Different from the existing methods by using constraint singularity or the chain singularity to synthesis metamorphic parallel mechanisms, based on the 3-RRR spherical parallel mechanism (Sm), according to the method of screw theory, a class of multimode actuated metamorphic parallel mechanisms with active hybrid suitable constrained branched chain by way of opening and locking actuated kinematic pair was presented. Using the screw theory, the degree freedom of the whole configurations of 3-SPS/SmPU multimode actuated metamorphic parallel mechanism of the proposed actuated metamorphic parallel mechanism with active hybrid suitable constrained branched chain was analyzed, the mechanism kinematics was studied according to the structure characteristics and geometric constraints of 3-SPS/SmPU actuated metamorphic parallel mechanism. The method of type synthesis multimode actuated metamorphic parallel mechanism with active hybrid suitable constrained branched chain can be also applied to type synthesis other actuated metamorphic parallel mechanisms, the metamorphic method was simple and effective, the inverse kinematics of the whole configurations was easy to solve, and constraint singularity and the chain singularity could be avoided effectively in the metamorphic process.