13.2.3 Redundancy

A mechanism model with a redundant constraint set can be thought of as having more than one constraint controlling the same degree of freedom. Since SetConstraints only allows models to be defined if they have equal numbers of constraints and degrees of freedom, the presence of one redundant constraint implies the presence of one unconstrained degree of freedom. CheckSystem may be used to detect such errors.

Here is a model with a redundant constraint set.

In[14]:=

The constraint position numbers given in the error message generated by CheckSystem refer to the position of the offending constraints in the current constraint list. For example, the current constraint vector has three expressions, the first two from Translate2 and the last from Orthogonal1. The positions {{1, 1}, {2, 1}} given by the error message refers to the first expression in constraint 1, the Translate2, and the first and only expression in constraint 2, the Orthogonal1.
CheckSystem is usually, but not always, able to detect redundancies in a constraint set. Because of the Euler generalized parameters used in the 3D constraint formulation, it is possible for CheckSystem to be unable to detect a redundancy if the current initial guesses for the Euler parameters do not constitute a valid set.
Specifically, a valid set of four Euler parameters representing an arbitrary angular orientation must satisfy the following relation.

If the Euler parameters in the current initial guesses do not satisfy this relationship, it is possible for CheckSystem to be unable to detect a redundant constraint set.
Another weakness in the redundancy checking used by Mech is that numerical inaccuracies may cause CheckSystem to report that more constraint expressions are participating in a redundancy than really are. This is only a problem in relatively large systems where numerical errors are more pronounced.