Dimensional Synthesis of 3PRS Parallel Mechanism Based on a Dimensionally Homogeneous Analytical Jacobian

Abstract:

Jacobian matrix plays a crucial role of kinematic synthesis of a parallel mechanism, however, can not directly be used for its nonhomogeneous physical units. This paper proposes the detailed formulation of the dimensionally homogeneous analytical Jacobian of 3PRS parallel mechanism. After defining a kinematic index and the design variables, the sensitivity that the index varies with dimension parameters is performed. Based on the two chosen case, it is also conducted that the index distributes in the prescribed workspace. Then, the kinematic characteristics of the system are discussed. These results provide the informative insight for choosing the optimal solution of the dimension parameters of 3PRS.

• Periodical: Applied Mechanics and Materials (Volume 455)
• Pages: 354-359
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.455.354
• Online since: November 2013
• Authors: Yong Gang Li*, Li Xin Xu, Hui Wang
• Keywords: Dimension Synthesis, Dimensionally Homogeneous, Jacobian, Parallel Mechanism

References

[1] K.E. Neumann, Robot. U.S. Patent 4, 732, 525. (1988).

[2] R. Clavel, Switzerland Patent CH1985005348856. (1985).

[3] N. Hennes, D. Staimer, in: Proceedings of 4th Chemnitz Parallel Kinematics Seminar, editted by Fraunhofer Institute for Machine Tools and Forming Technology, Chemnitz, Germany. Zwickau: Verlag Wissenschaftliche Scripten, (2004).

DOI: 10.17973/mmsj.2021_7_2021076

[4] L.W. Tsai, S. Joshi: Kinematics and optimization of a spatial 3-UPU parallel manipulator, ASME Journal of Mechanical Design, Vol. 122(2000), pp.439-446.

DOI: 10.1115/1.1311612

[5] K. Badescu, C. Mavroidis: Workspace optimization of 3-legged UPU and UPS parallel platforms with joint constraints, ASME Journal of Mechaical Design, Vol. 126(2004), pp.291-300.

DOI: 10.1115/1.1667922

[6] J.P. Merlet: Jcobian, manipulability, condition number, and accuracy of parallel robots, ASME Jornal of Mechanical Design, Vol. 128(2006), pp.199-206.

DOI: 10.1115/1.2121740

[7] C.M. Gosselin: The optimum design of robotic manipulators using dexterity indices, Journal of Robotics and Autonomous Systems, Vol. 9 (1992), pp.213-226.

DOI: 10.1016/0921-8890(92)90039-2

[8] S.G. Kim, J. Ryu: New dimensionally homogeneous jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators, IEEE Trasactions on Robotics and Automation, Vol. 19 (2003), pp.731-736.

DOI: 10.1109/tra.2003.814496

[9] G. Pond G, J .A. Carretero: Formulating Jacobian matrices for the dexterity analysis of parallel manipulators, Mechanism and Machine Theory, Vol. 41(2006), pp.1505-1519.

DOI: 10.1016/j.mechmachtheory.2006.01.003

[10] H.T. Liu, T. Huang, D. G. Chetwynd: A method to formulate dimensionally homogeneous Jacobian of parallel manipulators, IEEE Trasactions on Robotics and Automation, Vol. 27 (2011), pp.150-156.

DOI: 10.1109/tro.2010.2082091