Drawing mainly on linear algebra and screw theory, this paper presents a general and systematic approach for force/motion/stiffness transmissibility analyses of redundantly actuated and overconstrained parallel manipulators. A set of normalized transmission indices is proposed for representing the closeness to singularities as well as for dimensional optimization of the redundantly actuated and overconstrained parallel manipulators. Four examples evolved from a 3-PRS parallel manipulator are used to illustrate the effectiveness of this approach. It is observed that the overconstraints have little effect on the kinematic performance of such a system, whereas the actuation redundancy can significantly improve the kinematic performance and enlarge the singularity-free workspace.