Abstract: Using the language of differential geometry, this paper provides a fine classification of singularities of general parallel robots. Based on the relations between singularity manifolds and singularity distributions, these singularities are further subclassified into first-order singularities and second-order ones. Furthermore, the second-order singularities can be distinguished as degenerate or nondegenerate singularities by whether they form continuous curves on configuration manifolds. This paper also gives an insight into the degenerate singularities, which can sometimes be a source of danger not only to the mechanism itself but also to workers to operate the mechanism. Finally, a planar two degrees-of-freedom mechanism with one redundant actuator is given to illuminate the method.