Modal Analysis of a 2R Flexible Platform Using Screw Theory

Abstract

Compliant mechanisms perform precision movements generated by the elastic deformation of their flexible elements. For most applications, resonance frequencies must be bounded by a defined range of values. Therefore, a modal analysis of the mechanisms is required at the initial stage of design. In this work, a novel flexible platform with 2 degrees of rotational freedom restricted by beam-type flexure elements is analyzed. The Screw Theory description of the movement of the mechanism is used for the rigid and the flexible elements. Using this formalism, the stiffness and mass matrices for a two-node beam element are derived and can be assembled using a standard finite-element-like procedure to perform the modal analysis of the mechanism. Starting from the desired movements, the mechanism is synthesized using screws and a hybrid (series/parallel) solution is proposed. The analytical results for the modal analysis obtained by Screw Theory are compared with the results of finite element analysis. Due to the computational efficiency, the analytical equations are chosen to be applied in the optimization of the designs.