Kinematic and stiffness analysis of lower-mobility parallel mechanisms based on QR decomposition

Abstract

A method to build the kinematic of lower-mobility parallel mechanism is mentioned based on the matrix QR decomposition. The forward and inverse kinematic model is built based on the first and second order influence matrix. The velocity and acceleration constraint matrix are also built. Based on the principle of virtual work, the flexibility matrix and directional stiffness are built. The coupling kinematic of the 3RPS mechanism is analyzed. The directional stiffness of 3RPS is analyzed to verify the structural constraint, and the directional stiffness is visually describes by the distribution of spherical coordinates.