A Design Approach for Flexible-Link Parallel Mechanisms using Kinematic Equivalence between Rigid and Elastic Chains

Continuous deformation of elastic rods/sheets makes flexible-link parallel mechanisms be able to generate dexterous motion and passive compliance, but simultaneously produces difficulties toward their structure design. Based on the principal axis decomposition of a compliance matrix, a kinematic equivalence method from rigid to elastic chains is proposed for structure synthesis of such mechanisms. Then, a validating model using minimum elastic potential energy as its objective is established to identify the existence of the equivalent elastic chains. Finally, cases of equivalence for a RPC chain and its application in the structure design of the corresponding low-DoF flexible-link parallel mechanism are studied through numerical kineto-statics analysis. The kinematics results demonstrate the feasibility and effectiveness of the design approach in this paper.