Kinematic analysis and multi-objective optimization of a 3-UPR parallel mechanism for a robotic leg

In this paper, a parallel mechanism with 3-UPR architecture for a robotic leg application is analyzed for design purposes. The proposed morphology is characterized by the convergence of the three chains to a single point of the moving platform. First, the mechanism is described and its inverse and forward kinematic problems are solved analytically. Its Jacobian matrix is computed to evaluate the singular positions of the end-effector. Then, workspace volume, manipulator dexterity, static efficiency and stiffness are chosen as objective functions for a multi-objective optimization in order to decide the geometrical parameters of the mechanism. The objective functions are mapped in the parameter space and an optimal solution is discussed as suitable for a future prototype.