Abstract
The mechanism composition principle based on Single-Open-Chain (SOC) unit is introduced in this chapter. The content deals with: (1) The mechanism composition principle based on SOC unit is proposed. Constraint degree of SOC is defined, which is used to describe constraint features of SOC unit to DOF of the mechanism. (2) A general method for decomposing an AKC into ordered SOCs is proposed. The coupling degree of an AKC is defined and is used to represent complexity of the AKC. (3) A general method for decomposing mechanism into ordered SOCs is proposed. Criteria for AKC determination is defined and is used to determine AKCs contained in the mechanism. (4) A general method for determination of DOF types is proposed based on the AKCs in the mechanism. And a general method for motion decoupling design based on partial DOF is proposed. (5) This mechanism composition principle could be used to establish a systematic theory for unified modeling of mechanism topology, kinematics and dynamics based on SOC unit (refer to Sect. 7.7).
References
Assur LV (1913) Investigation of Plane Hinged Mechanisms with Lower Pairs from the Point of View of Their Structure and Classification (in Russian): Part I, II. Bull. Petrograd Polytech Inst 20 :329–386. Bull Petrograd Polytech Inst 21 (1914) 187–283, (vols. 21–23, 1914–1916)
Dobrovolskii VV (1939) Main principles of rational classification. AS USSR
Verho A (1973) An extension of the concept of the group. Mech Mach Theor 8(2):249–256. doi:10.1016/0094-114X(73)90059-1
Manolescu NI (1979) A unified method for the formation of all planar jointed kinematic chains and Baranov trusses. Environ Plann B 6(4):447–454
Galletti C (1986) A note on modular approaches to planar linkage kinematic analysis. Mech Mach Theor 21(5):385–391
Fanghella P (1988) Kinematics of spatial linkages by group algebra: a structure-based approach. Mech Mach Theor 23(3):171–183. doi:10.1016/0094-114X(88)90102-4
Ceresole E, Fanghella P, Galletti C (1996) Assur’s groups, AKCs, basic trusses, SOCs, etc.: modular kinematics of planar linkages. In: Proceedings of the 1996 ASME design engineering technical conference 96-DETC/MECH-1027
Mruthyunjaya TS (2003) Kinematic structure of mechanisms revisited. Mech Mach Theor 38:279–320
Servatius B, Shai O, Whiteley W (2010) Combinatorial Characterization of the Assur graphs from engineering. Eur J Comb 31(4):1091–1104
Shai O, Sljoka A, Whiteley W (2013) Directed graphs, decompositions, and spatial rigidity. Discr Appl Math 161:3028–3047
Reuleaux F (1876) Theoretische kinematic. Fridrich vieweg, Braunschweig, Germany, 1875 (Kennedy ABW, (1876) The kinematics of machinery. Reprinted Dover 1963)
Franke R (1951) Vom Aufbau der Getriebe, Vol. 1”, Beuthvertrieb, Berlin, 1943, 2nd edition, VDI, Verlag (1958). R~ Franke, Vom Aufbau der Getriebe, Vol. 1, 2nd edition VDI Verlag (1958).R~ Franke, Getriebe
Beyer R., 1963, “ The Kinematic Synthesis of Mechanisms”, McGraw-hill Book Comp
Hain K (1967) Applied kinematics, second edn. McGraw-Hill, New York
Woo LS (1967) Type synthesis of plane linkages. ASME J Eng Ind B 89:159–172
Tischler C, Samuel A, Hunt KH (1995) Kinematic chains for robot hands—I. Orderly number-synthesis. Mech Mach Theor 30(8):1193–1215. Retrieved from http://www.sciencedirect.com/science/article/pii/0094114X9500043X
Wittenburg J (1977) Dynamics of Systems of Rigid Bodies. Teubner, Stuttgart
Dobrjanskyj L, Freudenstein F (1967) Some applications of graph theory to the structural analysis of mechanisms. J Eng Ind 89:153–158
Paul B (1979) Kinematics and dynamics of planar machinery. Prentice-Hall Inc, New Jersey
Kinzel GL et al (1984) The analysis of planar linkages using a modular approach. Mech Mach Theor 19:165–172
Sohn WJ, Freudenstein F (1989) An application of dual graphs to the automatic generation of the kinematic structure of mechanisms. ASME J Mech Trans Auto Design 111(4):494–497
Tuttle ER et al (1989) Enumeration of basic kinematic chains using the theory of finite groups. Trans ASME J Mech Trans Auto Design 111(4):498–503
Waldron KJ, Sreenivasan SV (1996) A study of the solvability of the position problem for multi-circuit mechanisms by way of example of the double butterfly linkage. ASME J Mech Design 118:390–395
Tsai L-W (1999) Robot analysis: the mechanics of serial and parallel manipulators. John Wiley, New York
McCarthy JM, Soh GS (2011) Geometric design of linkages. Springer, New York
Yang T-L, Yao F-H (1988) The topological characteristics and automatic generation of structural analysis and synthesis of plane mechanisms, part 1-theory, part 2-application. In: Proceedings of ASME mechanisms conference, vol (1). pp 179–190
Yang T-L, Yao F-H (1992) The topological characteristics and automatic generation of structural analysis and synthesis of spatial mechanisms, part 1-topological characteristics of mechanical network; part 2-automatic generation of structure types of kinematic chains. In: Proceedings of ASME mechanisms conference DE-47. pp 179–190
