Abstract
Topological structure of mechanisms and the symbolic representation are introduced in this chapter. The content deals with: (1) A new element for describing topological structure - geometric constraint type (the type of geometrical constraints to pair axes imposed by links, is proposed. This new element and the other two traditional elements (type of kinematic pair, connection relation between links) formed the three basic elements of topological structure. (2) The mechanism topological structure described using these three basic elements and the corresponding symbolic representation are independent of motion position of the mechanism and the fixed coordinate system. This feature is called the topological structure invariance during motion process. (3) The symbolic representation of topological structure and the topological structure invariance could be used for establishing the position and orientation characteristics (POC) equation for serial mechanisms, the POC equation for parallel mechanisms (PMs) and their operation rules (refer to Chaps. 4–5). (4) Any serial mechanisms or multi-loop spatial mechanisms can be generated by connecting single-open-chain (SOC) in parallels or in series. The SOC unit is a new structure unit of mechanisms proposed by authors, which could be used for establishing the POC equation for serial mechanisms (refer to Chap. 4), the POC equation for PMs (refer to Chap. 5), the DOF formula (refer to Chap. 6) and the coupling degree formula (refer to Chap. 7).
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References
Ionescu TG (2003) Terminology for mechanisms and machine science. Mech Mach Theor 38
Mruthyunjaya TS (2003) Kinematic structure of mechanisms revisited. Mech Mach Theor 38:279–320
Franke R (1951) Von Aufbau der Getribe, vol 1, Beuthvertrieb, Berlin, 1943, vol 2, VDI, Dusseldorf
Hain K (1967) Applied Kinematics, 2nd edn. McGraw-Hill, New York
Wittenburg J (1977) Dynamics of systems of rigid bodies. Teubner, Stuttgart
Paul B (1979) Kinematics and dynamics of planar machinery. Prentice-Hall Inc, New Jersey
Sohn WJ, Freudenstein F (1989) An application of dual graphs to the automatic generation of the kinematic structure of mechanisms. ASME J Mech Trans Autom Des 111(4):494–497
Yang T-L (1983) Structural analysis and number synthesis of spatial mechanisms. In: Proceedings of the 6th world congress on the theory of machines and mechanisms, New Delhi, vol 1, pp 280–283
Yang T-L (1986) Kinematic structural analysis and synthesis of over-constrained spatial single loop chains. In: Proceedings of the 19-th Biennial Mechanisms Conference, Columbus, ASME paper 86-DET-189
Yang T-L, Yao F-H (1992) The topological characteristics and automatic generation of structural analysis and synthesis of spatial mechanisms. In: Proceedings of ASME Mechanisms Conference, Phoenix, DE-47, pp 179–90
Yang T-L, Jin Q et al (2001) A general method for type synthesis of rank-deficient parallel robot mechanisms based on SOC unit. Mach Sci Technol 20(3):321–325
Yang T-L, Jin Q, Liu A-X, Shen H-P, Luo Y-F (2002) Structural synthesis and classification of the 3-DOF translation parallel robot mechanisms based on the unites of single-open chain. Chin J Mech Eng 38(8):31–36. doi:10.3901/JME.2002.08.031
Jin Q, Yang T-L (2004) Theory for topology synthesis of parallel manipulators and its application to three-dimension-translation parallel manipulators. ASME J Mech Des 126:625–639
Yang T-L (2004) Theory of topological structure for robot mechanisms. China Machine Press, Beijing
Yang T-L, Liu A-X, Luo Y-F, Shen H-P et al (2009) Position and orientation characteristic equation for topological design of robot mechanisms. ASME J Mech Des 131: 021001-1–021001-17
Yang T-L, Sun D-J (2012) A general DOF formula for parallel mechanisms and multi-loop spatial mechanisms. ASME J Mech Robot 4(1):011001-1–011001-17
Yang T-L, Liu A-X, Luo Y-F, Shen H-P et al (2013) On the correctness and strictness of the position and orientation characteristic equation for topological design of robot mechanisms. ASME J Mech Robot 5:021009-1–021009-18
Yang T-L, Liu A-X, Shen H-P, et al (2015) Composition principle based on SOC unit and coupling degree of BKC for general spatial mechanisms. In: The 14th IFToMM world congress, Taipei, Taiwan, 25–30 Oct 2015. doi: 10.6567/IFToMM.14TH.WC.OS13.135
Yang T-L, Liu A-X, Shen H-P et al (2012) Theory and application of robot mechanism topology. China Science press, Beijing
Dizioglu B (1978) Theory and practice of spatial mechanisms with special positions of the axes. Mech Mach Theor 13(2):139–153
Herve JM (1978) Analyse Structurelle des Meanismes Dar Groupe des delacements. Mech Mach Theor 4:437–450
Baker JE (1979) The Bennett, Goldberg and Myard linkages—in perspective. Mech Mach Theor 14:239–253
Baker JE (1980) An analysis of the bricard linkages. Mech Mach Theor 15:267–286
Jin Q, Yang T-L (2002) Over-constraint analysis on spatial 6-link loops. Mech Mach Theor 37(3):267–278
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Yang, TL., Liu, A., Shen, H., Hang, L., Luo, Y., Jin, Q. (2018). Topological Structure of Mechanisms and Its Symbolic Representation. In: Topology Design of Robot Mechanisms. Springer, Singapore. https://doi.org/10.1007/978-981-10-5532-4_2
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DOI: https://doi.org/10.1007/978-981-10-5532-4_2
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