Generalized shooting method for analyzing compliant mechanisms

We consider here a class of compliant mechanisms that consist of one or more flexible beams, the manipulation of which relies on the deflection of the flexible beams. As compared with traditional rigid-body mechanisms, compliant mechanisms have the advantages of no relative moving parts and thus involve no wear, backlash, noises and lubrication. In this paper, we present a formulation based on shooting method (SM) along with two numerical solvers to facilitate the analysis and the design process of a compliant mechanism. Unlike finite difference method (FDM) or finite element method (FEM) that offers accurate solutions at discrete nodes, the computed solution of SM, which treats the boundary value problem (BVP) as an initial value problem, is continuous. Three example compliant mechanisms are formulated to illustrate the generalized shooting method and the computed results are validated by comparing those obtained using FEM.