Kinematics and dynamics of a 4-PRUR Schönflies parallel manipulator by means of screw theory and the principle of virtual work

In this work the kinematics and dynamics of a 4-PRUR parallel manipulator with actuated prismatic joints performing the 3T1R motion are investigated by means of the theory of screws and the principle of virtual work. The loss rotations of the moving platform are easily explained by determining and elucidating the effect of two independent constraint couples. Meanwhile, the input-output equations of velocity and acceleration of the robot are obtained in compact form by a systematic application of the properties of exclusive reciprocal screws. To this aim, in order to generate full rank Jacobian matrices, four pseudo revolute joints connecting the limbs to the fixed platform are added to the robot. The dynamic analysis of the robot is reported through the formulation of the generalized forces affecting the motion of any body of the parallel manipulator based on a harmonious combination of the theory of screws and the principle of virtual work. A case study is included with the purpose to exemplify the viability of the method.