Forces.ForceAndTorque" import SI = Modelica.SIunits; import Modelica.Mechanics.MultiBody.Types; extends Modelica.Mechanics.MultiBody.Interfaces.PartialTwoFrames; extends ObsoleteModelica3.Icons.ObsoleteModel; Modelica.Mechanics.MultiBody.Interfaces.Frame_resolve frame_resolve "If connected, the input signals are resolved in this frame" annotation (Placement(transformation( origin={40,100}, extent={{-16,-16},{16,16}}, rotation=90))); Modelica.Blocks.Interfaces.RealInput load[6] "[1:6] = x-, y-, z-coordinates of force and x-, y-, z-coordiantes of torque resolved in frame_b or frame_resolved (if connected)" annotation (Placement(transformation( origin={-60,120}, extent={{-20,-20},{20,20}}, rotation=270))); parameter Boolean animation=true "= true, if animation shall be enabled"; parameter Real N_to_m(unit="N/m") = world.defaultN_to_m " Force arrow scaling (length = force/N_to_m)" annotation (Dialog(group="if animation = true", enable=animation)); parameter Real Nm_to_m(unit="N.m/m") = world.defaultNm_to_m " Torque arrow scaling (length = torque/Nm_to_m)" annotation (Dialog(group="if animation = true", enable=animation)); input SI.Diameter forceDiameter=world.defaultArrowDiameter " Diameter of force arrow" annotation (Dialog(group="if animation = true", enable=animation)); input SI.Diameter torqueDiameter=forceDiameter " Diameter of torque arrow" annotation (Dialog(group="if animation = true", enable=animation)); input SI.Diameter connectionLineDiameter=forceDiameter " Diameter of line connecting frame_a and frame_b" annotation (Dialog(group="if animation = true", enable=animation)); input Types.Color forceColor=Modelica.Mechanics.MultiBody.Types.Defaults.ForceColor " Color of force arrow" annotation (Dialog(group="if animation = true", enable=animation)); input Types.Color torqueColor=Modelica.Mechanics.MultiBody.Types.Defaults.TorqueColor " Color of torque arrow" annotation (Dialog(group="if animation = true", enable=animation)); input Types.Color connectionLineColor=Modelica.Mechanics.MultiBody.Types.Defaults.SensorColor " Color of line connecting frame_a and frame_b" annotation (Dialog(group="if animation = true", enable=animation)); input Types.SpecularCoefficient specularCoefficient = world.defaultSpecularCoefficient "Reflection of ambient light (= 0: light is completely absorbed)" annotation (Dialog(group="if animation = true", enable=animation)); SI.Position r_0[3] "Position vector from origin of frame_a to origin of frame_b resolved in world frame"; SI.Force f_b_0[3] "frame_b.f resoved in world frame"; SI.Torque t_b_0[3] "frame_b.t resoved in world frame"; annotation ( __Dymola_obsolete="Based on a packed result signal which is not a good design. Use instead Modelica.Mechanics.MultiBody.Forces.ForceAndTorque", preferedView="info", Diagram(coordinateSystem(preserveAspectRatio=false, extent={{-100, -100},{100,100}}), graphics), Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Rectangle( extent={{-98,99},{99,-98}}, lineColor={255,255,255}, fillColor={255,255,255}, fillPattern=FillPattern.Solid), Text( extent={{-59,55},{72,30}}, lineColor={192,192,192}, textString="resolve"), Text(extent={{-136,-52},{149,-113}}, textString="%name"), Polygon( points={{100,21},{84,55},{69,39},{100,21}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line( points={{40,100},{40,0}}, color={95,95,95}, pattern=LinePattern.Dot), Polygon( points={{-95,1},{-64,11},{-64,-10},{-95,1}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Polygon( points={{-100,20},{-86,53},{-70,42},{-100,20}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line( points={{-60,100},{40,100}}, color={95,95,95}, pattern=LinePattern.Dot), Polygon( points={{94,0},{65,12},{65,-11},{94,0}}, lineColor={0,0,0}, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Line(points={{-64,0},{-20,0}}, color={0,0,0}), Line(points={{20,0},{65,0}}, color={0,0,0}), Line(points={{-79,47},{-70,61},{-59,72},{-45,81},{-32,84},{-20, 85}}, color={0,0,0}), Line(points={{76,47},{66,60},{55,69},{49,74},{41,80},{31,84},{ 20,85}}, color={0,0,0})}), Documentation(info="

The 6 signals of the load connector are interpreted as the x-, y- and z-coordinates of a force and as the x-, y-, and z-coordinates of a torque acting at the frame connector to which frame_b of this component is attached. If connector frame_resolve is not connected, the force and torque coordinates are with respect to frame_b. If connector frame_resolve is connected, the force and torque coordinates are with respect to frame_resolve. In this case the force and torque in connector frame_resolve are set to zero, i.e., this connector is solely used to provide the information of the coordinate system, in which the force/torque coordinates are defined. The input signals are mapped to the force and torque in the following way: 

   force  = load[1:3]
   torque = load[4:6]

Additionally, a force and torque acts on frame_a in such a way that the force and torque balance between frame_a and frame_b is fulfilled.

An example how to use this model is given in the following figure:

This leads to the following animation (the yellow cylinder characterizes the line between frame_a and frame_b of the ForceAndTorque component, i.e., the force and torque acts with negative sign also on the opposite side of this cylinder, but for clarity this is not shown in the animation):

")); annotation ( Coordsys( extent=[-100, -100; 100, 100], grid=[1, 1], component=[20, 20]), Window( x=0.18, y=0.01, width=0.8, height=0.82), Documentation(info=" An external force element exerts the inport signal as negative force on the connector frame (the force vector is resolved in the world frame). "), Icon(Text(extent=[-132, 99; 128, 39], string="%name"), Polygon(points=[-100, 10; 49, 10; 49, 31; 100, 0; 49, -31; 49, -10; -100, -10; -100, 10], style( color=0, gradient=0, fillColor=0, fillPattern=1))), Diagram(Polygon(points=[-90, 10; 40, 10; 40, 31; 91, 0; 40, -31; 40, -10; -90, -10; -90, 10], style( color=0, gradient=0, fillColor=0, fillPattern=1)))); protected SI.Position f_in_m[3]=frame_b.f/N_to_m "Force mapped from N to m for animation"; SI.Position t_in_m[3]=frame_b.t/Nm_to_m "Torque mapped from Nm to m for animation"; Modelica.Mechanics.MultiBody.Visualizers.Advanced.Arrow forceArrow( diameter=forceDiameter, color=forceColor, specularCoefficient=specularCoefficient, R=frame_b.R, r=frame_b.r_0, r_tail=f_in_m, r_head=-f_in_m) if world.enableAnimation and animation; Modelica.Mechanics.MultiBody.Visualizers.Advanced.DoubleArrow torqueArrow( diameter=torqueDiameter, color=torqueColor, specularCoefficient=specularCoefficient, R=frame_b.R, r=frame_b.r_0, r_tail=t_in_m, r_head=-t_in_m) if world.enableAnimation and animation; Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape connectionLine( shapeType="cylinder", lengthDirection=r_0, widthDirection={0,1,0}, length=Modelica.Math.Vectors.length( r_0), width=connectionLineDiameter, height=connectionLineDiameter, color=connectionLineColor, specularCoefficient=specularCoefficient, r=frame_a.r_0) if world.enableAnimation and animation; equation if cardinality(frame_resolve) == 0 then frame_b.f = -load[1:3]; frame_b.t = -load[4:6]; f_b_0 = Modelica.Mechanics.MultiBody.Frames.resolve1(frame_b.R, frame_b.f); t_b_0 = Modelica.Mechanics.MultiBody.Frames.resolve1(frame_b.R, frame_b.t); frame_resolve.r_0 = zeros(3); frame_resolve.R = Modelica.Mechanics.MultiBody.Frames.nullRotation(); else f_b_0 = -Modelica.Mechanics.MultiBody.Frames.resolve1(frame_resolve.R, load[1:3]); t_b_0 = -Modelica.Mechanics.MultiBody.Frames.resolve1(frame_resolve.R, load[4:6]); frame_b.f = Modelica.Mechanics.MultiBody.Frames.resolve2(frame_b.R, f_b_0); frame_b.t = Modelica.Mechanics.MultiBody.Frames.resolve2(frame_b.R, t_b_0); frame_resolve.f = zeros(3); frame_resolve.t = zeros(3); end if; // Force and torque balance r_0 = frame_b.r_0 - frame_a.r_0; zeros(3) = frame_a.f + Modelica.Mechanics.MultiBody.Frames.resolve2(frame_a.R, f_b_0); zeros(3) = frame_a.t + Modelica.Mechanics.MultiBody.Frames.resolve2(frame_a.R, t_b_0 + cross(r_0, f_b_0)); end ForceAndTorque; end Forces; package Interfaces "Connectors and partial models for 3-dim. mechanical components" partial model PartialCutForceSensor "Obsolete model. Use instead instead a model from Modelica.Mechanics.MultiBody.Sensors" extends Modelica.Icons.RotationalSensor; extends ObsoleteModelica3.Icons.ObsoleteModel; Modelica.Mechanics.MultiBody.Interfaces.Frame_a frame_a "Coordinate system with one cut-force and cut-torque" annotation (Placement( transformation(extent={{-116,-16},{-84,16}}, rotation=0))); Modelica.Mechanics.MultiBody.Interfaces.Frame_b frame_b "Coordinate system with one cut-force and cut-torque" annotation (Placement( transformation(extent={{84,-16},{116,16}}, rotation=0))); Modelica.Mechanics.MultiBody.Interfaces.Frame_resolve frame_resolve "If connected, the output signals are resolved in this frame (cut-force/-torque are set to zero)" annotation (Placement(transformation( origin={80,-100}, extent={{-16,-16},{16,16}}, rotation=270))); annotation ( Window( x=0.37, y=0.02, width=0.6, height=0.65), __Dymola_obsolete="Model equations depend on cardinality(..) which will become obsolete in the Modelica language. Use instead a model from Modelica.Mechanics.MultiBody.Sensors", Documentation(info="

