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Direct kinematics of 3DOF planar parallel mechanisms: A discussion

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2006
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Conference Paper

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Oetomo, Denny and Liaw, Hwee Choo and Alici, Gursel and Shirinzadeh, Bijian and Zhong, Yongmin. 2006. Direct kinematics of 3DOF planar parallel mechanisms: A discussion, in Billingsley, J. (ed), The 13th Annual Conference on Mechatronics and Machine Vision in Practice, Dec 5-7 2006. Toowoomba, QLD: Curran Associates.
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Proceedings of the 13th Annual Conference on Mechatronics and Machine Vision in Practice
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The 13th Annual Conference on Mechatronics and Machine Vision in Practice
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Abstract

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. 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 improves 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.