Power requirement comparison in the 3-RPR planar parallel robot dynamics

Recursive matrix relations for kinematics and dynamics of the commonly known 3-RPR planar parallel robots are established in this paper. Three identical planar legs connecting to the moving platform are located in the same plane. Knowing the motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities and accelerations of the robot. Further, the principle of virtual work is used in the inverse dynamic problem. Several matrix equations offer iterative expressions and graphs for the power requirement comparison of each of three actuators in two different actuation schemes: revolute actuators and prismatic actuators. For the same evolution of the moving platform in the vertical plane, the power distribution upon the three actuators depends on the actuating configuration, but the total power absorbed by the set of three actuators is the same, at any instant, for both driving systems.