Energy optimization of a planar parallel manipulator with kinematically redundant degrees of freedom

In this paper, a planar parallel manipulator with kinematically redundant degrees of freedom is investigated. First of all, the manipulator is illustrated and then formulation for trajectory generation for the end-effector is described and a trajectory is formulated for a special case. Jacobian matrices are obtained by using constraints equations at the next section. After that, inverse dynamics problem is solved by Kane´s method and equation of motion is obtained. Then it is shown that for a non-redundant mechanism, there is singularity in the prescribed trajectory of the end-effector and it causes the torques become infinity. After that, energy optimization and singularity avoidance optimization are done for a 6-DOF manipulator and torque and force of all actuators of the manipulator are obtained.