Enumeration of Optimal Pin-Jointed Bistable Compliant Mechanisms

Recently, a new type of mechanism called compliant mechanism has been developed and applied mainly in the field of micro-mechanics. A compliant mechanism has flexible parts to stabilize the structure, which is contrary to the conventional unstable mechanism. Although a compliant mechanism is usually modeled as a continuum with elastic joints, it is possible to generate the similar mechanism by a bar-joint system. Ohsaki and Nishiwaki (Struct. Multidisc. Optim., Vol. 30, pp. 327-334, 2005) presented a method for generating flexible multistable bar-joint mechanisms using nonlinear programming approach. However, due to high nonlinearity of the problem, the nonlinear programming problem should be solved many times starting from different initial solutions to obtain several types of mechanisms. Since the compliant bar-joint mechanism is usually statically determinate, the optimization problem can be solved easily if the design space is limited to statically determinate structures. In this paper, we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-joint frameworks, which are regarded as statically determinate trusses in structural engineering. Bistable mechanisms utilizing snapthrough behavior are generated from the statically determinate trusses. In the numerical examples, many bistable compliant mechanisms are generated to show the effectiveness of the proposed method.