Distributed-parameter dynamic model and optimized design of a four-link pendulum with flexure hinges

A four-link pendulum, with two flexure hinges, is presented. The system is described by a non-linear distributed-parameter model. By assuming the deformation of a compliant link is identical to the static deflection, the model number of degrees of freedom reduces to two. The finite element results validate the analytic model. A search is conducted to select the designs that determine the free extremity moving along a prescribed trajectory. A pendulum prototype produced a quasi-elliptical trajectory, according to model predictions.