model JointSSP "Spherical - spherical - prismatic joint aggregation with mass (no constraints, no potential states)"
import Modelica.Mechanics.MultiBody.Types;
extends Interfaces.PartialTwoFramesDoubleSize;
Modelica.Mechanics.MultiBody.Interfaces.Frame_b frame_ib "Coordinate system at origin of frame_b fixed at connecting rod of spherical and prismatic joint"
annotation (Placement(transformation(
origin = {80, 100},
extent = {
{-8, 8},
{8, -8}},
rotation = 270)));
Modelica.Mechanics.MultiBody.Interfaces.Frame_b frame_im "Coordinate system at origin of spherical joint in the middle fixed at connecting rod of spherical and prismatic joint"
annotation (Placement(transformation(
origin = {0, 100},
extent = {
{8, -8},
{-8, 8}},
rotation = 270)));
Modelica.Mechanics.Translational.Interfaces.Flange_a axis "1-dim. translational flange that drives the prismatic joint"
annotation (Placement(transformation(extent = {
{95, 75},
{105, 85}})));
Modelica.Mechanics.Translational.Interfaces.Flange_b bearing "1-dim. translational flange of the drive bearing of the prismatic joint"
annotation (Placement(transformation(extent = {
{105, 35},
{95, 45}})));
parameter Boolean animation = true "= true, if animation shall be enabled";
parameter Boolean showMass = true "= true, if point mass on rod 1 shall be shown (provided animation = true and rod1Mass > 0)";
parameter SI.Length rod1Length(min = Modelica.Constants.eps, start = 1) "Distance between the origins of the two spherical joints";
parameter SI.Mass rod1Mass(min = 0) = 0 "Mass of rod 1 (= point mass located in middle of rod connecting the two spherical joints)";
parameter Modelica.Mechanics.MultiBody.Types.Axis n_b = {0, 0, 1} "Axis of prismatic joint fixed and resolved in frame_b";
parameter SI.Position rRod2_ib[3] = {1, 0, 0} "Vector from origin of frame_ib to spherical joint in the middle, resolved in frame_ib";
parameter SI.Position s_offset = 0 "Relative distance offset of prismatic joint (distance between frame_b and frame_ib = 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 SI.Diameter sphereDiameter = world.defaultJointLength "Diameter of the spheres representing the two spherical joints"
annotation (Dialog(
tab = "Animation",
group = "if animation = true",
enable = animation));
input Types.Color sphereColor = Modelica.Mechanics.MultiBody.Types.Defaults.JointColor "Color of the spheres representing the two spherical joints"
annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animation = true",
enable = animation));
parameter SI.Diameter rod1Diameter = sphereDiameter / Types.Defaults.JointRodDiameterFraction "Diameter of rod 1 connecting the two spherical joints"
annotation (Dialog(
tab = "Animation",
group = "if animation = true",
enable = animation));
input Types.Color rod1Color = Modelica.Mechanics.MultiBody.Types.Defaults.RodColor "Color of rod 1 connecting the two spherical joint"
annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animation = true",
enable = animation));
parameter SI.Diameter rod2Diameter = rod1Diameter "Diameter of rod 2 connecting the revolute joint and spherical joint 2"
annotation (Dialog(
tab = "Animation",
group = "if animation = true",
enable = animation));
input Types.Color rod2Color = rod1Color "Color of rod 2 connecting the revolute joint and spherical joint 2"
annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animation = true",
enable = animation));
parameter Types.Axis boxWidthDirection = {0, 1, 0} "Vector in width direction of prismatic joint box, resolved in frame_b"
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 Types.Color boxColor = Modelica.Mechanics.MultiBody.Types.Defaults.JointColor "Color of prismatic joint box"
annotation (Dialog(
colorSelector = true,
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));
parameter Boolean checkTotalPower = false "= true, if total power flowing into this component shall be determined (must be zero)"
annotation (Dialog(tab = "Advanced"));
Real aux "Denominator used to compute force in rod connecting universal and spherical joint";
SI.Force f_rod "Constraint force in direction of the rod (positive, if rod is pressed)";
