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How to constrain a mechanical component to be vertical at all times using the Multibody library?

Fabián Peña

Posted 1 year ago

POSTED BY: Fabián Peña

4 Replies

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Updating Name

Posted 1 year ago

How about this model? model KeepVertical Modelica.Blocks.Math.Gain gain1(k = -1) annotation(Placement(visible = true, transformation(origin = {50, -10}, extent = {{10, -10}, {-10, 10}}, rotation = 0))); Modelica.Mechanics.MultiBody.Sensors.RelativeAngles relativeAngles1 annotation(Placement(visible = true, transformation(origin = {80, -40}, extent = {{-10, 10}, {10, -10}}, rotation = 0))); Modelica.Mechanics.Rotational.Sources.Position position1 annotation(Placement(visible = true, transformation(origin = {14.21, -10}, extent = {{10, -10}, {-10, 10}}, rotation = 0))); Modelica.Mechanics.MultiBody.Parts.Body body(r_0.start = {0.0, 2, 0.0}) annotation(Placement(visible = true, transformation(origin = {-80, -120}, extent = {{-10, -10}, {10, 10}}, rotation = -90))); inner Modelica.Mechanics.MultiBody.World world annotation(Placement(visible = true, transformation(origin = {-120, 80}, extent = {{-10, -10}, {10, 10}}, rotation = -360))); Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation1(r = {0.0, -1, 0.0}) annotation(Placement(visible = true, transformation(origin = {-80, 0}, extent = {{-10, -10}, {10, 10}}, rotation = -90))); Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation2(r = {0.0, -1, 0.0}) annotation(Placement(visible = true, transformation(origin = {-80, -80}, extent = {{-10, -10}, {10, 10}}, rotation = -90))); Modelica.Mechanics.MultiBody.Joints.Revolute revolute2(phi.start = 0.174532925199433, useAxisFlange = false) annotation(Placement(visible = true, transformation(origin = {-80, 40}, extent = {{10, -10}, {-10, 10}}, rotation = 90))); Modelica.Mechanics.MultiBody.Parts.Body body1(r_0.start = {0.0, 2, 0.0}) annotation(Placement(visible = true, transformation(origin = {-40, 60}, extent = {{-10, -10}, {10, 10}}, rotation = -270))); Modelica.Mechanics.MultiBody.Joints.Revolute revolute3(useAxisFlange = true) annotation(Placement(visible = true, transformation(origin = {-40, -10}, extent = {{-10, -10}, {10, 10}}, rotation = -90))); Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation3(r = {0.0, -0.5, 0.0}) annotation(Placement(visible = true, transformation(origin = {-40, 20}, extent = {{-10, 10}, {10, -10}}, rotation = 270))); equation connect(fixedTranslation2.frame_b, body.frame_a) annotation(Line(visible = true, origin = {-80, -100}, points = {{0, 10}, {0, -10}}, color = {95, 95, 95}, thickness = 0.5)); connect(world.frame_b, revolute2.frame_a) annotation(Line(visible = true, origin = {-90, 70}, points = {{-20, 10}, {10, 10}, {10, -20}}, color = {95, 95, 95}, thickness = 0.5)); connect(revolute2.frame_b, fixedTranslation1.frame_a) annotation(Line(visible = true, origin = {-80, 20}, points = {{0, 10}, {0, -10}}, color = {95, 95, 95}, thickness = 0.5)); connect(fixedTranslation2.frame_a, fixedTranslation1.frame_b) annotation(Line(visible = true, origin = {-80, -40}, points = {{0, -30}, {0, 30}}, color = {95, 95, 95}, thickness = 0.5)); connect(fixedTranslation1.frame_b, revolute3.frame_b) annotation(Line(visible = true, points = {{-20, 2.912}, {-20, -27.088}, {20, -27.088}, {20, -7.088}}, color = {95, 95, 95}, thickness = 0.5, origin = {-60, -12.912})); connect(fixedTranslation3.frame_a, body1.frame_a) annotation(Line(visible = true, origin = {-40, 40}, points = {{0, -10}, {0, 10}}, color = {95, 95, 95}, thickness = 0.5)); connect(revolute3.frame_a, fixedTranslation3.frame_b) annotation(Line(visible = true, origin = {-40, 5}, points = {{0, -5}, {0, 5}}, color = {95, 95, 95}, thickness = 0.5)); connect(world.frame_b, relativeAngles1.frame_b) annotation(Line(visible = true, origin = {43.879, 40}, points = {{-153.879, 40}, {56.121, 40}, {56.121, -80}, {46.121, -80}}, color = {95, 95, 95}, thickness = 0.5)); connect(gain1.u, relativeAngles1.angles[3]) annotation(Line(visible = true, origin = {74, -16.333}, points = {{-12, 6.333}, {6, 6.333}, {6, -12.667}}, color = {0, 0, 127})); connect(revolute3.axis, position1.flange) annotation(Line(visible = true, origin = {-12.895, -10}, points = {{-17.105, 0}, {17.105, 0}})); connect(position1.phi_ref, gain1.y) annotation(Line(visible = true, origin = {32.605, -10}, points = {{-6.395, 0}, {6.395, 0}}, color = {0, 0, 127})); connect(revolute3.frame_b, relativeAngles1.frame_a) annotation(Line(visible = true, origin = {-3.333, -33.333}, points = {{-36.667, 13.333}, {-36.667, -6.667}, {73.333, -6.667}}, color = {95, 95, 95}, thickness = 0.5)); annotation(uses(Modelica(version = "4.0.0")), Diagram(coordinateSystem(extent = {{-240, -143.033}, {210, 100}}, preserveAspectRatio = true, initialScale = 0.1, grid = {10, 10}))); end KeepVertical;

