Active compliant control strategy of 3RPS/UPS parallel machine with redundant actuating leg based on lagrange equation

The equations of kinematical compatibility between redundant actuating leg and non-redundant actuating legs of 3RPS/UPS PKM were deduced. Based on the principle of virtual work, Lagrange dynamical equation of 3RPS PKM was derived, consequently the robust trajectory tracking control model was established. The dynamical equation of redundant actuating leg was presented, and the target impedance control model was built up. By using the fuzzy PID method, the appropriate force working on the redundant actuating leg was automatically tracked, so that the internal force of machine was maintained within a reasonable range, and the compliant control strategy of redundantly actuating leg was implemented. The availability of the compliance control model was verified through simulation analysis.