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Direct kinematics of 3DOF planar parallel mechanisms: A Discussion

Conference Paper


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.

Publication Date


  • 2006

Citation


  • Oetomo, D., Liaw, H. C., Alici, G., Shirinzadeh, B., & Zhong, Y. (2006). Direct kinematics of 3DOF planar parallel mechanisms: A Discussion. In 13th Annual International Conference on Mechatronics and Machine Vision in Practice 2006 (pp. 151-163).

Scopus Eid


  • 2-s2.0-84877616796

Web Of Science Accession Number


Start Page


  • 151

End Page


  • 163

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.

Publication Date


  • 2006

Citation


  • Oetomo, D., Liaw, H. C., Alici, G., Shirinzadeh, B., & Zhong, Y. (2006). Direct kinematics of 3DOF planar parallel mechanisms: A Discussion. In 13th Annual International Conference on Mechatronics and Machine Vision in Practice 2006 (pp. 151-163).

Scopus Eid


  • 2-s2.0-84877616796

Web Of Science Accession Number


Start Page


  • 151

End Page


  • 163