How about this model?

model KeepVertical
  Modelica.Blocks.Math.Gain gain1(k = -1) annotation(Placement(visible = true, transformation(origin = {50, -10}, extent = {{10, -10}, {-10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Sensors.RelativeAngles relativeAngles1 annotation(Placement(visible = true, transformation(origin = {80, -40}, extent = {{-10, 10}, {10, -10}}, rotation = 0)));
  Modelica.Mechanics.Rotational.Sources.Position position1 annotation(Placement(visible = true, transformation(origin = {14.21, -10}, extent = {{10, -10}, {-10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.Body body(r_0.start = {0.0, 2, 0.0}) annotation(Placement(visible = true, transformation(origin = {-80, -120}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
  inner Modelica.Mechanics.MultiBody.World world annotation(Placement(visible = true, transformation(origin = {-120, 80}, extent = {{-10, -10}, {10, 10}}, rotation = -360)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation1(r = {0.0, -1, 0.0}) annotation(Placement(visible = true, transformation(origin = {-80, 0}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation2(r = {0.0, -1, 0.0}) annotation(Placement(visible = true, transformation(origin = {-80, -80}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute2(phi.start = 0.174532925199433, useAxisFlange = false) annotation(Placement(visible = true, transformation(origin = {-80, 40}, extent = {{10, -10}, {-10, 10}}, rotation = 90)));
  Modelica.Mechanics.MultiBody.Parts.Body body1(r_0.start = {0.0, 2, 0.0}) annotation(Placement(visible = true, transformation(origin = {-40, 60}, extent = {{-10, -10}, {10, 10}}, rotation = -270)));
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute3(useAxisFlange = true) annotation(Placement(visible = true, transformation(origin = {-40, -10}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation3(r = {0.0, -0.5, 0.0}) annotation(Placement(visible = true, transformation(origin = {-40, 20}, extent = {{-10, 10}, {10, -10}}, rotation = 270)));
equation
  connect(fixedTranslation2.frame_b, body.frame_a) annotation(Line(visible = true, origin = {-80, -100}, points = {{0, 10}, {0, -10}}, color = {95, 95, 95}, thickness = 0.5));
  connect(world.frame_b, revolute2.frame_a) annotation(Line(visible = true, origin = {-90, 70}, points = {{-20, 10}, {10, 10}, {10, -20}}, color = {95, 95, 95}, thickness = 0.5));
  connect(revolute2.frame_b, fixedTranslation1.frame_a) annotation(Line(visible = true, origin = {-80, 20}, points = {{0, 10}, {0, -10}}, color = {95, 95, 95}, thickness = 0.5));
  connect(fixedTranslation2.frame_a, fixedTranslation1.frame_b) annotation(Line(visible = true, origin = {-80, -40}, points = {{0, -30}, {0, 30}}, color = {95, 95, 95}, thickness = 0.5));
  connect(fixedTranslation1.frame_b, revolute3.frame_b) annotation(Line(visible = true, points = {{-20, 2.912}, {-20, -27.088}, {20, -27.088}, {20, -7.088}}, color = {95, 95, 95}, thickness = 0.5, origin = {-60, -12.912}));
  connect(fixedTranslation3.frame_a, body1.frame_a) annotation(Line(visible = true, origin = {-40, 40}, points = {{0, -10}, {0, 10}}, color = {95, 95, 95}, thickness = 0.5));
  connect(revolute3.frame_a, fixedTranslation3.frame_b) annotation(Line(visible = true, origin = {-40, 5}, points = {{0, -5}, {0, 5}}, color = {95, 95, 95}, thickness = 0.5));
  connect(world.frame_b, relativeAngles1.frame_b) annotation(Line(visible = true, origin = {43.879, 40}, points = {{-153.879, 40}, {56.121, 40}, {56.121, -80}, {46.121, -80}}, color = {95, 95, 95}, thickness = 0.5));
  connect(gain1.u, relativeAngles1.angles[3]) annotation(Line(visible = true, origin = {74, -16.333}, points = {{-12, 6.333}, {6, 6.333}, {6, -12.667}}, color = {0, 0, 127}));
  connect(revolute3.axis, position1.flange) annotation(Line(visible = true, origin = {-12.895, -10}, points = {{-17.105, 0}, {17.105, 0}}));
  connect(position1.phi_ref, gain1.y) annotation(Line(visible = true, origin = {32.605, -10}, points = {{-6.395, 0}, {6.395, 0}}, color = {0, 0, 127}));
  connect(revolute3.frame_b, relativeAngles1.frame_a) annotation(Line(visible = true, origin = {-3.333, -33.333}, points = {{-36.667, 13.333}, {-36.667, -6.667}, {73.333, -6.667}}, color = {95, 95, 95}, thickness = 0.5));
  annotation(uses(Modelica(version = "4.0.0")), Diagram(coordinateSystem(extent = {{-240, -143.033}, {210, 100}}, preserveAspectRatio = true, initialScale = 0.1, grid = {10, 10})));
end KeepVertical;