SI.Power totalPower "Total power flowing into this element, if checkTotalPower=true (otherwise dummy)";
Modelica.Mechanics.MultiBody.Joints.Internal.PrismaticWithLengthConstraint prismatic(animation = animation, length = rod1Length, n = n_b, s_offset = s_offset, s_guess = s_guess, boxWidthDirection = boxWidthDirection, boxWidth = boxWidth, boxHeight = boxHeight, specularCoefficient = specularCoefficient, boxColor = boxColor) annotation (Placement(transformation(extent = {
{75, -20},
{35, 20}})));
Modelica.Mechanics.MultiBody.Joints.SphericalSpherical rod1(animation = animation, showMass = showMass, m = rod1Mass, rodLength = rod1Length, rodDiameter = rod1Diameter, sphereDiameter = sphereDiameter, rodColor = rod1Color, kinematicConstraint = false, specularCoefficient = specularCoefficient, sphereColor = sphereColor, constraintResidue = rod1.f_rod - f_rod) annotation (Placement(transformation(extent = {
{-89, -20},
{-49, 20}})));
Modelica.Mechanics.MultiBody.Parts.FixedTranslation rod2(animation = animation, width = rod2Diameter, height = rod2Diameter, specularCoefficient = specularCoefficient, color = rod2Color, r = rRod2_ib) annotation (Placement(transformation(extent = {
{15, -20},
{-25, 20}})));
Sensors.RelativePosition relativePosition(resolveInFrame = Modelica.Mechanics.MultiBody.Types.ResolveInFrameAB.frame_a) annotation (Placement(transformation(extent = {
{60, -70},
{40, -90}})));
Modelica.Blocks.Sources.Constant position_b[3](k = rRod2_ib) annotation (Placement(transformation(extent = {
{-20, -50},
{0, -30}})));
equation
if checkTotalPower then
totalPower = frame_a.f * Frames.resolve2(frame_a.R, der(frame_a.r_0)) + frame_b.f * Frames.resolve2(frame_b.R, der(frame_b.r_0)) + frame_ib.f * Frames.resolve2(frame_ib.R, der(frame_ib.r_0)) + frame_im.f * Frames.resolve2(frame_im.R, der(frame_im.r_0)) + frame_a.t * Frames.angularVelocity2(frame_a.R) + frame_b.t * Frames.angularVelocity2(frame_b.R) + frame_ib.t * Frames.angularVelocity2(frame_ib.R) + frame_im.t * Frames.angularVelocity2(frame_im.R) + axis.f * der(axis.s) + bearing.f * der(bearing.s) + (-rod1Mass) * (der(rod1.v_CM_0) - world.gravityAcceleration(rod1.r_CM_0)) * rod1.v_CM_0;
else
totalPower = 0;
end if;
connect(prismatic.axis,axis) annotation (Line(points = {
{39, 14},
{40, 14},
{40, 60},
{90, 60},
{90, 80},
{100, 80}}));
connect(prismatic.bearing,bearing) annotation (Line(points = {
{63, 14},
{63, 40},
{100, 40}}));
connect(prismatic.frame_a,frame_b) annotation (Line(
points = {
{75, 0},
{100, 0}},
color = {95, 95, 95},
thickness = 0.5));
connect(prismatic.frame_b,rod2.frame_a) annotation (Line(
points = {
{35, 0},
{15, 0}},
color = {95, 95, 95},
thickness = 0.5));
connect(rod1.frame_a,frame_a) annotation (Line(
points = {
{-89, 0},
{-100, 0}},
color = {95, 95, 95},
thickness = 0.5));
connect(rod2.frame_a,frame_ib) annotation (Line(
points = {
{15, 0},
{26, 0},
{26, 70},
{80, 70},
{80, 100}},
color = {95, 95, 95},
thickness = 0.5));
connect(rod2.frame_b,frame_im) annotation (Line(
points = {
{-25, 0},
{-35, 0},
{-35, 60},
{0, 60},
{0, 100}},
color = {95, 95, 95},
thickness = 0.5));
connect(rod2.frame_b,rod1.frame_b) annotation (Line(
points = {
{-25, 0},
{-49, 0}},
color = {95, 95, 95},
thickness = 0.5));
connect(position_b.y,prismatic.position_b) annotation (Line(
points = {
{1, -40},
{20, -40},
{20, -12},
{31, -12}},
color = {0, 0, 127}));
connect(relativePosition.frame_a,frame_b) annotation (Line(
points = {
{60, -80},
{96, -80},
{96, 0},
{100, 0}},
color = {95, 95, 95},
pattern = LinePattern.Dot));
connect(relativePosition.frame_b,frame_a) annotation (Line(
points = {
{40, -80},
{-95, -80},
{-95, 0},
{-100, 0}},
color = {95, 95, 95},
pattern = LinePattern.Dot));
connect(relativePosition.r_rel,prismatic.position_a) annotation (Line(
points = {
{50, -69},
{50, -50},
{90, -50},
{90, -12},
{79, -12}},
color = {0, 0, 127}));
aux = prismatic.e * Frames.resolveRelative(rod1.eRod_a, rod1.frame_a.R, rod1.frame_b.R);
f_rod = (-prismatic.f - prismatic.e * (frame_ib.f + frame_im.f)) / noEvent(if abs(aux) < 1e-10 then 1e-10 else aux);
annotation (
