Generalized shooting method for analyzing compliant mechanisms with curved members

We consider here a class of compliant mechanisms consisting 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. This paper presents a formulation based on shooting method (SM) and two numerical solvers for analyzing compliant mechanisms consisting of multiple flexible members that may be initially straight or curved. Five compliant mechanisms, which are chosen to illustrate both initially straight and curved members and different types of joint/ contact conditions, are formulated to exemplify analyses using the generalized shooting method for a wide spectrum of applications. The advantages of the generalized SM over the finite difference FD and finite element FE methods are demonstrated numerically. Unlike FD or FE methods that rely on fine discretization of beam members to improve its accuracy, the generalized SM that treats the boundary value problem (BVP) as an initial value problem can achieve higher-order accuracy relatively easily, and hence is more efficient computationally. In addition, the computed results were validated experimentally. It is expected that the generalized SM presented here will offer designers a useful analysis tool, and will effectively facilitate the process of design and optimization of compliant mechanisms.