Abstract: A method for force analysis of the overconstrained parallel mechanism (PM) is proposed considering the link’s spatial composite elastic deformations, including bending, tensile, and torsional deformations. Stiffness matrix of the supporting limb’s overconstraint wrenches is put forward and defined, and the mapping relation between the magnitudes of the constraint wrenches and the elastic deformations of the supporting limb’s end is established. Incorporating the force balance equation of the moving platform, the general analytical expression for the solution of each supporting limb’s constraint wrenches is derived. The internal relation between the constraint wrenches imposed on the moving platform and the actual reactions of the kinematic joints is analyzed, and the actuated forces/torques and reactions of all the passive kinematic joints are solved. Based on ADAMS simulation software, a method to set up the force simulation model of the overconstrained PM is put forward, the established rigid-flexible model is completely consistent with the theoretical model, and the error between the simulation result and the theoretical calculation result is less than 2%, which effectively verifies the correctness of the proposed method for force analysis of the overconstrained PM.

Key words: constraint wrench, force analysis, overconstrained paralel mechanism, simulation model, stiffness matrix