Motion constraints from contact geometry: representation and analysis

A method to determine constraints on translational and rotational motion of planar and 3-D objects from their contact geometry is presented. Translations are represented by spatial vectors and rotations by axes in space. For each of these, a geometric realization (M _a) of the space of motion parameters is created. Subspaces in M_a that represent the range of values of motion parameters that are disallowed due to the contact are identified. The geometric realization makes it easier to visualize results, provides a good measure of the extent of restraints between objects, reduces computations by eliminating redundant constraints, and simplifies computation of new constraints. The proposed representation can be used effectively to automate the evaluation of motion constraints