Modelling and online computation of the dynamics of a parallel kinematic with six degrees-of-freedom

The nonlinear equations of motions of a parallel robot with six degrees-of-freedom (DOF) are presented for the use in real-time computation of the inverse dynamics. The formulation is based on the Newton-Euler equations that provide the presentation of the forces exerted by each body. Therefore, with regard to real-time needs, small influences can be detected and assessed. The presented equations of motion result in a model containing as the DOF six independent tool center point (TCP) coordinates. The requirement that the mechanical parts should be free from backlash involves the existence of increased friction forces due to pre-stressed joints. The frictional behavior is modelled, and the parameters describing the friction model are identified and optimized. Some experiments are presented, and the comparison between the measured and the online-simulated actuation forces shows good accordance.