Methodological Thinking on the Construction and Development of Advanced Mechanism Studies

doi:10.3901/JME.2025.05.138

Abstract

Abstract: In the past 100 years, corresponding to the development of mechanical systems, four mechanism theoretical systems based on link-joint modeling, Assur group modeling, loop modeling, and single-open-chain modeling are proposed. In the past 40 years, with the development of robot mechanism as the background, four mechanism topology theories based on screw theory, velocity space, displacement subgroup/submanifold, and based on position and orientation characteristics set have been proposed. At the methodological level, this research aims to reveal some deep-seated regularities of the four theoretical systems of mechanism and the four system theories of mechanism topology. For example, the basic structure of the theoretical system (including basic problem- basic concept-basic principle-basic formula-design method), the basic problems of mechanism topology, kinematics and dynamics and their internal relations, the mode analysis method of multi-body system and the hierarchy, symmetry and order of unit structures. The basic concepts and principles proposed by non-logical thinking are the source of its original innovation, and the theoretical system is formed by logical reasoning. Meanwhile some laws of constructing different theoretical systems are further revealed. For example, different theoretical systems are derived from different basic concepts and principles proposed by non-logical thinking. The inner relation among different levels such as basic concepts, basic formulas, operation rules and design methods. The intrinsic nature of the mechanism. Mechanism topology is the main basis for mechanism to become an independent subject. Methodological thinking contributes to the further development of academic research so as to arouse the resonance of subsequent development.

Key words: mechanism science, topology, kinematics, dynamics, theoretical system, basic architecture, pattern analysis, basic concepts, basic principle

CLC Number:

TH112

YANG Tingli, LI Ju, LUO Yufeng, SHEN Huiping. Methodological Thinking on the Construction and Development of Advanced Mechanism Studies[J]. Journal of Mechanical Engineering, 2025, 61(5): 138-152.

