Projective synthesis of planar compliant mechanisms

Abstract

In this paper, a novel method for the synthesis of planar compliant mechanisms, based on projective geometry, is presented. The projective synthesis method exploits the antiprojective polarity in the weighted projective plane, enabling the extension of single-point to single-body relations. The method consists of a top-down procedure that, starting from the load–displacement requirements, defines the elastic suspension as a system of substructures in series and parallel arrangements, according to the prescribed topology. The geometric decomposition intrinsically guarantees positive definiteness of the kinetostatic relations at any level. Multiple solutions to the synthesis problem can be generated. The method has been implemented to the synthesis of compliant mechanisms with open and closed chains, and numerical simulations have been performed to validate the theoretical model.