This is a base class for 3-dim. mechanical components with two frames and one output port in order to measure the cut-force and/or cut-torque acting between the two frames and to provide the measured signals as output for further processing with the blocks of package Modelica.Blocks.

"), Icon(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}, grid={1,1}), graphics={ Line(points={{-70,0},{-101,0}}, color={0,0,0}), Line(points={{70,0},{100,0}}, color={0,0,0}), Line(points={{-80,-100},{-80,0}}, color={0,0,127}), Text( extent={{-132,76},{129,124}}, textString="%name", lineColor={0,0,255}), Text( extent={{-118,55},{-82,30}}, lineColor={128,128,128}, textString="a"), Text( extent={{83,55},{119,30}}, lineColor={128,128,128}, textString="b"), Text( extent={{-31,-72},{100,-97}}, lineColor={192,192,192}, textString="resolve"), Line( points={{80,0},{80,-100}}, color={95,95,95}, pattern=LinePattern.Dot)}), Diagram(coordinateSystem( preserveAspectRatio=true, extent={{-100,-100},{100,100}}, grid={1,1}), graphics={ Line(points={{-70,0},{-100,0}}, color={0,0,0}), Line(points={{70,0},{100,0}}, color={0,0,0}), Line(points={{-80,-100},{-80,0}}, color={0,0,127}), Line( points={{80,0},{80,-100}}, color={95,95,95}, pattern=LinePattern.Dot)})); protected outer Modelica.Mechanics.MultiBody.World world; equation defineBranch(frame_a.R, frame_b.R); assert(cardinality(frame_a) > 0, "Connector frame_a of cut-force/-torque sensor object is not connected"); assert(cardinality(frame_b) > 0, "Connector frame_b of cut-force/-torque sensor object is not connected"); // frame_a and frame_b are identical frame_a.r_0 = frame_b.r_0; frame_a.R = frame_b.R; // force and torque balance zeros(3) = frame_a.f + frame_b.f; zeros(3) = frame_a.t + frame_b.t; // deduce cut-force if cardinality(frame_resolve) == 1 then // frame_resolve is connected frame_resolve.f = zeros(3); frame_resolve.t = zeros(3); else // frame_resolve is NOT connected frame_resolve.r_0 = zeros(3); frame_resolve.R = Modelica.Mechanics.MultiBody.Frames.nullRotation(); end if; end PartialCutForceSensor; end Interfaces; package Joints package Internal model RevoluteWithLengthConstraint "Obsolete model. Use instead Modelica.Mechanics.MultiBody.Joints.Internal.RevoluteWithLengthConstraint" import SI = Modelica.SIunits; import Cv = Modelica.SIunits.Conversions; extends Modelica.Mechanics.MultiBody.Interfaces.PartialTwoFrames; extends ObsoleteModelica3.Icons.ObsoleteModel; Modelica.Mechanics.Rotational.Interfaces.Flange_a axis "1-dim. rotational flange that drives the joint" annotation (Placement(transformation(extent={{10,90},{-10,110}}, rotation=0))); Modelica.Mechanics.Rotational.Interfaces.Flange_b bearing "1-dim. rotational flange of the drive bearing" annotation (Placement(transformation(extent={{-50,90},{-70,110}}, rotation= 0))); Modelica.Blocks.Interfaces.RealInput position_a[3] "Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of revolute joint" annotation (Placement(transformation(extent={{-140,-80},{-100,-40}}, rotation=0))); Modelica.Blocks.Interfaces.RealInput position_b[3] "Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of revolute joint" annotation (Placement(transformation(extent={{140,-80},{100,-40}}, rotation= 0))); parameter Boolean animation=true "= true, if animation shall be enabled"; parameter SI.Position lengthConstraint=1 "Fixed length of length constraint"; parameter Modelica.Mechanics.MultiBody.Types.Axis n={0,0,1} "Axis of rotation resolved in frame_a (= same as in frame_b)" annotation (Evaluate=true); parameter Cv.NonSIunits.Angle_deg phi_offset=0 "Relative angle offset (angle = phi + from_deg(phi_offset))"; parameter Cv.NonSIunits.Angle_deg phi_guess=0 "Select the configuration such that at initial time |phi - from_deg(phi_guess)|is minimal"; parameter SI.Distance cylinderLength=world.defaultJointLength "Length of cylinder representing the joint axis" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); parameter SI.Distance cylinderDiameter=world.defaultJointWidth "Diameter of cylinder representing the joint axis" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); input Modelica.Mechanics.MultiBody.Types.Color cylinderColor=Modelica.Mechanics.MultiBody.Types.Defaults.JointColor "Color of cylinder representing the joint axis" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); input Modelica.Mechanics.MultiBody.Types.SpecularCoefficient specularCoefficient=world.defaultSpecularCoefficient "Reflection of ambient light (= 0: light is completely absorbed)" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); parameter Boolean axisTorqueBalance=true "= true, if torque balance of flange axis with the frame_b connector (axis.tau = -e*frame_b.t) shall be defined. Otherwise this equation has to be provided outside of this joint" annotation (Dialog(tab="Advanced")); final parameter Boolean positiveBranch(fixed=false) "Based on phi_guess, selection of one of the two solutions of the non-linear constraint equation"; final parameter Real e[3](each final unit="1")=Modelica.Math.Vectors.normalize( n) "Unit vector in direction of rotation axis, resolved in frame_a"; SI.Angle phi "Rotation angle of revolute joint"; Modelica.Mechanics.MultiBody.Frames.Orientation R_rel "Relative orientation object from frame_a to frame_b"; SI.Angle angle "= phi + from_deg(phi_offset) (relative rotation angle between frame_a and frame_b)"; SI.Torque tau "= axis.tau (driving torque in the axis)"; annotation ( structurallyIncomplete, preferedView="info", __Dymola_obsolete="Obsolete model that is not balanced. Use instead Modelica.Mechanics.MultiBody.Joints.Internal.RevoluteWithLengthConstraint", Window( x=0.05, y=0.09, width=0.65, height=0.69), Icon(coordinateSystem( preserveAspectRatio=false, extent={{-100,-100},{100,100}}, grid={1,1}), graphics={ Rectangle( extent={{-30,10},{10,-10}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle( extent={{-100,-60},{-30,60}}, lineColor={0,0,0}, fillPattern=FillPattern.HorizontalCylinder, fillColor={192,192,192}), Rectangle( extent={{30,-60},{100,60}}, lineColor={0,0,0}, fillPattern=FillPattern.HorizontalCylinder, fillColor={192,192,192}), Text(extent={{-139,-168},{137,-111}}, textString="%name"), Rectangle(extent={{-100,60},{-30,-60}}, lineColor={0,0,0}), Rectangle(extent={{30,60},{100,-60}}, lineColor={0,0,0}), Text( extent={{-142,-108},{147,-69}}, lineColor={0,0,0}, textString="n=%n"), Line(points={{-60,60},{-60,90}}, color={0,0,0}), Line(points={{-20,70},{-60,70}}, color={0,0,0}), Line(points={{-20,80},{-20,60}}, color={0,0,0}), Line(points={{20,80},{20,60}}, color={0,0,0}), Line(points={{20,70},{41,70}}, color={0,0,0}), Polygon( points={{-9,30},{10,30},{30,50},{-29,50},{-9,30}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Polygon( points={{10,30},{30,50},{30,-51},{10,-31},{10,30}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle( extent={{-10,90},{10,50}}, lineColor={0,0,0}, fillPattern=FillPattern.VerticalCylinder, fillColor={192,192,192})}), Diagram(coordinateSystem( preserveAspectRatio=false, extent={{-100,-100},{100,100}}, grid={1,1}), graphics={ Rectangle( extent={{-100,-60},{-30,60}}, lineColor={0,0,0}, fillPattern=FillPattern.HorizontalCylinder, fillColor={192,192,192}), Rectangle( extent={{-30,10},{10,-10}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle( extent={{30,-60},{100,60}}, lineColor={0,0,0}, fillPattern=FillPattern.HorizontalCylinder, fillColor={192,192,192}), Line(points={{-60,60},{-60,96}}, color={0,0,0}), Line(points={{-20,70},{-60,70}}, color={0,0,0}), Line(points={{-20,80},{-20,60}}, color={0,0,0}), Line(points={{20,80},{20,60}}, color={0,0,0}), Line(points={{20,70},{41,70}}, color={0,0,0}), Polygon( points={{-9,30},{10,30},{30,50},{-29,50},{-9,30}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Polygon( points={{10,30},{30,50},{30,-51},{10,-31},{10,30}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle( extent={{-10,50},{10,100}}, lineColor={0,0,0}, fillPattern=FillPattern.VerticalCylinder, fillColor={192,192,192})}), Documentation(info="

