Analysis on the Instantaneous Stiffness of the 3-RPS Parallel Machine

Abstract:

Based on the screw theory, the force analysis of the 3-RPS parallel machine is illuminated. Been equivalent to a 6-chain parallel machine, the deformation harmony equation of the parallel machine under the outside generalized force is interpreted. The instantaneous stiffness model of the parallel machine, which includes the change of the force Jacobian matrix, is established. Considering the deviation of the position and orientation of the moving platform, which is resulted from the distortion of the PRS chains of the parallel machine, the influence of the change of the Jacobian matrix to the instantaneous stiffness model of the 3-RPS parallel machine is analyzed, and furthermore, it is verified with an instance.

• Periodical: Key Engineering Materials (Volumes 407-408)
• Pages: 63-67
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.407-408.63
• Online since: February 2009
• Authors: Xian Guo Han, Xue Liang Cui, Wu Yi Chen
• Keywords: Deformation Harmony Equation, Instantaneous Stiffness Model, Jacobian Matrix

References

[1] CLÈNMENT GOSSELIN: Stiffness mapping for parallel manipulators. IEEE Transactions on Robotics and Automatin, 1990, 6 (3): 377-382.

DOI: 10.1109/70.56657

[2] CLINTON C. M. Zhang G: Stiffness modeling of a Stewart-platform-based milling machine. Transaction of NAMRI/SME, vol. 115(1997): 335-340.

[3] Zhang Jingzhu, Xu Cheng, Guo Kai: Property study on the rigidity and flexibility of 6-dimensional force/moment sensor based on Stewart configuration. Journal of Machine Design, Vol. 24(2007) No. 7: 6-8.

[4] Wang Shijun, Huang Yu-mei: Determination Method of Branch Stiffness and Load for Parallel Machine Tool Journal of Xi'an University of Technology, Vol. 20(2004) No. 2: 117-121.

[5] Chen Jiqing, Lan Feng-chong: Instantaneous Stiffness Analysis and Application in Stewart Parallel Machine Tools Journal of Nanjing University of Science and Technology, Vol. 31(2007), No. 4: 482-486.

[6] Zhao Tieshi, Zhao Yanzhi, Bian Hui Lina: Continuous Stiffness Nonlinear Mapping of Spatial Parallel Mechanism Chinese Journal of Mechanical Engineering, Vol. 44(2008) No. 8: 20-25.

DOI: 10.3901/jme.2008.08.020

[7] Zhao Tieshi, Zhao Yongsheng, Huang Zhen: Physical and mathematical conditions of existence of axes about which platform of deficient-rank parallel robots can rotate continuously. ROBOT, Vol. 21(1999), No. 5: 347-351.

[8] Han Xianguo Chen Wuyi: The method to solve the compatibility equation of distortion of over constraint parallel manipulator based on kinematic constraint [J]. Mechanics in Engineering, Vol. 27(2005) No. 3: 65-68.

[9] Huang Zhen, Zhao Tieshi, Zhao Yongsheng: Advanced spatial mechanism. (Higher Education Press, 2006).