POSTED BY: Updating Name

Ankit Naik

Ankit Naik, Wolfram Mathcore

Posted 1 year ago

You could set the "useAxisFlange" option to "true" and provide it with an angle source. model KeepVertical Modelica.Mechanics.MultiBody.Parts.Body body(r_0.start = {0.0, 2, 0.0}) annotation(Placement(visible = true, transformation(origin = {90, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0))); inner Modelica.Mechanics.MultiBody.World world annotation(Placement(visible = true, transformation(origin = {-120, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0))); Modelica.Mechanics.MultiBody.Joints.Revolute revolute1(useAxisFlange = true) annotation(Placement(visible = true, transformation(origin = {0, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0))); Modelica.Mechanics.Rotational.Sources.Position position1 annotation(Placement(visible = true, transformation(origin = {-20, -0}, extent = {{-10, -10}, {10, 10}}, rotation = 0))); Modelica.Blocks.Sources.Constant const annotation(Placement(visible = true, transformation(origin = {-80, -0}, extent = {{-10, -10}, {10, 10}}, rotation = 0))); Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation1(r = {0.0, 1, 0.0}) annotation(Placement(visible = true, transformation(origin = {-50, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0))); Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation2(r = {0.0, 1, 0.0}) annotation(Placement(visible = true, transformation(origin = {50, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0))); Modelica.Mechanics.MultiBody.Joints.Revolute revolute2(useAxisFlange = false, phi.start = 0.0174532925199433) annotation(Placement(visible = true, transformation(origin = {-82.531, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0))); equation connect(position1.flange, revolute1.axis) annotation(Line(visible = true, origin = {-3.333, -10}, points = {{-6.667, 10}, {3.333, 10}, {3.333, -20}})); connect(const.y, position1.phi_ref) annotation(Line(visible = true, origin = {-50.5, -0}, points = {{-18.5, -0}, {18.5, 0}}, color = {0, 0, 127})); connect(fixedTranslation1.frame_b, revolute1.frame_a) annotation(Line(visible = true, origin = {-25, -40}, points = {{-15, 0}, {15, 0}}, color = {95, 95, 95}, thickness = 0.5)); connect(revolute1.frame_b, fixedTranslation2.frame_a) annotation(Line(visible = true, origin = {25, -40}, points = {{-15, 0}, {15, 0}}, color = {95, 95, 95}, thickness = 0.5)); connect(fixedTranslation2.frame_b, body.frame_a) annotation(Line(visible = true, origin = {70, -40}, points = {{-10, 0}, {10, 0}}, color = {95, 95, 95}, thickness = 0.5)); connect(world.frame_b, revolute2.frame_a) annotation(Line(visible = true, origin = {-101.265, -40}, points = {{-8.735, 0}, {8.735, 0}}, color = {95, 95, 95}, thickness = 0.5)); connect(revolute2.frame_b, fixedTranslation1.frame_a) annotation(Line(visible = true, origin = {-66.265, -40}, points = {{-6.265, 0}, {6.265, 0}}, color = {95, 95, 95}, thickness = 0.5)); annotation(uses(Modelica(version = "4.0.0")), Diagram(coordinateSystem(extent = {{-150, -100}, {138.043, 100}}, preserveAspectRatio = true, initialScale = 0.1, grid = {10, 10}))); end KeepVertical;