Joint where frame_b rotates around axis n which is fixed in frame_a. The two frames coincide when \"phi + phi_offset = 0\", where \"phi_offset\" is a parameter with a zero default and \"phi\" is the rotation angle.

This variant of the revolute joint is designed to work together with a length constraint in a kinematic loop. This means that the angle of the revolute joint, phi, is computed such that the length constraint is fulfilled.

Usually, this joint should not be used by a user of the MultiBody library. It is only provided to built-up the Modelica.Mechanics.MultiBody.Joints.Assemblies.JointXYZ joints.

"), uses(Modelica(version="3.0"))); protected SI.Position r_a[3]=position_a "Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of revolute joint"; SI.Position r_b[3]=position_b "Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of revolute joint"; Real e_r_a "Projection of r_a on e"; Real e_r_b "Projection of r_b on e"; Real A "Coefficient A of equation: A*cos(phi) + B*sin(phi) + C = 0"; Real B "Coefficient B of equation: A*cos(phi) + B*sin(phi) + C = 0"; Real C "Coefficient C of equation: A*cos(phi) + B*sin(phi) + C = 0"; Real k1 "Constant of quadratic equation"; Real k2 "Constant of quadratic equation"; Real k1a(start=1); Real k1b; Real kcos_angle "= k1*cos(angle)"; Real ksin_angle "= k1*sin(angle)"; Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape cylinder( shapeType="cylinder", color=cylinderColor, specularCoefficient=specularCoefficient, length=cylinderLength, width=cylinderDiameter, height=cylinderDiameter, lengthDirection=e, widthDirection={0,1,0}, r_shape=-e*(cylinderLength/2), r=frame_a.r_0, R=frame_a.R) if world.enableAnimation and animation; function selectBranch "Determine branch which is closest to initial angle=0" import Modelica.Math.*; input SI.Length L "Length of length constraint"; input Real e[3](each final unit="1") "Unit vector along axis of rotation, resolved in frame_a (= same in frame_b)"; input SI.Angle angle_guess "Select the configuration such that at initial time |angle-angle_guess|is minimal (angle=0: frame_a and frame_b coincide)"; input SI.Position r_a[3] "Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of revolute joint"; input SI.Position r_b[3] "Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of revolute joint"; output Boolean positiveBranch "Branch of the initial solution"; protected Real e_r_a "Projection of r_a on e"; Real e_r_b "Projection of r_b on e"; Real A "Coefficient A of equation: A*cos(phi) + B*sin(phi) + C = 0"; Real B "Coefficient B of equation: A*cos(phi) + B*sin(phi) + C = 0"; Real C "Coefficient C of equation: A*cos(phi) + B*sin(phi) + C = 0"; Real k1 "Constant of quadratic equation"; Real k2 "Constant of quadratic equation"; Real kcos1 "k1*cos(angle1)"; Real ksin1 "k1*sin(angle1)"; Real kcos2 "k2*cos(angle2)"; Real ksin2 "k2*sin(angle2)"; SI.Angle angle1 "solution 1 of nonlinear equation"; SI.Angle angle2 "solution 2 of nonlinear equation"; algorithm /* The position vector r_rel from frame_a to frame_b of the length constraint element, resolved in frame_b of the revolute joint is given by (T_rel is the planar transformation matrix from frame_a to frame_b of the revolute joint): r_rel = r_b - T_rel*r_a The length constraint can therefore be formulated as: r_rel*r_rel = L*L with (r_b - T_rel*r_a)*(r_b - T_rel*r_a) = r_b*r_b - 2*r_b*T_rel*r_a + r_a*transpose(T_rel)*T_rel*r_a = r_b*r_b + r_a*r_a - 2*r_b*T_rel*r_a follows (1) 0 = r_a*r_a + r_b*r_b - 2*r_b*T_rel*r_a - L*L The vectors r_a, r_b and parameter L are NOT a function of the angle of the revolute joint. Since T_rel = T_rel(angle) is a function of the unknown angle of the revolute joint, this is a non-linear equation in this angle. T_rel = [e]*tranpose([e]) + (identity(3) - [e]*transpose([e]))*cos(angle) - skew(e)*sin(angle); with r_b*T_rel*r_a = r_b*(e*(e*r_a) + (r_a - e*(e*r_a))*cos(angle) - cross(e,r_a)*sin(angle) = (e*r_b)*(e*r_a) + (r_b*r_a - (e*r_b)*(e*r_a))*cos(angle) - r_b*cross(e,r_a)*sin(angle) follows for the constraint equation (1) (2) 0 = r_a*r_a + r_b*r_b - L*L - 2*(e*r_b)*(e*r_a) - 2*(r_b*r_a - (e*r_b)*(e*r_a))*cos(angle) + 2*r_b*cross(e,r_a)*sin(angle) or (3) A*cos(angle) + B*sin(angle) + C = 0 with A = -2*(r_b*r_a - (e*r_b)*(e*r_a)) B = 2*r_b*cross(e,r_a) C = r_a*r_a + r_b*r_b - L*L - 2*(e*r_b)*(e*r_a) Equation (3) is solved by computing sin(angle) and cos(angle) independently from each other. This allows to compute angle in the range: -180 deg <= angle <= 180 deg */ e_r_a := e*r_a; e_r_b := e*r_b; A := -2*(r_b*r_a - e_r_b*e_r_a); B := 2*r_b*cross(e, r_a); C := r_a*r_a + r_b*r_b - L*L - 2*e_r_b*e_r_a; k1 := A*A + B*B; k2 := sqrt(k1 - C*C); kcos1 := -A*C + B*k2; ksin1 := -B*C - A*k2; angle1 := atan2(ksin1, kcos1); kcos2 := -A*C - B*k2; ksin2 := -B*C + A*k2; angle2 := atan2(ksin2, kcos2); if abs(angle1 - angle_guess) <= abs(angle2 - angle_guess) then positiveBranch := true; else positiveBranch := false; end if; end selectBranch; initial equation positiveBranch = selectBranch(lengthConstraint, e, Cv.from_deg(phi_offset + phi_guess), r_a, r_b); equation Connections.branch(frame_a.R, frame_b.R); axis.tau = tau; axis.phi = phi; bearing.phi = 0; angle = Cv.from_deg(phi_offset) + phi; // transform kinematic quantities from frame_a to frame_b frame_b.r_0 = frame_a.r_0; R_rel = Modelica.Mechanics.MultiBody.Frames.planarRotation( e, angle, der(angle)); frame_b.R = Modelica.Mechanics.MultiBody.Frames.absoluteRotation(frame_a.R, R_rel); // Transform the force and torque acting at frame_b to frame_a zeros(3) = frame_a.f + Modelica.Mechanics.MultiBody.Frames.resolve1(R_rel, frame_b.f); zeros(3) = frame_a.t + Modelica.Mechanics.MultiBody.Frames.resolve1(R_rel, frame_b.t); if axisTorqueBalance then /* Note, if axisTorqueBalance is false, the force in the length constraint must be calculated such that the driving Torque in direction of the rotation axis is: axis.tau = -e*frame_b.t; If axisTorqueBalance=true, this equation is provided here. As a consequence, the force in the length constraint and the second derivative of 'angle' will be part of a linear algebraic system of equations (otherwise, it might be possible to remove this force from the linear system). */ tau = -e*frame_b.t; end if; // Compute rotation angle (details, see function "selectBranch") e_r_a = e*r_a; e_r_b = e*r_b; A = -2*(r_b*r_a - e_r_b*e_r_a); B = 2*r_b*cross(e, r_a); C = r_a*r_a + r_b*r_b - lengthConstraint*lengthConstraint - 2*e_r_b*e_r_a; k1 = A*A + B*B; k1a = k1 - C*C; assert(k1a > 1.e-10, " Singular position of loop (either no or two analytic solutions; the mechanism has lost one-degree-of freedom in this position). Try first to use another Modelica.Mechanics.MultiBody.Joints.Assemblies.JointXXX component. In most cases it is best that the joints outside of the JointXXX component are revolute and NOT prismatic joints. If this also lead to singular positions, it could be that this kinematic loop cannot be solved analytically. In this case you have to build up the loop with basic joints (NO aggregation JointXXX components) and rely on dynamic state selection, i.e., during simulation the states will be dynamically selected in such a way that in no position a degree of freedom is lost. "); k1b = Modelica.Mechanics.MultiBody.Frames.Internal.maxWithoutEvent(k1a, 1.0e-12); k2 = sqrt(k1b); kcos_angle = -A*C + (if positiveBranch then B else -B)*k2; ksin_angle = -B*C + (if positiveBranch then -A else A)*k2; angle = Modelica.Math.atan2(ksin_angle, kcos_angle); end RevoluteWithLengthConstraint; model PrismaticWithLengthConstraint "Obsolete model. Use instead Modelica.Mechanics.MultiBody.Joints.Internal.PrismaticWithLengthConstraint" import SI = Modelica.SIunits; import Cv = Modelica.SIunits.Conversions; extends Modelica.Mechanics.MultiBody.Interfaces.PartialTwoFrames; extends ObsoleteModelica3.Icons.ObsoleteModel; Modelica.Mechanics.Translational.Interfaces.Flange_a axis "1-dim. translational flange that drives the joint" annotation (Placement(transformation(extent={{70,80},{90,60}}, rotation=0))); Modelica.Mechanics.Translational.Interfaces.Flange_b bearing "1-dim. translational flange of the drive bearing" annotation (Placement(transformation(extent={{-30,80},{-50,60}}, rotation=0))); Modelica.Blocks.Interfaces.RealInput position_a[3] "Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of revolute joint" annotation (Placement(transformation(extent={{-140,-80},{-100,-40}}, rotation=0))); Modelica.Blocks.Interfaces.RealInput position_b[3] "Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of revolute joint" annotation (Placement(transformation(extent={{140,-80},{100,-40}}, rotation= 0))); parameter Boolean animation=true "= true, if animation shall be enabled"; parameter SI.Position length=1 "Fixed length of length constraint"; parameter Modelica.Mechanics.MultiBody.Types.Axis n={1,0,0} "Axis of translation resolved in frame_a (= same as in frame_b)" annotation (Evaluate=true); parameter SI.Position s_offset=0 "Relative distance offset (distance between frame_a and frame_b = s(t) + s_offset)"; parameter SI.Position s_guess=0 "Select the configuration such that at initial time |s(t0)-s_guess|is minimal"; parameter Modelica.Mechanics.MultiBody.Types.Axis boxWidthDirection = {0,1,0} "Vector in width direction of box, resolved in frame_a" annotation (Evaluate=true, Dialog(tab="Animation", group= "if animation = true", enable=animation)); parameter SI.Distance boxWidth=world.defaultJointWidth "Width of prismatic joint box" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); parameter SI.Distance boxHeight=boxWidth "Height of prismatic joint box" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); input Modelica.Mechanics.MultiBody.Types.Color boxColor=Modelica.Mechanics.MultiBody.Types.Defaults.JointColor "Color of prismatic joint box" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); input Modelica.Mechanics.MultiBody.Types.SpecularCoefficient specularCoefficient=world.defaultSpecularCoefficient "Reflection of ambient light (= 0: light is completely absorbed)" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); parameter Boolean axisForceBalance=true "= true, if force balance of flange axis with the frame_b connector (axis.f = -e*frame_b.f) shall be defined. Otherwise this equation has to be provided outside of this joint" annotation (Dialog(tab="Advanced")); final parameter Boolean positiveBranch(fixed=false) "Selection of one of the two solutions of the non-linear constraint equation"; final parameter Real e[3](each final unit="1")=Modelica.Math.Vectors.normalize( n) "Unit vector in direction of translation axis, resolved in frame_a"; SI.Position s "Relative distance between frame_a and frame_b along axis n = s + s_offset)"; SI.Position distance "Relative distance between frame_a and frame_b along axis n"; SI.Position r_rel_a[3] "Position vector from frame_a to frame_b resolved in frame_a"; SI.Force f "= axis.f (driving force in the axis)"; annotation ( structurallyIncomplete, preferedView="info", __Dymola_obsolete="Obsolete model that is not balanced. Use instead Modelica.Mechanics.MultiBody.Joints.Internal.PrismaticWithLengthConstraint", Window( x=0.05, y=0.09, width=0.65, height=0.69), Icon(coordinateSystem( preserveAspectRatio=false, extent={{-100,-100},{100,100}}, grid={1,1}), graphics={ Rectangle( extent={{-30,-40},{100,30}}, lineColor={0,0,255}, pattern=LinePattern.None, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle(extent={{-30,40},{100,-40}}, lineColor={0,0,0}), Rectangle( extent={{-100,-60},{-30,50}}, lineColor={0,0,255}, pattern=LinePattern.None, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle( extent={{-100,50},{-30,60}}, lineColor={0,0,255}, pattern=LinePattern.None, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Rectangle( extent={{-30,30},{100,40}}, lineColor={0,0,255}, pattern=LinePattern.None, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Text(extent={{-136,-170},{140,-113}}, textString="%name"), Rectangle(extent={{-100,60},{-30,-60}}, lineColor={0,0,0}), Line(points={{100,-40},{100,-60}}), Rectangle( extent={{100,40},{90,80}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Text( extent={{-136,-116},{153,-77}}, lineColor={0,0,0}, textString="n=%n")}), Diagram(coordinateSystem( preserveAspectRatio=false, extent={{-100,-100},{100,100}}, grid={1,1}), graphics={ Line(points={{-30,-50},{-30,50}}, color={0,0,0}), Line(points={{0,-67},{90,-67}}, color={128,128,128}), Text( extent={{31,-68},{68,-81}}, lineColor={128,128,128}, textString="s"), Line(points={{-100,-67},{0,-67}}, color={128,128,128}), Polygon( points={{-39,-64},{-29,-67},{-39,-70},{-39,-64}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Text( extent={{-77,-70},{-43,-85}}, lineColor={128,128,128}, textString="s_offset"), Line(points={{-100,-71},{-100,-51}}, color={128,128,128}), Line(points={{-30,-73},{-30,-33}}, color={128,128,128}), Line(points={{100,-70},{100,-30}}, color={128,128,128}), Polygon( points={{90,-64},{100,-67},{90,-70},{90,-64}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Rectangle( extent={{-100,50},{-30,60}}, lineColor={0,0,255}, pattern=LinePattern.None, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Rectangle( extent={{-100,-60},{-30,50}}, lineColor={0,0,255}, pattern=LinePattern.None, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle(extent={{-30,40},{100,-40}}, lineColor={0,0,0}), Rectangle( extent={{-30,-40},{100,30}}, lineColor={0,0,255}, pattern=LinePattern.None, fillColor={192,192,192}, fillPattern=FillPattern.Solid), Rectangle( extent={{-30,30},{100,40}}, lineColor={0,0,255}, pattern=LinePattern.None, fillColor={0,0,0}, fillPattern=FillPattern.Solid), Rectangle(extent={{-100,60},{-30,-60}}, lineColor={0,0,0}), Line(points={{100,-40},{100,-60}}), Text(extent={{42,91},{57,76}}, textString="f"), Line(points={{40,75},{70,75}}, color={0,0,255}), Polygon( points={{-21,78},{-31,75},{-21,72},{-21,78}}, lineColor={0,0,255}, fillColor={0,0,255}, fillPattern=FillPattern.Solid), Line(points={{-8,75},{-31,75}}, color={0,0,255}), Text(extent={{-21,90},{-6,75}}, textString="f"), Polygon( points={{60,78},{70,75},{60,72},{60,78}}, lineColor={0,0,255}, fillColor={0,0,255}, fillPattern=FillPattern.Solid), Line(points={{-30,64},{70,64}}, color={128,128,128}), Polygon( points={{60,67},{70,64},{60,61},{60,67}}, lineColor={128,128,128}, fillColor={128,128,128}, fillPattern=FillPattern.Solid), Text( extent={{0,63},{37,50}}, lineColor={128,128,128}, textString="s"), Rectangle( extent={{100,40},{90,80}}, lineColor={0,0,0}, fillColor={192,192,192}, fillPattern=FillPattern.Solid)}), Documentation(info="

