Direct kinematics of 3DOF planar parallel mechanisms: a discussion
This paper presents the direct kinematic solutions of 3DOF planar parallel mechanisms, specifically of the 3RRR mechanism. The direct kinematic problem of the mechanism generally results in a polynomial solution. To obtain an analytical (closed-form) solution, it is necessary for the polynomial to be of degree 4 or less. This paper presents a special configuration that reduces the polynomial solution to a 4th degree. This special configuration further decouples the direct kinematics of the position and the orientation of the end-effector into two cascaded quadratic equations. A numerical example is carried out to verify the results of this simplification. The existence of the closed-form solution would increase the accuracy of the direct kinematic solution and improve computational efficiency, as numerical iterative method is not required. This result provides an efficient computational method for a very useful configuration of planar parallel manipulators.
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