Dynamic modeling of a flexible-link planar parallel platform using a substructuring approach

A substructuring dynamic modeling procedure for closed-loop flexible-link mechanisms is proposed and applied to a planar parallel platform developed in our laboratory. The lagrange finite element (FE) formulation is used to model flexible linkages, in which both translational and rotary degrees of freedom exist. Craig–Bampton mode sets that represent the essential dynamic behavior of the flexible linkages are extracted from these FE models using component mode synthesis theory and assembled to form a complete dynamic model of the closed-loop parallel platform through the application of the constrained Lagrange’s equation. Simulation of a typical pick-and-place task with a proportional, integral, and derivative control law shows that the model presented is capable of representing essential system dynamic behavior.