Forward/Reverse Velocity and Acceleration Analyses for a Class of Lower-Mobility Parallel Mechanisms

In the family of lower-mobility (degrees of freedom N_f<6) parallel mechanisms, there is a class of mechanisms whose degrees of freedom equal the number of single-degree-of-freedom pairs in each limb. This paper proposes a novel forward/reverse kinematic analyses method for this class of mechanisms, which can build N_f×N_f square Jacobian matrix and N_f×N_f×N_f cubic Hessian matrix. Thus both forward/reverse velocity and acceleration analyses for this class of mechanisms are derivable. In this method, the formulas for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic pairs), the more effective the method is. In the rear part of the paper, a 5-DOF mechanism 3-RCRR is analyzed as an example.