Abstract: We address the question of identifying the configuration
space singularities of linkages, i.e., points where the configuration
space is not locally a submanifold of Euclidean space. Because the
configuration space cannot be smoothly parameterized at such points,
these singularity types have a significantly negative impact on the
kinematics of the linkage. It is known that Jacobian methods do not
provide sufficient conditions for the existence of CS-singularities.
Herein, we present several additional algebraic criteria that provide
the sufficient conditions. Further, we use those criteria to analyze
certain classes of planar linkages. These examples will also show
how the presented criteria can be checked using algorithmic methods.