Yang T-L (1996) Basic theory of mechanical system: structure, kinematic and dynamic. China machine Press, Beijing
Yang T-L, Yao F-H, Zhang M (1998) A comparative study on some modular approaches for analysis and synthesis of planar linkages: part I—modular structural analysis and modular kinematic analysis. In: Proceedings of the ASME mechanisms conference Atlanta, DETC98/MECH-5920
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. The 14th IFToMM World Congress, Taipei, Taiwan, 25–30 October 2015. doi: 10.6567/IFToMM.14TH.WC.OS13.135
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, Sun D-J (2012) A general DOF formula for parallel mechanisms and multi-loop spatial mechanisms. ASME J Mech Robot 4(1):011001
Yang T-L, Liu A-X, Luo Y-F et al (2012) Theory and application of robot mechanism topology. China Science Press, Beijing
Jin Q, Yang T-L (2004) Synthesis and analysis of a group of 3-degree-of-freedom partially decoupled parallel manipulators. ASME J Mech Des 126:301–306
Carricato Marco (2005) Fully isotropic four-degrees-of-freedom parallel mechanisms for Schoenflies motion. Int J Robot Res 24(5):397–414
Sébastien B, Arakelian V, Guégan S (2008) Design and prototyping of a partially decoupled 4-DOF 3T1R parallel manipulator with high-load carrying capacity. J Mech Design 130:122303
Lee Chung-Ching, Hervé Jacques M (2009) Uncoupled actuation of overconstrained 3T-1R hybrid parallel manipulators. Robotica 27:103–117
Carricato M (2009) Decoupled and homokinetic transmission of rotational motion via constant-velocity joints in closed-chain orientational manipulators. J Mech Robot 1:041008
Glazunov Victor (2010) Design of decoupled parallel manipulators by means of the theory of screws. Mech Mach Theor 45:239–250
Carricato Marco, Parenti-Castelli Vincenzo (2004) A novel fully decoupled two degrees of freedom parallel wrist. Int J Robot Res 23(6):661–667
Kong X, Gosselin CM (2002) Type synthesis of linear translational parallel manipulators. Adv Robot Kinematics—Theor Appl 411–420
Li Weimin, Gao Feng, Zhang Jianjun (2005) R-CUBE, a decoupled parallel manipulator only with revolute joints. Mech Mach Theor 40:467–473
Shen H-P, Yang T-L (2000) A new method and automatic generation for kinematic analysis of complex planar linkages based on the ordered SOC. In: Proceedings of ASME mechanisms conference, vol 70. pp 493–500
Shen H-P, Ting K-L, Yang T-L (2000) Configuration analysis of complex multiloop linkages and manipulators. Mech Mach Theor 35(3):353–362
Hang L-B, Jin Q, Jin Wu, Yang T-L (2000) A general study of the number of assembly configurations for multi-circuit planar linkages. J Southeast Univ (English Ed.) 16(1):46–51
Nicolas R, Federico T (2012) On closed-form solutions to the position analysis of Baranov trusses. Mech Mach Theor 50:179–196
Hahn E, Shai O (2016) A single universal construction rule for the structural synthesis of mechanisms. In: Proceedings of the ASME international design engineering technical conference IDETC/CIE 2016-59133
Hahn E, Shai O (2016) Construction of Baranov trusses using a single universal construction rule. In: Proceedings of the ASME international design engineering technical conference IDETC/CIE 2016-59134
Shi Z-X, Luo Y-F, Hang L-B, Yang T-L (2007) A simple method for inverse kinematic analysis of the general 6R serial robot. ASME J Mech Design 129(8):793–798
Feng Z-Y, Zhang C, Yang T-L (2006) Direct displacement solution of 4-DOF spatial parallel mechanism based on ordered single-open-chain. Chinese J Mech Eng 42(7):35–38
Shi Z-X, Luo Y-F, Yang T-L (2006) Modular method for kinematic analysis of parallel manipulators based on ordered SOCs. In: Proceedings of the ASME 31th mechanisms and robots confernce DETC2006-99089
Huiping S, Guowei S, Jiaming D, Ting-li Y (2017) A novel 3T1R parallel robot 2PaRSS: design and kinematics. In: Proceedings of the ASME 2017 international design engineering technical conferences, Ohio, DETC2017-67265
Zhang J-Q, Yang T-L (1994) A new method and automatic generation for dynamic analysis of complex planar mechanisms based on the SOC. In: Proceedings of 1994 ASME mechanisms conference, vol 71. pp 215–220
Yang T-L, Li H-L, Luo Y-F (1991) On the structure of dynamic equation of any mechanical system. Chinese J Mech Eng 27(4):1–15
Yang T-L, Yao F-H, Zhang M (1998) A comparative study on some modular approaches for analysis and synthesis of planar linkages: Part II — Modular Dynamic Analysis, Modular Structural Synthesis and Modular Kinematic Synthesis,” Proc. of the ASME Mechanisms Conf., DETC98/MECH-6058
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Yang, TL., Liu, A., Shen, H., Hang, L., Luo, Y., Jin, Q. (2018). Mechanism Composition Principle Based on Single-Open-Chain Unit. In: Topology Design of Robot Mechanisms. Springer, Singapore. https://doi.org/10.1007/978-981-10-5532-4_7
Download citation
DOI: https://doi.org/10.1007/978-981-10-5532-4_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-5531-7
Online ISBN: 978-981-10-5532-4
eBook Packages: EngineeringEngineering (R0)