References

[1] REULEAUX F. Theoretische kinematic[M]. Germany，1876.
[2] FRANKE R. Vom aufbau der getriebe[M]. Berlin：Beuthvertrieb，1943. FRANKE R. Structure of gearboxes[M]. Berlin：Beuthvertrieb，1943.
[3] BEYER R. The kinematic synthesis of mechanisms[M]. McGraw-hill Book Comp，1963.
[4] HAIN K. Applied kinematics[M]. New York：McGraw-Hill，1967.
[5] WOO L S. Type synthesis of plane linkages[J]. ASME Journal of Engineering for Industry，1967，89：159-172.
[6] TISCHLER C，SAMUEL A，HUNT K H. Kinematic chains for robot hands—I. orderly number-synthesis[J]. Mechanism and Machine Theory，1995，30(8)：1193-1215.
[7] WITTENBURG J. Dynamics of systems of rigid bodies[M]. Stuttgart：Teubner，1977.
[8] MRUTHYUNJAYA T S. Kinematic structure of mechanisms revisited[J]. Mechanism and Machine Theory，2003，38：279-320.
[9] ASSUR L V. Investigation of plane hinged mechanisms with lower pairs from the point of view of their structure and classification：Part I，II[J]. Bull. Petrograd Polytech. Inst.，1913，20：329-386.
[10] DOBROVOLSKII V V. Main principles of rational classification[M]. AS USSR，1939.
[11] VERHO A. An extension of the concept of the group[J]. Mechanism and Machine Theory，1973，8(2)：249-256.
[12] MANOLESCU N I. A unified method for the formation of all planar jointed kinematic chains and Baranov trusses[J]. Environment and Planning B，1979，6(4)：447-454.
[13] GALLETTI C. A note on modular approaches to planar linkage kinematic analysis[J]. Mechanism and Machine Theory，1986，21(5)：385-391.
[14] FANGHELLA P. Kinematics of spatial linkages by group algebra：a structure-based approach[J]. Mechanism and Machine Theory，1988，23(3)：171-183.
[15] CERESOLE E，FANGHELLA P，GALLETTI C. Assur’s groups，AKCs，basic Trusses，SOCs，etc.：modular kinematics of planar linkages[C]// Proc. of 1996 ASME Design Engineering Technical Conf.，1996：96-DETC/MECH-1027.
[16] SERVATIUS B，SHAI O，WHITELEY W. Combinatorial characterization of the Assur graphs from engineering[J]. European Journal of Combinatorics，2010，31(4)：1091-1104.
[17] NICOLAS R，FEDERICO T. On closed-form solutions to the position analysis of baranov trusses[J]. Mechanism and Machine Theory，2012，50：179-196.
[18] SHAI O，SLJOKA A，WHITELEY W. Directed graphs，decompositions，and spatial rigidity[J]. Discrete Applied Mathematics，2013，161：3028-3047.
[19] HAHN E，SHAI O. Construction of Baranov trusses using a single universal construction rule[C]// Proc. of the ASME International Design Engineering Technical Conf.，2016：IDETC/CIE 2016-59134.
[20] DOBRJANSKYJ L，FREUDENSTEIN F. Some applications of graph theory to the structural analysis of mechanisms[J]. Jnl. Engineering for Industry，1967，89：153-158.
[21] PAUL B. Kinematics and dynamics of planar machinery[M]. New Jersey：Prentice-Hall，Inc.，1979.
[22] KINZEL G L，CHANG C H. The analysis of planar linkages using a modular approach[J]. Mechanism and Machine Theory，1984，19：165-172.
[23] SOHN W J，FREUDENSTEIN F. An application of dual graphs to the automatic generation of the kinematic structure of mechanisms[J]. ASME J. of Mech. Trans. and Auto. in Design，1989，111(4)：494-497.
[24] TUTTLE E R，PETERSON S W，TITUS J E. Enumeration of basic kinematic chains using the theory of finite groups[J]. Trans. ASME J. of Mech. Trans. and Auto. in Design，1989，111(4)：498-503.
[25] WALDRON K J，SREENIVASAN S V. A study of the solvability of the position problem for multi-circuit mechanisms by way of example of the double butterfly linkage[J]. ASME J. of Mechanical Design，1996，118：390-395.
[26] TSAI L W. Robot analysis：the mechanics of serial and parallel manipulators[M]. New York：John Wiley，1999.
[27] MCCARTHY J M，SOH G S. Geometric design of linkages[M]. New York：Springer，2011.
[28] 刘辛军，于靖军，孔宪文. 机器人机构学[M]. 北京：机械工业出版社，2021. LIU Xinjun，YU Jingjun，KONG Xianwen. Robot mechanism[M]. Beijing：China Machine Press，2021.
[29] YANG T L. Structural analysis and number synthesis of spatial mechanisms[C]// Proc. of the Sixth World Congress on the Theory of Machine and Mechanisms，New Delhi，1983：280-283.
[30] YANG T L. A method of kinematic analysis by arbitrarily prescribed input and to planar multi-loop chains[C]// Proc. of the 6th World Conf. on the Theory of Machine and Mmechanisms，New Delhi，1983：195-198.
[31] YANG T L. Structural character of planar complex mechanisms and methods of kinematic and kinetostatic analysis by imaginary unknown parameters[C]// Proc. of the ASME Design Engineering Technical Conf.，1986：86-DET-180.
[32] YANG T L，YAO F H. The topological characteristics and automatic generation of structural analysis and synthesis of plane mechanisms，part 1-theory，part 2-application//[C] Proc. of ASME Mechanisms Conf.，1988：179-190.
[33] 杨廷力，李惠良，罗玉峰. 关于任意机械系统动力学方程的结构[J]. 机械工程学报，1991，27(4)：1-15. YANG Tingli，LI Huiliang，LUO Yufeng. On the structure of dynamic equations of arbitrary mechanical systems[J]. Journal of Mechanical Engineering，1991，27(4)：1-15.
[34] YANG T L，YAO F H. 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[C]// Proc. of ASME Mechanisms Conf.，DE-47，1992：179-190.
[35] ZHANG J Q，YANG T L. A new method and automatic generation for dynamic analysis of complex planar mechanisms based on the SOC[C]// Proc. of 1994 ASME Mechanisms Conf.，1994：215-220.
[36] 杨廷力. 机构学理论研究进展[J]. 机械工程学报，1995，31(2)：1-25. YANG Tingli. Advances in mechanism theory[J]. Journal of Mechanical Engineering，1995，31(2)：1-25.
[37] 杨廷力. 机械系统基本理论--结构学，运动学，动力学[M]. 北京：机械工业出版社，1996. YANG Tingli. Basic theory of mechanical systems—structure，kinematics，dynamics[M]. Beijing：China Machine Press，1996.