Documentation(info = "<html>\n<p>\nThis component consists of a <strong>spherical</strong> joint 1 at frame_a, a <strong>prismatic</strong>\njoint at frame_b and a <strong>spherical</strong> joint 2 which is connected via rod 1\nto the spherical joint 1 and via rod 2 to the prismatic joint, see the default\nanimation in the following figure (the axes vectors are not part of the\ndefault animation):\n</p>\n\n<p>\n<img src=\"modelica://Modelica/Resources/Images/Mechanics/MultiBody/Joints/JointSSP.png\" alt=\"model Joints.Assemblies.JointSSP\">\n</p>\n\n<p>\nBesides an optional point mass in the middle of rod 1,\nthis joint aggregation has no mass and no inertia,\nand introduces neither constraints nor potential state variables.\nIt should be used in kinematic loops whenever possible since\nthe non-linear system of equations introduced by this joint aggregation\nis solved <strong>analytically</strong> (i.e., a solution is always computed, if a\nunique solution exists).\n</p>\n<p>\nAn additional <strong>frame_ib</strong> is present. It is <strong>fixed</strong> in rod 2\nconnecting the prismatic and the spherical joint at the side of the prismatic\njoint that is connected to this rod (= rod2.frame_a = prismatic.frame_a).\n</p>\n<p>\nAn additional <strong>frame_im</strong> is present. It is <strong>fixed</strong> in rod 2\nconnecting the prismatic and the spherical joint at the side of spherical\njoint 2 that is connected to this rod (= rod2.frame_b).\nIt is always parallel to <strong>frame_ib</strong>.\n</p>\n<p>\nThe easiest way to define the parameters of this joint is by moving the\nMultiBody system in a <strong>reference configuration</strong> where <strong>all frames</strong>\nof all components are <strong>parallel</strong> to each other (alternatively,\nat least frame_b and frame_ib of the JointSSP joint\nshould be parallel to each other when defining an instance of this\ncomponent).\n</p>\n</html>"),
Icon(
coordinateSystem(
preserveAspectRatio = true,
extent = {
{-100, -100},
{100, 100}},
initialScale = 0.2),
graphics = {
Text(
extent = {
{-140, -40},
{140, -65}},
lineColor = {0, 0, 255},
textString = "%name"),
Ellipse(
extent = {
{-100, -30},
{-40, 30}},
fillPattern = FillPattern.Sphere,
fillColor = {192, 192, 192}),
Ellipse(
extent = {
{-93, -22},
{-48, 23}},
lineColor = {160, 160, 164},
fillColor = {255, 255, 255},
fillPattern = FillPattern.Solid),
Rectangle(
extent = {
{-63, 33},
{-39, -33}},
lineColor = {255, 255, 255},
fillColor = {255, 255, 255},
fillPattern = FillPattern.Solid),
Ellipse(
extent = {
{-40, -30},
{20, 30}},
fillPattern = FillPattern.Sphere,
fillColor = {192, 192, 192}),
Ellipse(
extent = {
{-33, -22},
{12, 23}},
lineColor = {192, 192, 192},
fillColor = {255, 255, 255},
fillPattern = FillPattern.Solid),
Rectangle(
extent = {
{-44, 31},
{-19, -30}},
lineColor = {255, 255, 255},
fillColor = {255, 255, 255},
fillPattern = FillPattern.Solid),
Ellipse(
extent = {
{-23, 10},
{-3, -10}},
fillPattern = FillPattern.Solid),
Rectangle(
extent = {
{19, 6},
{61, -6}},
fillPattern = FillPattern.HorizontalCylinder,
fillColor = {192, 192, 192}),
Text(
extent = {
{89, 115},
{132, 92}},
lineColor = {128, 128, 128},
textString = "ib"),
Ellipse(
extent = {
{-80, 11},
{-60, -9}},
fillPattern = FillPattern.Solid),
Rectangle(
extent = {
{-62, 6},
{-21, -5}},
fillPattern = FillPattern.HorizontalCylinder,
fillColor = {192, 192, 192}),
Line(
points = {
{19, 6},
{19, 80},
{0, 80},
{0, 100}},
color = {95, 95, 95},
thickness = 0.5),
Text(
extent = {
{-49, 114},
{-11, 92}},
lineColor = {128, 128, 128},
textString = "im"),
Rectangle(
extent = {
{50, 20},
{80, -20}},
fillColor = {192, 192, 192},
fillPattern = FillPattern.Solid),
Rectangle(
extent = {
{80, 30},
{100, -30}},
fillColor = {192, 192, 192},
fillPattern = FillPattern.Solid),
Rectangle(
extent = {
{50, 14},
{80, 20}},
pattern = LinePattern.None,
fillPattern = FillPattern.Solid,
lineColor = {0, 0, 255}),
Rectangle(
extent = {
{80, 24},
{100, 30}},
pattern = LinePattern.None,
fillPattern = FillPattern.Solid,
lineColor = {0, 0, 255}),
Line(
points = {
{50, 6},
{50, 80},
{80, 80},
{80, 100}},
color = {95, 95, 95},
thickness = 0.5),
Line(
points = {
{101, 80},
{80, 80}},
color = {95, 95, 95},
thickness = 0.5),
Line(
points = {
{99, 40},
{90, 40},
{90, 30}},
color = {95, 95, 95},
thickness = 0.5)}));
end JointSSP;