Strategy for resolving kinematic over-constrained mechanism

Dear sir,
I would try the function of AnyBody as a multi-body dynamics solver.
Because I’m interested in designing some fitness equipments.

I made a anybody script file which includes the four-bar links. It’s very famous.

Numbers of bodies = 4
Numbers of Joints = 4 revolute Joints + 1 Fixed Joint
Numbers of Drivers = 1

#DOF = 4 X 6 = 24
#CONSTRAINTS = 4 X 5 + 1 X 6 + 1 X 1 = 27

So if I use these joints, this system can be kinematically over-constrained system. Then I could not perform any simulation.

Then, I changed joint construction.
-> 2 revolute joints, 1 cylindrical joint, 1 spherical joint, 1 fixed joint

Then, #CONSTRAINTS = 2 X 5 + 1 X 4 + 3 X 1 + 1 X 6 + 1 X 1 = 24

Then #DOF is same as #CONSTRAINTS, so I could perform the simulation.

I attached twe anyscript files. “WorkingModel.zip” and “RedundantModel.zip”

But in CAD system, even there are four revolute joints in the model, CAD system can perform a kinematic analysis.

I think if there are redundant constraints in model, the jacobian matrix becomes singular, so kinematic analysis can’t be performed. Is it right?

I heard that some dynamic solver like ADAMS, can handle redundant constraints. Its strategy is to modify joint types. But it seems heuristic.

I saw that new version of anybody can handle kinematic over-constrained problems due to motion capture markers. Then, can new version of anybody handle models that are kinematically over-constrained due to joints?

  • John Jung

Hi John Jung,

You used the correct method by changing the joints type so that the system becomes kinematically determinate. There are others posible combinations (3 revolute joints and 2 linear constraint on the last joint for example) but the one you chose looks good to me also.

It is right that the up coming version 4.1 will be able to handle over determinated kinematic. But this will have to used carrefuly. What haapens is that the over constrained systems will be managed by what we call “soft constraints”. Concretly a soft constraint will mean that the kinematic tolerance is infinite on this particular constraint.
So a for example an over constrained segment with two diferent soft constraints (driving it to two diferent positions) will be floating somewhere in between those constraints. And the constraint will be seen as solved by the system.
This is not really what you want in the joint of a mechanism.

So even if the soft constraints are an extremly good tool for driving a model with markers, it should be used wisely for things such as a rigid mechanism.
A good use could be to optimise some parameters of the mechanism such as bar length, so that it fit the best possible in a system that will be over constrained when really constructed. But otherwise my opinion is that for mechanisms the way to go is still by altering the joints type in order to free the redundant constraints.

Best regards, Sylvain.

Thanks for your kind help, Sylvain.

Yes sylvain,
A constraint optimization problem can be defined as a regular constraint satisfaction problemin which constraints are weighted and the goal is to find a solution maximizing the weight of satisfied constraints.
Alternatively, a constraint optimization problem can be defined as a regular constraint satisfaction problem augumented with a number of “local” cost functions. The aim of constraint optimization is to find a solution to the problem whose cost, evaluated as the sum of the cost functions, is maximized or minimized. The regular constraints are called hard constraints, while the cost functions are called soft constraints. These names illustrate that hard constraints are to be necessarily satisfied, while soft constraints only express a preference of some solutions (those having a high or low cost) over other ones (those having lower/higher cost).

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