Kinematic analysis of translational 3-DOF micro parallel mechanism using matrix method

TLDR: The matrix method can calculate a compliance matrix with less nodes of matrix than conventional finite element method and is well applicable to a flexure mechanism with circular notched hinges as the authors' micro parallel mechanism because it is approximate to the Rahmen structure.

Abstract: We apply the matrix method to kinematic analysis of our translational 3-DOF micro parallel mechanism for an instance of general flexure mechanisms. The matrix method has been well developed in architecture to analyze a frame structure. We found that this method is well applicable to such a flexure mechanism with circular notched hinges as our micro parallel mechanism because it is approximate to the Rahmen structure. Our matrix method can calculate a compliance matrix with less nodes of matrix than conventional finite element method. First, the compliance matrices of a circular notched hinge and some other beams are defined and the coordinate transformations of compliance matrix are introduced. Next, an analysis of our micro parallel mechanism is demonstrated.