An effective pseudo-rigid-body method for beam-based compliant mechanisms

Beam-based compliant mechanisms have been widely used in many precision applications due to their large-displacement characteristic. Meanwhile, a simple and accurate analytical tool is no doubt useful to assist design and optimize these mechanisms. The pseudo-rigid-body (PRB) model is such a good alternative. The PRB model in a traditional sense, however, is too approximate to calculate some precise characteristics such as center-shift of a flexural joint. In this paper, a new method is proposed to easily establish simple and accurate PRB models for a variety of beam-based compliant mechanisms. As is well known, for most of the beam-based compliant mechanisms, there is usually an instantaneous center of rotation (ICR) on each beam, and the beam can be considered as a fixed-guided beam with one end fixed while the other end moves along a certain curve that usually is an approximate arc around the ICR. In this case, the behavior of beams can be imitated by a rigid bar with two pin-joints. One of the pin-joints is directly added at the end of the rigid bar. The position of the other is determined by the characteristic radius factor, and a torsional spring is added at the position to represent the beam's stiffness. The modeling method is used to analyze two commonly used beam-based compliant mechanisms as examples, i.e. a parallel linear spring stage and a cross strip pivot. The performances of precision, stiffness and stroke for the two mechanisms are investigated, and the method is validated by comparing the results with other research work presented in the literatures. Both cases show the method is intuitive and accurate, and it will be useful in the early phases of the design for beam-based compliant mechanisms.