Kinematic analysis of a translational 3-d.o.f. micro-parallel mechanism using the matrix method

In this paper, we applied the matrix method to kinematic analysis of our translational 3-d.o.f. micro-parallel mechanism for an instance of general flexure mechanisms. The matrix method has been well developed in architecture to analyze frame structures. We found that this method is well suited to such a flexure mechanism with circular notched hinges as our micro-parallel mechanism because it can be approximated to a Rahmen structure. Our matrix method can calculate a compliance matrix with less matrix nodes than the conventional finite element method. First, the compliance matrices of a circular notched hinge and some other beams are defined, and the coordinate transformations of the compliance matrix are introduced. Secondly, an analysis of our micro-parallel mechanism is demonstrated.