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Help debugging singular model in SystemModeler

skippa
Posted 10 years ago

I am trying to build a model for "walking sticks". It would look like this when done:

stick model

and here is the top part animated (in mathematica): animation

I built the top part of the top part (z2-z3-z4) but for some reason I get "Model is structurally singular" error. Any idea why would be appreciated.

model WalkingSticks
  inner Modelica.Mechanics.MultiBody.World world(gravityType = Modelica.Mechanics.MultiBody.Types.GravityTypes.NoGravity) annotation(Placement(visible = true, transformation(origin = {48, -86}, extent = {{-10, -10}, {10, 10}}, rotation = -270)));
  parameter Modelica.SIunits.Length z1 = 15;
  parameter Modelica.SIunits.Length z2 = 2.78;
  parameter Modelica.SIunits.Length z3 = 20.02;
  parameter Modelica.SIunits.Length z4 = 12;
  parameter Modelica.SIunits.Length z5 = 20.02;
  parameter Modelica.SIunits.Length z6 = 12;
  parameter Modelica.SIunits.Length d = 0.1;
  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Z2(r = {z2, 0, 0}, diameter = d) annotation(Placement(visible = true, transformation(origin = {48, -4}, extent = {{-10, -10}, {10, 10}}, rotation = -270)));
  Modelica.Mechanics.MultiBody.Joints.Revolute RA0(w.start = 1) annotation(Placement(visible = true, transformation(origin = {48, -44}, extent = {{-10, -10}, {10, 10}}, rotation = -270)));
  Modelica.Mechanics.MultiBody.Joints.Revolute R23 annotation(Placement(visible = true, transformation(origin = {26, 22}, extent = {{-10, -10}, {10, 10}}, rotation = -540)));
  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Z3(r = {z3, 0, 0}, diameter = d) annotation(Placement(visible = true, transformation(origin = {-20, 22}, extent = {{-10, -10}, {10, 10}}, rotation = -360)));
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation(r = {-z1, 0, 0}) annotation(Placement(visible = true, transformation(origin = {0, -72}, extent = {{-10, -10}, {10, 10}}, rotation = -180)));
  Modelica.Mechanics.MultiBody.Parts.BodyCylinder Z4(r = {z4, 0, 0}, diameter = d) annotation(Placement(visible = true, transformation(origin = {-56, -40}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
  Modelica.Mechanics.MultiBody.Joints.Revolute R34 annotation(Placement(visible = true, transformation(origin = {-56, 4}, extent = {{-10, -10}, {10, 10}}, rotation = -450)));
  Modelica.Mechanics.MultiBody.Joints.Revolute RB0 annotation(Placement(visible = true, transformation(origin = {-34, -72}, extent = {{-10, -10}, {10, 10}}, rotation = -180)));
equation
  connect(RB0.frame_b, Z4.frame_b) annotation(Line(visible = true, origin = {-52, -64.667}, points = {{8, -7.333}, {-4, -7.333}, {-4, 14.667}}));
  connect(RB0.frame_a, fixedTranslation.frame_b) annotation(Line(visible = true, origin = {-17, -72}, points = {{-7, 0}, {7, 0}}));
  connect(RA0.frame_a, world.frame_b) annotation(Line(visible = true, origin = {48, -65}, points = {{0, 11}, {0, -11}}));
  connect(fixedTranslation.frame_a, world.frame_b) annotation(Line(visible = true, origin = {35.333, -73.333}, points = {{-25.333, 1.333}, {12.667, 1.333}, {12.667, -2.667}}));
  connect(R34.frame_b, Z4.frame_a) annotation(Line(visible = true, origin = {-56, -18}, points = {{0, 12}, {-0, -12}}));
  connect(Z3.frame_a, R34.frame_a) annotation(Line(visible = true, origin = {-47.333, 19.333}, points = {{17.333, 2.667}, {-8.667, 2.667}, {-8.667, -5.333}}));
  connect(R23.frame_b, Z3.frame_b) annotation(Line(visible = true, origin = {3, 22}, points = {{13, 0}, {-13, 0}}));
  connect(R23.frame_a, Z2.frame_b) annotation(Line(visible = true, origin = {44, 16.667}, points = {{-8, 5.333}, {4, 5.333}, {4, -10.667}}));
  connect(Z2.frame_a, RA0.frame_b) annotation(Line(visible = true, origin = {48, -24}, points = {{0, 10}, {0, -10}}));
  annotation(experiment(StopTime = 12.56637), Icon(coordinateSystem(extent = {{-100, -100}, {100, 100}}, preserveAspectRatio = true, initialScale = 0.1, grid = {2, 2})), Diagram(coordinateSystem(extent = {{-100, -100}, {100, 100}}, preserveAspectRatio = true, initialScale = 0.1, grid = {2, 2})));
end WalkingSticks;
POSTED BY: skippa
9 Replies
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Johan Rhodin
Johan Rhodin
Posted 10 years ago

