IdealWheelJoint

model IdealWheelJoint "Ideal wheel joint"
    extends PlanarMechanics.VehicleComponents.Wheels.BaseClasses.WheelBase(final useHeatPort = false);

    outer PlanarWorld planarWorld "planar world model";
    parameter StateSelect stateSelect = StateSelect.default "Priority to use acceleration as states"
        annotation (
            HideResult = true,
            Dialog(tab = "Advanced"));
    parameter SI.Length r[2] "Driving direction of the wheel at angle phi = 0";
    final parameter SI.Length l = Modelica.Math.Vectors.length(r) "Length of r";
    final parameter Real e[2](each final unit = "1") = Modelica.Math.Vectors.normalizeWithAssert(r) "Unit vector in direction of r";
    Real e0[2] "Unit vector in direction of r resolved w.r.t. inertial frame";
    Real R[2,2] "Rotation matrix";
    SI.Angle phi_roll(start = 0) "Roll angle of the wheel"
        annotation (Dialog(
            group = "Initialization",
            showStartAttribute = true));
    SI.AngularVelocity w_roll(final stateSelect = stateSelect, start = 0) "Roll velocity of wheel"
        annotation (Dialog(
            group = "Initialization",
            showStartAttribute = true));
    SI.Velocity v[2] "Velocity";
    SI.Velocity v_long "Driving velocity in (longitudinal) driving direction";
    SI.Acceleration a(stateSelect = stateSelect, start = 0) "Acceleration of driving velocity"
        annotation (Dialog(
            group = "Initialization",
            showStartAttribute = true));
    SI.Force f_long "Longitudinal force";
    parameter Boolean animate = true "= true, if animation shall be enabled"
        annotation (Dialog(group = "Animation"));
    parameter SI.Length zPosition = planarWorld.defaultZPosition "Position z of the body"
        annotation (Dialog(
            tab = "Animation",
            group = "if animation = true",
            enable = animate));
    parameter SI.Length diameter = 0.1 "Diameter of the rims"
        annotation (Dialog(
            tab = "Animation",
            group = "if animation = true",
            enable = animate));
    parameter SI.Length width = diameter * (0.6) "Width of the wheel"
        annotation (Dialog(
            tab = "Animation",
            group = "if animation = true",
            enable = animate));
    input MB.Types.SpecularCoefficient specularCoefficient = planarWorld.defaultSpecularCoefficient "Reflection of ambient light (= 0: light is completely absorbed)"
        annotation (Dialog(
            tab = "Animation",
            group = "if animation = true",
            enable = animate));
    MB.Visualizers.Advanced.Shape cylinder(shapeType = "cylinder", color = {63, 63, 63}, specularCoefficient = specularCoefficient, length = width, width = radius * 2, height = radius * 2, lengthDirection = {-e0[2], e0[1], 0}, widthDirection = {0, 0, 1}, r_shape = -0.03 * {-e0[2], e0[1], 0}, r = MB.Frames.resolve1(planarWorld.R, {frame_a.x, frame_a.y, zPosition}) + planarWorld.r_0, R = planarWorld.R) if planarWorld.enableAnimation and animate;
    MB.Visualizers.Advanced.Shape rim1(shapeType = "cylinder", color = {195, 195, 195}, specularCoefficient = specularCoefficient, length = radius * 2, width = diameter, height = diameter, lengthDirection = {0, 0, 1}, widthDirection = {1, 0, 0}, r_shape = {0, 0, -radius}, r = MB.Frames.resolve1(planarWorld.R, {frame_a.x, frame_a.y, zPosition}) + planarWorld.r_0, R = MB.Frames.absoluteRotation(planarWorld.R, MB.Frames.planarRotation({-e0[2], e0[1], 0}, flange_a.phi, 0))) if planarWorld.enableAnimation and animate;
    MB.Visualizers.Advanced.Shape rim2(shapeType = "cylinder", color = {195, 195, 195}, specularCoefficient = specularCoefficient, length = radius * 2, width = diameter, height = diameter, lengthDirection = {0, 0, 1}, widthDirection = {1, 0, 0}, r_shape = {0, 0, -radius}, r = MB.Frames.resolve1(planarWorld.R, {frame_a.x, frame_a.y, zPosition}) + planarWorld.r_0, R = MB.Frames.absoluteRotation(planarWorld.R, MB.Frames.planarRotation({-e0[2], e0[1], 0}, flange_a.phi + 0.5 * Modelica.Constants.pi, 0))) if planarWorld.enableAnimation and animate;
equation
    {frame_a.fx, frame_a.fy} * e0 = f_long;
    R = {{cos(frame_a.phi), -sin(frame_a.phi)}, {sin(frame_a.phi), cos(frame_a.phi)}};
    a = der(v_long);
    v = v_long * e0;
    v = der({frame_a.x, frame_a.y});
    e0 = R * e;
    lossPower = 0;
    phi_roll = flange_a.phi;
    v_long = radius * w_roll;
    w_roll = der(phi_roll);
    frame_a.t = 0;
    -f_long * radius = flange_a.tau;

    annotation (
        Documentation(
            info = "<html>\n<p>\nThe ideal wheel joint enforces the constraints of ideal rolling on the x,y-plane.\n</p>\n<p>\nThe constraint is that the velocity of the virtual point of contact shall be zero.\nThis constrains is split into two components:\n</p>\n<ul>\n  <li>no lateral velocity</li>\n  <li>the longitudinal velocity has to equal the rolling velocity times the radius.</li>\n</ul>\n<p>\nThe radius of the wheel can be specified by the parameter <strong>radius</strong>.\nThe driving direction (for phi&nbsp;=&nbsp;0) can be specified by the\nparameter&nbsp;<strong>r</strong>.\n</p>\n<p>\nThe wheel contains a&nbsp;2D frame connector for the steering on the plane.\nThe rolling motion of the wheel can be actuated by the 1D flange connector.\n</p>\n<p>\nFor examples of usage see the local\n<a href=\"modelica://PlanarMechanics.VehicleComponents.Examples\">Examples package</a>.\n</p>\n</html>",
            revisions = "<html>\n<p>\n<img src=\"modelica://PlanarMechanics/Resources/Images/dlr_logo.png\" alt=\"DLR logo\">\n<strong>Developed 2010 at the DLR Institute of System Dynamics and Control</strong>\n</p>\n</html>"),
        Icon(graphics = {
            Text(
                extent = {
                    {-150, -30}, 
                    {150, -60}},
                textColor = {0, 0, 0},
                textString = "radius=%radius")}));
end IdealWheelJoint;