Joint where frame_b is translated along axis n which is fixed in frame_a. The two frames coincide when \"s + s_offset = 0\", where \"s_offset\" is a parameter with a zero default and \"s\" is the relative distance.

This variant of the prismatic joint is designed to work together with a length constraint in a kinematic loop. This means that the relative distance \"s\" of the joint is computed such that the length constraint is fulfilled.

Usually, this joint should not be used by a user of the MultiBody library. It is only provided to built-up the Modelica.Mechanics.MultiBody.Joints.Assemblies.JointXYZ joints.

"), uses(Modelica(version="3.0"))); protected SI.Position r_a[3]=position_a "Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of revolute joint"; SI.Position r_b[3]=position_b "Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of revolute joint"; Modelica.SIunits.Position rbra[3] "= rb - ra"; Real B "Coefficient B of equation: s*s + B*s + C = 0"; Real C "Coefficient C of equation: s*s + B*s + C = 0"; Real k1 "Constant of quadratic equation solution"; Real k2 "Constant of quadratic equation solution"; Real k1a(start=1); Real k1b; Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape box( shapeType="box", color=boxColor, specularCoefficient=specularCoefficient, length=if noEvent(abs(s + s_offset) > 1.e-6) then s + s_offset else 1.e-6, width=boxWidth, height=boxHeight, lengthDirection=e, widthDirection=boxWidthDirection, r=frame_a.r_0, R=frame_a.R) if world.enableAnimation and animation; function selectBranch "Determine branch which is closest to initial angle=0" import Modelica.Math.*; input SI.Length L "Length of length constraint"; input Real e[3](each final unit="1") "Unit vector along axis of translation, resolved in frame_a (= same in frame_b)"; input SI.Position d_guess "Select the configuration such that at initial time |d-d_guess|is minimal (d: distance between origin of frame_a and origin of frame_b)"; input SI.Position r_a[3] "Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of prismatic joint"; input SI.Position r_b[3] "Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of prismatic joint"; output Boolean positiveBranch "Branch of the initial solution"; protected Modelica.SIunits.Position rbra[3] "= rb - ra"; Real B "Coefficient B of equation: d*d + B*d + C = 0"; Real C "Coefficient C of equation: d*d + B*d + C = 0"; Real k1 "Constant of quadratic equation solution"; Real k2 "Constant of quadratic equation solution"; Real d1 "solution 1 of quadratic equation"; Real d2 "solution 2 of quadratic equation"; algorithm /* The position vector r_rel from frame_a to frame_b of the length constraint element, resolved in frame_b of the prismatic joint (frame_a and frame_b of the prismatic joint are parallel to each other) is given by: r_rel = d*e + r_b - r_a The length constraint can therefore be formulated as: r_rel*r_rel = L*L with (d*e + r_b - r_a)*(d*e + r_b - r_a) = d*d + 2*d*e*(r_b - r_a) + (r_b - r_a)*(r_b - r_a) follows (1) 0 = d*d + d*2*e*(r_b - r_a) + (r_b - r_a)*(r_b - r_a) - L*L The vectors r_a, r_b and parameter L are NOT a function of the distance d of the prismatic joint. Therefore, (1) is a quadratic equation in the single unknown "d": (2) d*d + B*d + C = 0 with B = 2*e*(r_b - r_a) C = (r_b - r_a)*(r_b - r_a) - L*L The solution is (3) d = - B/2 +/- sqrt(B*B/4 - C) */ rbra := r_b - r_a; B := 2*(e*rbra); C := rbra*rbra - L*L; k1 := B/2; k2 := sqrt(k1*k1 - C); d1 := -k1 + k2; d2 := -k1 - k2; if abs(d1 - d_guess) <= abs(d2 - d_guess) then positiveBranch := true; else positiveBranch := false; end if; end selectBranch; initial equation positiveBranch = selectBranch(length, e, s_offset + s_guess, r_a, r_b); equation Connections.branch(frame_a.R, frame_b.R); axis.f = f; axis.s = s; bearing.s = 0; distance = s_offset + s; // relationships of frame_a and frame_b quantities r_rel_a = e*distance; frame_b.r_0 = frame_a.r_0 + Modelica.Mechanics.MultiBody.Frames.resolve1( frame_a.R, r_rel_a); frame_b.R = frame_a.R; zeros(3) = frame_a.f + frame_b.f; zeros(3) = frame_a.t + frame_b.t + cross(r_rel_a, frame_b.f); if axisForceBalance then /* Note, if axisForceBalance is false, the force in the length constraint must be calculated such that the driving force in direction of the translation axis is: axis.f = -e*frame_b.f; If axisForceBalance=true, this equation is provided here. As a consequence, the force in the length constraint will be part of a linear algebraic system of equations (otherwise, it might be possible to remove this force from the linear system). */ f = -e*frame_b.f; end if; // Compute translational distance (details, see function "selectBranch") rbra = r_b - r_a; B = 2*(e*rbra); C = rbra*rbra - length*length; k1 = B/2; k1a = k1*k1 - C; assert(noEvent(k1a > 1.e-10), " Singular position of loop (either no or two analytic solutions; the mechanism has lost one-degree-of freedom in this position). Try first to use another Modelica.Mechanics.MultiBody.Joints.Assemblies.JointXXX component. If this also lead to singular positions, it could be that this kinematic loop cannot be solved analytically with a fixed state selection. In this case you have to build up the loop with basic joints (NO aggregation JointXXX components) and rely on dynamic state selection, i.e., during simulation the states will be dynamically selected in such a way that in no position a degree of freedom is lost. "); k1b = Modelica.Mechanics.MultiBody.Frames.Internal.maxWithoutEvent(k1a, 1.0e-12); k2 = sqrt(k1b); distance = -k1 + (if positiveBranch then k2 else -k2); end PrismaticWithLengthConstraint; end Internal; end Joints; package Sensors "Sensors to measure variables" model AbsoluteSensor "Obsolete model. Use instead Modelica.Mechanics.MultiBody.Sensors.AbsoluteSensor" import SI = Modelica.SIunits; import Modelica.Mechanics.MultiBody.Frames; import Modelica.Mechanics.MultiBody.Types; extends Modelica.Mechanics.MultiBody.Interfaces.PartialAbsoluteSensor(final n_out=3*((if get_r_abs then 1 else 0) + (if get_v_abs then 1 else 0) + ( if get_a_abs then 1 else 0) + (if get_angles then 1 else 0) + (if get_w_abs then 1 else 0) + (if get_z_abs then 1 else 0))); extends ObsoleteModelica3.Icons.ObsoleteModel; Modelica.Mechanics.MultiBody.Interfaces.Frame_resolve frame_resolve "If connected, the output signals are resolved in this frame" annotation (Placement(transformation( origin={0,100}, extent={{-16,-16},{16,16}}, rotation=270))); parameter Boolean animation=true "= true, if animation shall be enabled (show arrow)"; parameter Boolean resolveInFrame_a=false "= true, if vectors are resolved in frame_a, otherwise in the world frame (if connector frame_resolve is connected, vectors are resolved in frame_resolve)"; parameter Boolean get_r_abs=true "= true, to measure the position vector from the origin of the world frame to the origin of frame_a in [m]"; parameter Boolean get_v_abs=false "= true, to measure the absolute velocity of the origin of frame_a in [m/s]"; parameter Boolean get_a_abs=false "= true, to measure the absolute acceleration of the origin of frame_a in [m/s^2]"; parameter Boolean get_angles=false "= true, to measure the 3 rotation angles to rotate the world frame into frame_a along the axes defined in 'sequence' below in [rad]"; parameter Boolean get_w_abs=false "= true, to measure the absolute angular velocity of frame_a in [rad/s]"; parameter Boolean get_z_abs=false "= true, to measure the absolute angular acceleration to frame_a in [rad/s^2]"; parameter Types.RotationSequence sequence( min={1,1,1}, max={3,3,3}) = {1,2,3} " Angles are returned to rotate world frame around axes sequence[1], sequence[2] and finally sequence[3] into frame_a" annotation (Evaluate=true, Dialog(group="if get_angles = true", enable=get_angles)); parameter SI.Angle guessAngle1=0 " Select angles[1] such that abs(angles[1] - guessAngle1) is a minimum" annotation (Dialog(group="if get_angles = true", enable=get_angles)); input SI.Diameter arrowDiameter=world.defaultArrowDiameter " Diameter of arrow from world frame to frame_a" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); input Types.Color arrowColor=Modelica.Mechanics.MultiBody.Types.Defaults.SensorColor " Color of arrow from world frame to frame_a" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); input Types.SpecularCoefficient specularCoefficient = world.defaultSpecularCoefficient "Reflection of ambient light (= 0: light is completely absorbed)" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); annotation ( __Dymola_obsolete="Based on a packed result signal which is not a good design. Use instead Modelica.Mechanics.MultiBody.Sensors.AbsoluteSensor", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={ Text( extent={{19,109},{150,84}}, lineColor={192,192,192}, textString="resolve"), Line( points={{-84,0},{-84,84},{0,84},{0,100}}, color={95,95,95}, pattern=LinePattern.Dot), Text( extent={{-132,52},{-96,27}}, lineColor={128,128,128}, textString="a")}), Diagram(coordinateSystem(preserveAspectRatio=false, extent={{-100, -100},{100,100}}), graphics={Line( points={{-84,0},{-84,82},{0,82},{0,98}}, color={95,95,95}, pattern=LinePattern.Dot)}), Documentation(info="

