A novel approach for forward dynamic analysis of 3-PRS parallel manipulator with consideration of friction effect

• We propose a novel decomposition approach to formulate the dynamic model of a 3-PRS (Prismatic, Revolute, Spherical) parallel manipulator. The dynamic model can be utilized to simulate the motion trajectory of the moving platform once the externally applied forces are given.
• The decomposition approach leads to a transformation matrix which can project the dynamic forces of the moving platform formulated in the task space into the joint space.
• The inverse of 21×21 augmented matrix formulated by conventional approach in solving forward dynamic problem can be decomposed into that of 6×6 and 15×15 matrices. The computational efficiency can therefore be improved about 23.5%.
• Each of the actuated legs can be decoupled to calculate the normal forces applied to the sliding planes of the prismatic joints.
• The effect of corresponding friction forces is included into consideration.

In this paper, a novel decomposition approach to formulate the dynamic model of a 3-Prismatic, Revolute, Spherical (3-PRS) parallel manipulator is proposed. Since the constraint forces arising from the holonomic constraints would not generate a net force or torque to manipulate the motion of the moving platform, the fact motivates to decompose the reaction forces applied to the connecting joints. The decomposition leads to a transformation matrix which can project the dynamic forces of the moving platform formulated in the task space into the joint space. A sufficient condition is determined to guarantee the existence of the projection matrix. Based on the proposed approach, the inverse of 21×21 augmented matrix formulated by conventional approach in solving forward dynamic problem can be decomposed into that of 6×6 and 15×15 matrices. The computational efficiency can therefore be improved about 23.5%. Besides, since the reaction forces can be calculated simultaneously, each of the actuated legs can be decoupled to calculate the normal forces applied to the sliding planes of the prismatic joints. This feature makes it possible to include the effect of corresponding friction forces into consideration. Since the normal forces applied to the sliding planes vary with the reaction forces, the corresponding friction forces are not only the function of sliding velocities but also the dynamics of the whole mechanism. Computer simulations are performed to verify the proposed approach and analyze the effect of the friction forces on the motion accuracy of the moving platform.