Singularity is a basic problem for parallel mechanism design because of its many negative influences on the mechanism performances. Traditionally, three kinds of singularities are suitable for analysis of the parallel mechanisms. By considering both the common and redundant actuation parallel mechanisms, general kinematic model is used to obtain input factor matrix and output factor matrix. Based on ranks of the two matrices, the singularity type becomes easy to judge. And the second kind of singularity can be reduced or eliminated by adding special redundant actuation sub-chains. A two-degree-of-freedom parallel mechanism is provided to illustrate the method about how to create the needed redundant actuation sub-chains.