Absolute kinematic quantities of frame_a are computed and provided at the output signal connector y in packed format in the order

  1. absolute position vector (= r_abs)
  2. absolute velocity vectory (= v_abs)
  3. absolute acceleration vector (= a_abs)
  4. 3 angles to rotate the world frame into frame_a (= angles)
  5. absolute angular velocity vector (= w_abs)
  6. absolute angular acceleration vector (= z_abs)

For example, if parameters get_v and get_w are true and all other get_XXX parameters are false, then y contains 6 elements: 

 y[1:3] = absolute velocity
 y[4:6] = absolute angular velocity

In the following figure the animation of an AbsoluteSensor component is shown. The light blue coordinate system is frame_a and the yellow arrow is the animated sensor.

If frame_resolve is connected to another frame, then the provided absolute kinematic vectors are resolved in this frame. If frame_resolve is not connected then the coordinate system in which the relative quantities are resolved is defined by parameter resolveInFrame_a. If this parameter is true, then the provided kinematic vectors are resolved in frame_a of this component. Otherwise, the kinematic vectors are resolved in the world frame. For example, if frame_resolve is not connected and if resolveInFrame_a = false, and get_v = true, then 

  y = der(frame_a.r) // resolved in world frame

is returned, i.e., the derivative of the distance frame_a.r_0 from the origin of the world frame to the origin of frame_a, resolved in the world frame.

Note, the cut-force and the cut-torque in frame_resolve are always zero, whether frame_resolve is connected or not.

If get_angles = true, the 3 angles to rotate the world frame into frame_a along the axes defined by parameter sequence are returned. For example, if sequence = {3,1,2} then the world frame is rotated around angles[1] along the z-axis, afterwards it is rotated around angles[2] along the x-axis, and finally it is rotated around angles[3] along the y-axis and is then identical to frame_a. The 3 angles are returned in the range 

    -p <= angles[i] <= p

There are two solutions for \"angles[1]\" in this range. Via parameter guessAngle1 (default = 0) the returned solution is selected such that |angles[1] - guessAngle1| is minimal. The transformation matrix between the world frame and frame_a may be in a singular configuration with respect to \"sequence\", i.e., there is an infinite number of angle values leading to the same transformation matrix. In this case, the returned solution is selected by setting angles[1] = guessAngle1. Then angles[2] and angles[3] can be uniquely determined in the above range.

Note, that parameter sequence has the restriction that only values 1,2,3 can be used and that sequence[1] ≠ sequence[2] and sequence[2] ≠ sequence[3]. Often used values are: 

  sequence = {1,2,3}  // Cardan angle sequence
           = {3,1,3}  // Euler angle sequence
           = {3,2,1}  // Tait-Bryan angle sequence

Exact definition of the returned quantities:

  1. r_abs is vector frame_a.r_0, resolved according to table below.
  2. v_abs is vector der(frame_a.r_0), resolved according to table below.
  3. a_abs is vector der(der(frame_a.r_0)), resolved according to table below.
  4. angles is a vector of 3 angles such that frame_a.R = Frames.axesRotations(sequence, angles).
  5. w_abs is vector Modelica.Mechanics.MultiBody.Frames.angularVelocity1(frame_a.R, der(frame_a.R)), resolved according to table below.
  6. z_abs is vector der(w_abs) (= derivative of absolute angular velocity of frame_a with respect to the world frame, resolved according to table below).
frame_resolve is resolveInFrame_a = vector is resolved in
connected true frame_resolve
connected false frame_resolve
not connected true frame_a
not connected false world frame

