Motion–force interaction performance analyses of redundantly actuated and overconstrained parallel robots with closed-loop subchains are an open problem considering two challenges: (a) how to take all the internal wrenches into account at the same level when the mobile platform suffers uncertain loads and (b) how to disclose the influence of the structural parameters inside the closed-loop subchains on the robot’s performance. To tackle this problem, based on the blocking-and-acting strategy, this paper proposes a new screw-based method to analyze the motion–force interaction performance of such parallel robots. Two aspects of performance are focused, i.e., the distal and proximal motion–force interactability. The two proposed indices focus on reflecting the load-carrying capacity and the motion-transmission capacity, respectively. To evaluate the comprehensive performance of the parallel robot at a certain pose, a local interaction index (LII) is defined as the minimum value of indices of the minimized distal and proximal interaction performance. The feasibility and validity of the proposed indices are illustrated by the motion–force interaction analysis of some redundantly actuated and overconstrained parallel robots with closed-loop subchains.