Dynamics of a four degrees-of-freedom parallel manipulator with parallelogram joints

A comprehensive dynamics analysis of a four degrees-of-freedom Schönflies parallel manipulator with parallelogram joints is presented. First, the manipulator kinematics and workspace analysis is performed. Then, the dynamics model is calculated using the Lagrangian formulation. The existence of parallelograms in the structure of the manipulator introduces passive variables in the model. Other authors have simplified the dynamics of the parallelograms in order to calculate the dynamics model more easily and eliminate these passive variables. In this work, the full dynamics of the manipulator is considered and passive variables are not eliminated. The model resulting from the Lagrange multiplier elimination produces a symmetric, positive-definite inertia matrix and the relation between the constraint Jacobian and the Jacobian of the constraint equations arises naturally. Finally, the dynamics model is experimentally validated using a prototype of the proposed manipulator.