Forward/inverse models using global coordinates for analytical design of compliant mechanisms

The analysis of compliant mechanisms has traditionally based on known initial shapes and external forces. For applications, it is often required to find an initial shape for the specified deformed shape of the mechanism. We present here the global coordinate model (GCM) with a numerical solver that is capable of forward and inverse analysis. The model uses the arc length as the independent variable so that the shape of straight and curved links can be easily expressed. The resulting governing equations are a generalization of Timoshenko's beam theory that accounts for the effects of bending and shear deformations on large-deflected links. The effect of shear deformation on link deflection will also be investigated. Systematic procedures are developed to analyze generic compliant mechanisms. Both forward and inverse illustrations are presented. Their applications for robotic handling of bio-material are also shown. It is expected that the proposed model can give more insight on the analysis and design of compliant mechanisms.