Identification of Configuration Space Singularities with Local Real Algebraic Geometry
We address the question of identifying configuration space singularities of linkages, i.e., points where the configuration space is not locally a submanifold of Euclidean space. These kinds of singularities have particularly bad implications for the kinematics of the linkage since the configuration space cannot be smoothly parameterized at such points. It is well known that Jacobian methods give no sufficient conditions on the existence of Configuration Space-Singularities. We present several useful algebraic criteria which give sufficient conditions and demonstrate them on some classes of planar linkages. This will also show how the presented criteria can be checked algorithmically.