Analysis of large-displacement compliant mechanisms using an incremental linearization approach

Compliant mechanisms transmit motion and force by deflection of their flexible members. They are usually made of a monolithic piece of material and thus involve no wear, backlash, noise, and lubrication. To predict more accurately their deflected shape in larger working range, the analysis of compliant mechanisms has usually based on nonlinear numerical techniques such as the finite element method. However, the problems of nonlinear analyses are their numerical instability and extensive computation time. These have limited further applications of compliant mechanisms. In this paper, the global coordinate model (GCM) with an incremental linearization approach is presented to turn the nonlinear problem into a sequence of linear problems. Both geometric and material nonlinearities are considered. As a result, numerous linear analysis techniques can be applied to facilitate design and prototyping of compliant mechanisms. Systematic procedures are developed to analyze generic compliant mechanisms that may include non-uniform or initially curved segments. Illustrations are shown with results validated experimentally and by comparing with the nonlinear finite element method. It is expected that the proposed approach can serve as a basis for broader applications of compliant mechanisms.