Derivation of the Mass Matrix for the McGill Schönflies Motion Generator

The aim of this paper is to address the elastodynamics behavior of the McGill Schönflies motion generator (SMG). A SMG is a four-degree-of-freedom parallel robot capable of producing motions proper for what is known as SCARA (selective-compliance assembly robot arm) systems. Elastodynamics refers to the modal analysis of a mechanical system composed of a combination of rigid and elastic bodies. Modal analysis, in turn, pertains to the dynamic response of the system at hand when subjected to “small” disturbances that take the system away from a nominal posture under “small amplitude” displacements. The elastodynamics model involves two main ingredients, the n × n mass and stiffness matrices. The work reported here focuses on the formulation of the 20 × 20 mass matrix of the underlying mechanical system.

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