Research on the inverse dynamics of the flexible multi-body systems for the hybrid polishing kinematics machine tool

The hybrid polishing kinematics machine tool (HPKMT) which is made up of "3 axes parallel + 2 axes series" is developed with the specially designed elastic polishing tool system for the polishing operation on the free-form surfaces by using the characteristic of the elastic polishing adequately by the authors. In order to control the HPKMT effectively, its characteristic of the kinematics and dynamics need be known deeply. Moreover, the problem of inverse dynamics is the theory foundation to apply dynamic control of the HPKMT. The analysis of the inverse of mechanism is the important part in the research of dynamics. On the basis of the differential equations of flexible multi-body dynamics, this paper discusses on the condition of knowing the trace, posture and velocity for the end of bodies how to solve the constraint force and constraint moment of each joint on the 3-PTT parallel mechanism and two-joint series mechanism.