Synthesis of Midline to Apex Type Griffis-Duffy Platforms using the Geometric Construction Method
From the viewpoint of mechanism synthesis, Midline to Apex Type Griffis-Duffy Platforms (abbreviated as GDPs), a type of parallel mechanisms with triangle bases and moving platforms are studied. According to motion out-put characteristics of GDPs, an aggregate formed by a series of SSC mechanisms with the same maximal height but different lengths is proposed. Then the GDP is treated as the composition of two 3-SS/C mechanisms constructed from the aggregate, while both of them conform to the compatible conditions of geometry. Contributed by this, once a 3-SS/C mechanism is given, a GDP can be obtained by designing the other obeying the same dimensional constraints. Based on the principle of inversion, the locus of one vertex of the unknown moving platform can be transformed by one side of the known base. With this geometric construction of dimensional constraints, a generalized GDP can be directly synthesized, as a result that three vertices of the moving platform lie on three circular arc loci respectively. This research shows that architecture singular GDP can be achieved by means of synthesis, and also provides a new perspective for the design of robot mechanisms using concise geometrical theorems and intuitive graphical methods.
Keywordsmechanism synthesis architecture singularity principle of inversion geometric construction loci
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This work is generalized from the thesis carried by the first author, when he studied for the degree of Master in Shanghai University of Engineering Science.
The authors would like to acknowledge the financial support of the Natural Science Foundation of China under Grant 51575017 and 51475050.
- 1.Huang, Z., Qu, Y.: Special configuration analysis of spatial parallel manipulators. Journal of Northeast Heavy Machinery Institute 13(2), 1-6 (1989). in Chinese.Google Scholar
- 2.Ma, O., Angeles, J.: Architecture singularities of parallel manipulators. International Journal of Robotics & Automation 7(1), 23-29 (1992).Google Scholar
- 3.Husty, M. L., Karger, A.:. Self-motions of Griffis-Duffy type parallel manipulators. In: Proceedings of the 2000 IEEE International Conference on Robotics and Automation, pp. 7-12. IEEE (2000).Google Scholar
- 6.Briot, S., Arakelian, V., Bonev, I. A., Chablat, D., & Wenger, P.: Self-Motions of General 3-RPR Planar Parallel Robots. The International Journal of Robotics Research 27(7), 855-866 (2008).Google Scholar
- 12.Yang, T. L., Liu, A., Shen, H., Hang, L., Luo, Y., & Jin, Q.: Topology Design of Robot Mechanisms. Springer, Singapore (2018).Google Scholar
- 15.Wu, K., Yu, J., Zong, G., & Kong, X.: A family of rotational parallel manipulators with equal-diameter spherical pure rotation. Journal of Mechanisms and Robotics 6(1), 011008 (2014).Google Scholar
- 16.Hartenberg, R. S., Denavit, J.: Cognate linkages. Machine Design 31(16), 149-152 (1959).Google Scholar
- 20.Griffis M. W., Duffy J.: Method and apparatus for controlling geometrically simple paral-lel mechanisms with distinctive connections. U.S. Patent 5,179,525 (1993).Google Scholar
- 21.Leonard, I. E., Lewis, J. E., Liu, A. C. F., & Tokarsky, G. W.: Classical Geometry: Euclid-ean, Transformational, Inversive, and Projective. John Wiley & Sons, New Jersey (2014).Google Scholar