")); protected SI.Position r_abs[3] "Dummy or position vector from origin of the world frame to origin of frame_a (resolved in frame_resolve, frame_a or world frame)"; SI.Velocity v_abs[3] "Dummy or velocity of origin of frame_a with respect to origin of world frame (resolved in frame_resolve, frame_a or world frame)"; SI.Acceleration a_abs[3] "Dummy or acceleration of origin of frame_a with respect to origin of word frame (resolved in frame_resolve, frame_a or world frame)"; SI.Angle angles[3] "Dummy or angles to rotate world frame into frame_a via 'sequence'"; SI.AngularVelocity w_abs[3] "Dummy or angular velocity of frame_a with respect to world frame (resolved in frame_resolve, frame_a or world frame)"; SI.AngularAcceleration z_abs[3] "Dummy or angular acceleration of frame_a with respect to world frame (resolved in frame_resolve, frame_a or world frame)"; SI.Velocity v_abs_0[3] "Dummy or absolute velocity of origin of frame_a resolved in world frame"; SI.AngularVelocity w_abs_0[3] "Dummy or absolute angular velocity of frame_a resolved in world frame"; parameter Integer i1=1; parameter Integer i2=if get_r_abs then i1 + 3 else i1; parameter Integer i3=if get_v_abs then i2 + 3 else i2; parameter Integer i4=if get_a_abs then i3 + 3 else i3; parameter Integer i5=if get_angles then i4 + 3 else i4; parameter Integer i6=if get_w_abs then i5 + 3 else i5; Modelica.Mechanics.MultiBody.Visualizers.Advanced.Arrow arrow( r_head=frame_a.r_0, diameter=arrowDiameter, specularCoefficient=specularCoefficient, color=arrowColor) if world.enableAnimation and animation; equation if get_angles then angles = Frames.axesRotationsAngles(frame_a.R, sequence, guessAngle1); else angles = zeros(3); end if; if cardinality(frame_resolve) == 1 then // frame_resolve is connected frame_resolve.f = zeros(3); frame_resolve.t = zeros(3); if get_r_abs then r_abs = Frames.resolve2(frame_resolve.R, frame_a.r_0); else r_abs = zeros(3); end if; if get_v_abs or get_a_abs then v_abs_0 = der(frame_a.r_0); v_abs = Frames.resolve2(frame_resolve.R, v_abs_0); else v_abs_0 = zeros(3); v_abs = zeros(3); end if; if get_a_abs then a_abs = Frames.resolve2(frame_resolve.R, der(v_abs_0)); else a_abs = zeros(3); end if; if get_w_abs or get_z_abs then w_abs_0 = Modelica.Mechanics.MultiBody.Frames.angularVelocity1(frame_a.R); w_abs = Frames.resolve2(frame_resolve.R, w_abs_0); else w_abs_0 = zeros(3); w_abs = zeros(3); end if; if get_z_abs then z_abs = Frames.resolve2(frame_resolve.R, der(w_abs_0)); else z_abs = zeros(3); end if; else // frame_resolve is NOT connected frame_resolve.r_0 = zeros(3); frame_resolve.R = Frames.nullRotation(); if get_r_abs then if resolveInFrame_a then r_abs = Modelica.Mechanics.MultiBody.Frames.resolve2(frame_a.R, frame_a.r_0); else r_abs = frame_a.r_0; end if; else r_abs = zeros(3); end if; if get_v_abs or get_a_abs then v_abs_0 = der(frame_a.r_0); if resolveInFrame_a then v_abs = Modelica.Mechanics.MultiBody.Frames.resolve2(frame_a.R, v_abs_0); else v_abs = v_abs_0; end if; else v_abs_0 = zeros(3); v_abs = zeros(3); end if; if get_a_abs then if resolveInFrame_a then a_abs = Modelica.Mechanics.MultiBody.Frames.resolve2(frame_a.R, der(v_abs_0)); else a_abs = der(v_abs_0); end if; else a_abs = zeros(3); end if; w_abs_0 = zeros(3); if get_w_abs or get_z_abs then if resolveInFrame_a then w_abs = Modelica.Mechanics.MultiBody.Frames.angularVelocity2(frame_a.R); else w_abs = Modelica.Mechanics.MultiBody.Frames.angularVelocity1(frame_a.R); end if; else w_abs = zeros(3); end if; if get_z_abs then /* if w_abs and z_abs are resolved in the world frame, we have z_abs = der(w_abs) if w_abs and z_abs are resolved in frame_a, we have z_abs = R*der(transpose(R)*w_abs) = R*(der(transpose(R))*w_abs + transpose(R)*der(w_abs))) = R*(transpose(R)*R*der(transpose(R))*w_abs + transpose(R)*der(w_abs))) = skew(w_abs)*w_abs + der(w_abs) = der(w_abs) // since cross(w_abs, w_abs) = 0 */ z_abs = der(w_abs); else z_abs = zeros(3); end if; end if; frame_a.f = zeros(3); frame_a.t = zeros(3); if get_r_abs then y[i1:i1 + 2] = r_abs; end if; if get_v_abs then y[i2:i2 + 2] = v_abs; end if; if get_a_abs then y[i3:i3 + 2] = a_abs; end if; if get_angles then y[i4:i4 + 2] = angles; end if; if get_w_abs then y[i5:i5 + 2] = w_abs; end if; if get_z_abs then y[i6:i6 + 2] = z_abs; end if; end AbsoluteSensor; model RelativeSensor "Obsolete model. Use instead Modelica.Mechanics.MultiBody.Sensors.RelativeSensor" import SI = Modelica.SIunits; import Modelica.Mechanics.MultiBody.Frames; import Modelica.Mechanics.MultiBody.Types; extends Modelica.Mechanics.MultiBody.Interfaces.PartialRelativeSensor(final n_out=3*((if get_r_rel then 1 else 0) + (if get_v_rel then 1 else 0) + ( if get_a_rel then 1 else 0) + (if get_angles then 1 else 0) + (if get_w_rel then 1 else 0) + (if get_z_rel then 1 else 0))); extends ObsoleteModelica3.Icons.ObsoleteModel; Modelica.Mechanics.MultiBody.Interfaces.Frame_resolve frame_resolve "If connected, the output signals are resolved in this frame" annotation (Placement(transformation( origin={-60,-100}, extent={{-16,-16},{16,16}}, rotation=270))); parameter Boolean animation=true "= true, if animation shall be enabled (show arrow)"; parameter Boolean resolveInFrame_a=true "= true, if relative vectors from frame_a to frame_b are resolved before differentiation in frame_a, otherwise in frame_b. If frame_resolve is connected, the vector and its derivatives are resolved in frame_resolve"; parameter Boolean get_r_rel=true "= true, to measure the relative position vector from the origin of frame_a to the origin of frame_b in [m]"; parameter Boolean get_v_rel=false "= true, to measure the relative velocity of the origin of frame_b with respect to frame_a in [m/s]"; parameter Boolean get_a_rel=false "= true, to measure the relative acceleration of the origin of frame_b with respect to frame_a in [m/s^2]"; parameter Boolean get_angles=false "= true, to measure the 3 rotation angles to rotate frame_a into frame_b along the axes defined in 'sequence' below in [rad]"; parameter Boolean get_w_rel=false "= true, to measure the relative angular velocity of frame_b with respect to frame_a in [rad/s]"; parameter Boolean get_z_rel=false "= true, to measure the relative angular acceleration of frame_b with respect to frame_a in [rad/s^2]"; parameter Types.RotationSequence sequence( min={1,1,1}, max={3,3,3}) = {1,2,3} " Angles are returned to rotate frame_a around axes sequence[1], sequence[2] and finally sequence[3] into frame_b" annotation (Evaluate=true, Dialog(group="if get_angles = true", enable=get_angles)); parameter SI.Angle guessAngle1=0 " Select angles[1] such that abs(angles[1] - guessAngle1) is a minimum" annotation (Dialog(group="if get_angles = true", enable=get_angles)); input SI.Diameter arrowDiameter=world.defaultArrowDiameter " Diameter of relative arrow from frame_a to frame_b" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); input Types.Color arrowColor=Modelica.Mechanics.MultiBody.Types.Defaults.SensorColor " Color of relative arrow from frame_a to frame_b" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); input Types.SpecularCoefficient specularCoefficient = world.defaultSpecularCoefficient "Reflection of ambient light (= 0: light is completely absorbed)" annotation (Dialog(tab="Animation", group="if animation = true", enable=animation)); SI.Position r_rel[3] "Dummy or relative position vector (resolved in frame_a, frame_b or frame_resolve)"; SI.Velocity v_rel[3] "Dummy or relative velocity vector (resolved in frame_a, frame_b or frame_resolve"; SI.Acceleration a_rel[3] "Dummy or relative acceleration vector (resolved in frame_a, frame_b or frame_resolve"; SI.Angle angles[3] "Dummy or angles to rotate frame_a into frame_b via 'sequence'"; SI.AngularVelocity w_rel[3] "Dummy or relative angular velocity vector (resolved in frame_a, frame_b or frame_resolve"; SI.AngularAcceleration z_rel[3] "Dummy or relative angular acceleration vector (resolved in frame_a, frame_b or frame_resolve"; Frames.Orientation R_rel "Dummy or relative orientation object from frame_a to frame_b"; protected SI.Position r_rel_ab[3] "Dummy or relative position vector resolved in frame_a or frame_b"; SI.Velocity der_r_rel_ab[3] "Dummy or derivative of relative position vector (resolved in frame_a, frame_b or frame_resolve)"; SI.AngularVelocity w_rel_ab[3] "Dummy or angular velocity of frame_b with respect to frame_a (resolved in frame_a or frame_b)"; Frames.Orientation R_resolve "Dummy or relative orientation of frame_a or frame_b with respect to frame_resolve"; parameter Integer i1=1; parameter Integer i2=if get_r_rel then i1 + 3 else i1; parameter Integer i3=if get_v_rel then i2 + 3 else i2; parameter Integer i4=if get_a_rel then i3 + 3 else i3; parameter Integer i5=if get_angles then i4 + 3 else i4; parameter Integer i6=if get_w_rel then i5 + 3 else i5; Modelica.Mechanics.MultiBody.Visualizers.Advanced.Arrow arrow( r=frame_a.r_0, r_head=frame_b.r_0 - frame_a.r_0, diameter=arrowDiameter, color=arrowColor, specularCoefficient) if world.enableAnimation and animation; annotation ( __Dymola_obsolete="Based on a packed result signal which is not a good design. Use instead Modelica.Mechanics.MultiBody.Sensors.RelativeSensor", Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100}, {100,100}}), graphics={Line( points={{-60,-94},{-60,-76},{0,-76},{0,-76}}, color={95,95,95}, pattern=LinePattern.Dot), Text( extent={{-157,-49},{-26,-74}}, lineColor={192,192,192}, pattern=LinePattern.Dot, textString="resolve")}), Diagram(coordinateSystem(preserveAspectRatio=false, extent={{-100, -100},{100,100}}), graphics={Line( points={{-60,-98},{-60,-76},{0,-76},{0,-76}}, color={95,95,95}, pattern=LinePattern.Dot)}), Documentation(info="

