A Systematic Procedure of Transfer Matrix Method to Analyze Compliant Mechanisms With Irregularly Connected Building Blocks

Kinetostatic and dynamic analyses are of significance in designing compliant mechanisms. The design challenge of complex configurations with irregular building blocks, however, not only leads to difficult modeling but would also results in large errors and even wrong results. In this article, a systematic procedure of the transfer matrix method is developed for kinetostatic and dynamic analyses of compliant mechanisms with irregular serial-parallel building blocks. To this end, a generalized transfer matrix is established by shifting end nodes of all adjacent flexure members to being coincided. Uniform transfer matrix formulations of purely parallel and parallel-clamped subchains are derived as well. The systematic procedure enables a concise analysis process without the requirement of cumbersome mathematical derivations to deal with irregular connection of flexure building blocks, thus facilitating a parametric modeling that is not only robust but also computationally efficient. A practical design is implemented to show the considerable reduction of modeling complexity and enhancement of prediction accuracy with the presented approach.