Mobility Characteristics of a Flexure-based Compliant Manipulator with Three Legs

A flexure-based compliant parallel manipulator (FCPM) is a kind of compliant mechanism characterized by a complicate topological structure and multiple degrees of freedom (DOFs). Compared with its rigid-counterpart, a FCPM becomes more complicate in its mobility analysis. In this paper, the screw theory is applied to the mobility analysis of our FCPM as an instance of general FCPM. Firstly, the compliance matrices of both compliant elements and the whole mechanism are calculated by using adjoint transformation of compliance matrix between different coordinate frames. Secondly, the mobility characteristics of the FCPM is investigated by proposing a concept of "primary mobility of a FCPM" and a method of quantifying the primary mobility of the FCPM providing that the compliance matrix of the manipulator should be calculated primarily. The theoretical result reveals that mobility characteristics of the FCPM with current design parameters can satisfy the designer\´s original desire