You could set the "useAxisFlange" option to "true" and provide it with an angle source.

model KeepVertical
  Modelica.Mechanics.MultiBody.Parts.Body body(r_0.start = {0.0, 2, 0.0}) annotation(Placement(visible = true, transformation(origin = {90, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  inner Modelica.Mechanics.MultiBody.World world annotation(Placement(visible = true, transformation(origin = {-120, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute1(useAxisFlange = true) annotation(Placement(visible = true, transformation(origin = {0, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.Rotational.Sources.Position position1 annotation(Placement(visible = true, transformation(origin = {-20, -0}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Blocks.Sources.Constant const annotation(Placement(visible = true, transformation(origin = {-80, -0}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation1(r = {0.0, 1, 0.0}) annotation(Placement(visible = true, transformation(origin = {-50, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation2(r = {0.0, 1, 0.0}) annotation(Placement(visible = true, transformation(origin = {50, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute2(useAxisFlange = false, phi.start = 0.0174532925199433) annotation(Placement(visible = true, transformation(origin = {-82.531, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
equation
  connect(position1.flange, revolute1.axis) annotation(Line(visible = true, origin = {-3.333, -10}, points = {{-6.667, 10}, {3.333, 10}, {3.333, -20}}));
  connect(const.y, position1.phi_ref) annotation(Line(visible = true, origin = {-50.5, -0}, points = {{-18.5, -0}, {18.5, 0}}, color = {0, 0, 127}));
  connect(fixedTranslation1.frame_b, revolute1.frame_a) annotation(Line(visible = true, origin = {-25, -40}, points = {{-15, 0}, {15, 0}}, color = {95, 95, 95}, thickness = 0.5));
  connect(revolute1.frame_b, fixedTranslation2.frame_a) annotation(Line(visible = true, origin = {25, -40}, points = {{-15, 0}, {15, 0}}, color = {95, 95, 95}, thickness = 0.5));
  connect(fixedTranslation2.frame_b, body.frame_a) annotation(Line(visible = true, origin = {70, -40}, points = {{-10, 0}, {10, 0}}, color = {95, 95, 95}, thickness = 0.5));
  connect(world.frame_b, revolute2.frame_a) annotation(Line(visible = true, origin = {-101.265, -40}, points = {{-8.735, 0}, {8.735, 0}}, color = {95, 95, 95}, thickness = 0.5));
  connect(revolute2.frame_b, fixedTranslation1.frame_a) annotation(Line(visible = true, origin = {-66.265, -40}, points = {{-6.265, 0}, {6.265, 0}}, color = {95, 95, 95}, thickness = 0.5));
  annotation(uses(Modelica(version = "4.0.0")), Diagram(coordinateSystem(extent = {{-150, -100}, {138.043, 100}}, preserveAspectRatio = true, initialScale = 0.1, grid = {10, 10})));
end KeepVertical;

POSTED BY: Ankit Naik

Fabián Peña

Posted 1 year ago

Hello Ankit, Thank you for your kind answer again. The strategy you propose does exactly what I need. The tilt angle of the pendulum is measured and the value it's used to drive the component that must remain vertical. It's a simple solution! Thank you very much! Cheers, Fabián

POSTED BY: Fabián Peña

Fabián Peña

Posted 1 year ago

Hello Ankit, Thank you very much for your kind reply. I checked the solution you proposed, and saw that the angle between the frames in the revolute joint is fixed with an angle source. This configuration makes the joint rigid, forcing the components connected to it rotate together. However, it does not keep one of the components vertical. By vertical, I mean parallel to the gravitational field. I see now that my original post was not clear enough. I hope the requirement is better described with this screenshot: Any help will be highly appreciated. Cheers, Fabián

POSTED BY: Fabián Peña

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