Relative kinematic quantities between frame_a and frame_b are determined and provided at the output signal connector y in packed format in the order

  1. relative position vector (= r_rel)
  2. relative velocity vectory (= v_rel)
  3. relative acceleration vector (= a_rel))
  4. 3 angles to rotate frame_a into frame_b (= angles)
  5. relative angular velocity vector (= w_rel)
  6. relative angular acceleration vector (= z_rel)

For example, if parameters get_v_rel and get_w_rel are true and all other get_XXX parameters are false, then y contains 6 elements: 

 y = relative velocity
 y = relative angular velocity

In the following figure the animation of a RelativeSensor component is shown. The light blue coordinate system is frame_a, the dark blue coordinate system is frame_b, and the yellow arrow is the animated sensor.

If parameter resolveInFrame_a = true, then the provided relative kinematic vectors of frame_b with respect to frame_a are resolved before differentiation in frame_a. If this parameter is false, the relative kinematic vectors are resolved before differentiation in frame_b. If frame_resolve is connected to another frame, then the kinematic vector as defined above and/or its required derivatives are resolved in frame_resolve. Note, derivatives of relative kinematic quantities are always performed with respect to frame_a (resolveInFrame_a = true) or with respect to frame_b (resolveInFrame_a = false). The resulting vector is then resolved in frame_resolve, if this connector is connected.

For example, if frame_resolve is not connected and if resolveInFrame_a = false, and get_v = true, then 

  y = v_rel 
    = der(r_rel)
is returned (r_rel = resolve2(frame_b.R, frame_b.r_0 - frame_a.r0)), i.e., the derivative of the relative distance from frame_a to frame_b, resolved in frame_b. If frame_resolve is connected, then 

  y = v_rel 
    = resolve2(frame_resolve.R, der(r_rel))

is returned, i.e., the previous relative velocity vector is additionally resolved in frame_resolve.

Note, the cut-force and the cut-torque in frame_resolve are always zero, whether frame_resolve is connected or not.

If get_angles = true, the 3 angles to rotate frame_a into frame_b along the axes defined by parameter sequence are returned. For example, if sequence = {3,1,2} then frame_a is rotated around angles[1] along the z-axis, afterwards it is rotated around angles[2] along the x-axis, and finally it is rotated around angles[3] along the y-axis and is then identical to frame_b. The 3 angles are returned in the range 

    -p <= angles[i] <= p

There are two solutions for \"angles[1]\" in this range. Via parameter guessAngle1 (default = 0) the returned solution is selected such that |angles[1] - guessAngle1| is minimal. The relative transformation matrix between frame_a and frame_b may be in a singular configuration with respect to \"sequence\", i.e., there is an infinite number of angle values leading to the same relative transformation matrix. In this case, the returned solution is selected by setting angles[1] = guessAngle1. Then angles[2] and angles[3] can be uniquely determined in the above range.

Note, that parameter sequence has the restriction that only values 1,2,3 can be used and that sequence[1] ≠ sequence[2] and sequence[2] ≠ sequence[3]. Often used values are: 

  sequence = {1,2,3}  // Cardan angle sequence
           = {3,1,3}  // Euler angle sequence
           = {3,2,1}  // Tait-Bryan angle sequence

Exact definition of the returned quantities (r_rel_ab, R_rel_ab, w_rel_ab are defined below the enumeration):

  1. r_rel is vector r_rel_ab, resolved according to table below.
  2. v_rel is vector der(r_rel_ab), resolved according to table below.
  3. a_rel is vector der(der(r_rel_ab)), resolved according to table below.
  4. angles is a vector of 3 angles such that R_rel_ab = Frames.axesRotations(sequence, angles).
  5. w_rel is vector w_rel_ab, resolved according to table below.
  6. z_rel is vector der(w_rel_ab), resolved according to table below.

using the auxiliary quantities

  1. r_rel_ab is vector frame_b.r_0 - frame_a.r_0, resolved either in frame_a or frame_b according to parameter resolveInFrame_a.
  2. R_rel_ab is orientation object Frames.relativeRotation(frame_a.R, frame_b.R).
  3. w_rel_ab is vector Frames.angularVelocity1(R_rel_ab, der(R_rel_ab)), resolved either in frame_a or frame_b according to parameter resolveInFrame_a.

and resolved in the following frame

frame_resolve is resolveInFrame_a = vector is resolved in
connected true frame_resolve
connected false frame_resolve
not connected true frame_a
not connected false frame_b

")); equation if get_angles or get_w_rel or get_z_rel then R_rel = Modelica.Mechanics.MultiBody.Frames.relativeRotation(frame_a.R, frame_b.R); else R_rel = Modelica.Mechanics.MultiBody.Frames.nullRotation(); end if; if get_angles then angles = Frames.axesRotationsAngles(R_rel, sequence, guessAngle1); else angles = zeros(3); end if; if cardinality(frame_resolve) == 1 then // frame_resolve is connected frame_resolve.f = zeros(3); frame_resolve.t = zeros(3); if resolveInFrame_a then R_resolve = Frames.relativeRotation(frame_a.R, frame_resolve.R); else R_resolve = Frames.relativeRotation(frame_b.R, frame_resolve.R); end if; if get_r_rel or get_v_rel or get_a_rel then if resolveInFrame_a then r_rel_ab = Frames.resolve2(frame_a.R, frame_b.r_0 - frame_a.r_0); else r_rel_ab = Frames.resolve2(frame_b.R, frame_b.r_0 - frame_a.r_0); end if; r_rel = Frames.resolve2(R_resolve, r_rel_ab); else r_rel_ab = zeros(3); r_rel = zeros(3); end if; if get_v_rel or get_a_rel then der_r_rel_ab = der(r_rel_ab); else der_r_rel_ab = zeros(3); end if; if get_v_rel then v_rel = Frames.resolve2(R_resolve, der_r_rel_ab); else v_rel = zeros(3); end if; if get_a_rel then a_rel = Frames.resolve2(R_resolve, der(der_r_rel_ab)); else a_rel = zeros(3); end if; if get_w_rel or get_z_rel then if resolveInFrame_a then w_rel_ab = Modelica.Mechanics.MultiBody.Frames.angularVelocity1(R_rel); else w_rel_ab = Modelica.Mechanics.MultiBody.Frames.angularVelocity2(R_rel); end if; w_rel = Frames.resolve2(R_resolve, w_rel_ab); else w_rel = zeros(3); w_rel_ab = zeros(3); end if; if get_z_rel then z_rel = Frames.resolve2(R_resolve, der(w_rel_ab)); else z_rel = zeros(3); end if; else // frame_resolve is NOT connected frame_resolve.r_0 = zeros(3); frame_resolve.R = Frames.nullRotation(); R_resolve = Frames.nullRotation(); r_rel_ab = zeros(3); der_r_rel_ab = zeros(3); w_rel_ab = zeros(3); if get_r_rel or get_v_rel or get_a_rel then if resolveInFrame_a then r_rel = Frames.resolve2(frame_a.R, frame_b.r_0 - frame_a.r_0); else r_rel = Frames.resolve2(frame_b.R, frame_b.r_0 - frame_a.r_0); end if; else r_rel = zeros(3); end if; if get_v_rel or get_a_rel then v_rel = der(r_rel); else v_rel = zeros(3); end if; if get_a_rel then a_rel = der(v_rel); else a_rel = zeros(3); end if; if get_w_rel or get_z_rel then if resolveInFrame_a then w_rel = Frames.angularVelocity1(R_rel); else w_rel = Frames.angularVelocity2(R_rel); end if; else w_rel = zeros(3); end if; if get_z_rel then z_rel = der(w_rel); else z_rel = zeros(3); end if; end if; frame_a.f = zeros(3); frame_a.t = zeros(3); frame_b.f = zeros(3); frame_b.t = zeros(3); if get_r_rel then y[i1:i1 + 2] = r_rel; end if; if get_v_rel then