Skippa,

You need to break the kinematic loop. You can do this by replacing R23 with the following:

  Modelica.Mechanics.MultiBody.Joints.RevolutePlanarLoopConstraint R23 annotation(Placement(visible = true, transformation(origin = {26, 22}, extent = {{-10, -10}, {10, 10}}, rotation = -540)));

Why is this necessary? From the documentation of RevolutePlanarLoopConstraint:

If a planar loop is present, e.g., consisting of 4 revolute joints where the joint axes are all parallel to each other, then there is no unique mathematical solution if all revolute joints are modelled with Joints.Revolute and the symbolic algorithms will fail. The reason is that, e.g., the cut-forces in the revolute joints perpendicular to the planar loop are not uniquely defined when 3-dim. descriptions of revolute joints are used. Usually, an error message will be printed pointing out this situation. In this case, one revolute joint in the loop has to be replaced by model Joints.RevolutePlanarLoopCutJoint. The effect is that from the 5 constraints of a 3-dim. revolute joint, 3 constraints are removed and replaced by appropriate known variables (e.g., the force in the direction of the axis of rotation is treated as known with value equal to zero; for standard revolute joints, this force is an unknown quantity)
POSTED BY: Johan Rhodin
Johan Rhodin
Johan Rhodin
Posted 10 years ago

I should also add that if you are planning to stay in 2D, I'd recommend the PlanarMechanics library from DLR. You can download it here: PlanarMechanics. It is easier to work with than the full 3D library included with SystemModeler.
POSTED BY: Johan Rhodin

Thanks for Johan's update. I tried the PlanarMechanics library quickly this afternoon and it works for me. You can take a look at the attachment.

The screenshots shows the assembly and the distance the Z3/Z4 joint and origin (Z2-ground) over time. Starting position is that Z2 pointing to the right horizontally and angular velocity is at constant of 0.8 rad per second.

Model

model

Result of simulation

simulation

Attachments:
POSTED BY: Shenghui Yang
skippa
skippa
Posted 10 years ago

Johan,

That seems to be the culprit, thanks. After I replaced one of the joints with RevolutePlanarLoopConstraint I was able to get a different result: solver would exit with errors until I changed length = zx attribute values into r = {zx, 0, 0} ones. Now SystemModeller can calculate the initial position, but I can't make it move, even though I have w=1 specified for RA0. My current model is attached.

As for planar mechanics - I don't think I can do that because I plan to assemble multiple joints like this in 3d.

model

Attachments:
POSTED BY: skippa
Johan Rhodin
Johan Rhodin
Posted 10 years ago

If you want to ensure that your value for initial value for the angular velocity is respected you can: Click on RA0, select the "Advanced" tab in the parameters view and change stateSelect from StateSelect.prefer to StateSelect.always.

POSTED BY: Johan Rhodin
skippa
skippa
Posted 10 years ago

This helps. Thanks a lot. Though I find exactly 0 documentation for this property in documentation. Can you briefly explain why is it necessary here?

Do you also think it should work if I replace all r={z4, 0, 0} with length=z4? I expect that it should, but it doesn't.

Once again, thanks for help.
POSTED BY: skippa
skippa
skippa
Posted 10 years ago

The other issue is why isn't RA0.phi linear???

RA0.phi
POSTED BY: skippa
skippa
skippa
Posted 10 years ago

Here's another surprise: in Mathematica WSMSimulate["WalkingSticks", {0, 12}, WSMParameterValues -> {"z12" -> 0.18}]; gives me: "The variables {"z12"}) can only be modified directly in the model, for example with WSMSetValues, and will be ignored for this simulation." I was hoping to do parameter sweep :(
POSTED BY: skippa
Johan Rhodin
Johan Rhodin
Posted 10 years ago

It's because that parameter potentially changes the whole configuration of the system and requires the model to be re-compiled.

POSTED BY: Johan Rhodin
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