A Screw Theory-Based Semi-Analytical Approach for Elastodynamics of the Tricept Robot

Taking the well-known Tricept robot as an example, this paper presents a semi-analytical approach for elastodynamic modeling of five or six degrees of freedom (DOF) hybrid robots composed of a 3-DOF parallel mechanism plus a 2- or 3-DOF wrist. Drawing heavily on screw theory combined with structural dynamics, the kinetic and elastic potential energies of the parallel mechanism and of the wrist are formulated using the dual properties of twist/wrench systems and a static condensation technique. This results in a 9-DOF dynamic model that enables the lower-order dynamic behavior over the entire workspace to be estimated in a very efficient and accurate manner. The lower-order natural frequencies and mode shapes estimated by the proposed approach are shown to have very good agreement with those obtained by a full-order finite element (FE) model. It thus provides a very time-effective tool for optimal design within a virtual prototyping framework for hybrid robot-based machine tools.