Stiffness Matrix Method for Displacement Analysis of Fully Spatial Compliant Mechanisms

Because of spherical joints existed in some spatial mechanisms, the pseudo-rigid-body model method extensively used in the analysis and design of a compliant mechanism with only revolute flexure joints was very limited in analyzing its kinematics. An expanded pseudo-rigid-body model method named as stiffness matrix method was presented to conduct the displacement analysis of fully spatial compliant mechanisms. Take a 6 RSS mechanism for instance, the stiffness matrix of the general flexure hinge was established by using the displacement matrix method in structural analysis. Through the transformations of a series of coordinate systems, force balance equations of nodes and end effector of the mechanism, deformation cooperation equations and close loop displacement equations of the mechanism were derived. On the above basis, displacement analysis of the mechanism was conducted with the stiffness matrix method, giving a relatively higher accurate solution by considering elastic deformation of all the mechanical members.