An improving analytically model with high accuracy for a micro manipulator

A proposed mathematical model is established for modal analysis of a micro manipulator. According to the geometric characteristics of the manipulator, the model is built by using finite element method with multipoint constraint equations, and the corresponding displacement coordinate matrix is obtained after that. Considering that the regular flexure hinge plays a key role, in this analysis process, the hinge is treated as a varied cross-section Euler-Bernoulli beam element and the finite element model is established by a new procedure which followed the element internal equilibrium principle consequently. The stiffness matrix, the mass matrix and the exact shape functions of the non-prismatic beam element can be obtained respectively. Furthermore, the influences of geometric parameters on the fundamental frequency can also be discussed.