[38] KONG X W，YANG T L. A new method for displacement analysis of multi-loop spatial linkages based on ordered single-open-chains[C]//Proc. of the ASME Mechanisms Conf.，1996：96-DETC/MECH-1552.
[39] YANG T L，YAO F H，ZHANG M，et al. A comparative study on some modular approaches for analysis and synthesis of planar linkages：part I—modular structural analysis and modular kinematic analysis[C]. Proc. of the ASME Mechanisms Conf.，1998：DETC98/MECH-5920.
[40] YANG T L，YAO F H，ZHANG M，et al. A comparative study on some modular approaches for analysis and synthesis of planar linkages：part II—modular dynamic analysis and modular structural synthesis[C]// Proc. of the ASME Mechanisms Conf.，1998：DETC98/MECH-6058.
[41] 刘安心，杨廷力. 机械系统运动学设计[M]. 北京：中国石化出版社，1999. LIU Anxin，YANG Tingli. Kinematic design of mechanical system[M]. Beijing：China Petrochemical Press，1999.
[42] LIU A X，YANG T L. Finding all solutions to unconstrained nonlinear optimization for approximate synthesis of planar linkages using continuation method[J]. ASME J. of Mechanical Design，1999，121(3)：368-374.
[43] LIU A X，YANG T L. Real continuation method and its application in kinematic synthesis[C]// Proc. of the ASME Mechanisms Conference，2002：DETC2000/MECH - 14192.
[44] 杨廷力，姚芳华. 多项式方程组的主项解耦消元法[J]. 数学的实践与认识，2002，32(6)：1007-1015. YANG Tingli，YAO Fanghua. An elimination method with decoupling of leading terms for polynomial set[J]. Mathematics In Practice and Theory，2002，32(6)：1007-1015.
[45] SHEN H P，TING K L，YANG T L. Configuration analysis of complex multiloop linkages and manipulators[J]. Mechanism and Machine Theory，2000，35(3)：353-362.
[46] HANG L B，JIN Q，JIN J W，et al. A general study of the number of assembly configurations for multi-circuit planar linkages[J]. Journal of Southeast University，2000，16(1)：46-51.
[47] JIN Q，YANG T L. Over-constraint analysis on spatial 6-link loops[J]. Mechanism and Machine Theory，2002，37(3)：267-278.
[48] FENG Z Y，ZHANG C，YANG T L. Direct displacement solution of 4-DOF spatial parallel mechanism based on ordered single-open-chain[J]. Chinese Journal of Mechanical Engineering，2006，42(7)，35-38.
[49] SHI Z X，LUO Y F，YANG T L. Modular method for kinematic analysis of parallel manipulators based on ordered SOCs[C]// Proc. of the ASME 31st mechanisms and Robots Conf.，2006：DETC2006-99089.
[50] SHI Z X，LUO Y F，HANG L B，et al. A simple method for inverse kinematic analysis of the general 6R serial robot[J]. ASME J. of Mechanical Design，2007，129(8)：793-798.
[51] 冯志友，张燕，杨廷力，等. 基于牛顿欧拉法的2UPS-2RPS并联机构的逆动力学分析[J]. 农业机械学报，2009，40(4)：193- 197. FENG Zhiyou，ZHANG Yan，YANG Tingli，et al. Inverse dynamics analysis of 2UPS-2RPS parallel mechanism based on Newton Euler method[J]. Transactions of the Chinese Society for Agricultural Machinery，2009，40(4)：193-197.
[52] 冯志友，何连才，杨廷力，等. 基于单开链单元的并联气液动连杆机构逆动力学分析[J]. 机械设计，2010(4)：58-61. FENG Z Y，HE L C，YANG T L，et al. Inverse dynamics analysis of parallel gas-hydraulic linkage based on single open chain element [J]. Mechanical Design，2010(4)：58-61.
[53] SHEN H P，YANG T L，LI J，et al. Evaluation of topological properties of parallel manipulators based on the topological characteristic indexes[J]. Robotic，2020，38(8)：1381- 1399.
[54] SHEN H P，CHABLAT D，ZEN B，et al. A translational three-degrees-of-freedom parallel mechanism with partial motion decoupling and analytic direct kinematics[J]. Journal of Mechanisms and Robotics，2020，12：021112-1-7.
[55] SHEN H P，ZHAO Y，LI J，et al. A novel partially-decoupled translational parallel manipulator with symbolic kinematics，singularity identification and workspace determination[J]. Mechanism and Machine Theory，2021，164：104388.
[56] 沈惠平. 基于拓扑特征的机器人机构运动学[M]. 北京：高等教育出版社，2021. SHEN Huiping. Kinematics of robot mechanism based on topological features[M]. Beijing：Higher Education Press，2021.
[57] FRISOLI A，CHECCACCI D，SALSEDO F，et al. Synthesis by screw algebra of translating in-parallel actuated mechanisms[M]. Dordrecht：Kluwer，2000.
[58] HUANG Z，LI Q C. General methodology for type synthesis of symmetrical lower-mobility parallel manipulators and several novel manipulators[J]. Int. J. Robotics Research，2002，21(2)：131-145.
[59] HUANG Z，LI Q C. Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method[J]. Int. J. Robotics，2003，22(1)：59-79.
[60] HUANG Z，LI Q C，DING H. Theory of parallel mechanisms [M]. Dordrecht：Springer，2012.
[61] 黄真，刘婧芳，李艳文. 论机构自由度：寻找了150年的自由度通用公式[M]，北京：科学出版社，2011. HUANG Zhen，LIU Jingfang，LI Yanwen. On the degree of freedom of mechanisms：searching for a general formula for degree of freedom for 150 years[M]. Beijing：Science Press，2011.
[62] KONG X W，GOSSELIN C. Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory[J]. IEEE Trans. Rob. Autom.，2004，20(2)：181-190.
[63] KONG X W，GOSSELIN C. Type synthesis of parallel mechanisms[M]. Springer Tracts in Advanced Robotics，2007.
[64] GOGU G. Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations[J]. Eur. J. Mech. A Solids，2004，23：1021-1039.
[65] GOGU G. Mobility of mechanisms：a critical review[J]. Mech Mach Theory，2005，40：1068-1097.
[66] GOGU G. Structural synthesis of parallel robots：part 1：methodology[M]. Springer，Dordrecht，2008.
[67] GOGU G. Structural synthesis of parallel robots：part 2：translational topologies with two and three degrees of freedom[M]. Dordrecht：Springer，2009.
[68] GOGU G. Structural synthesis of parallel robots：part 3：topologies with planar motion of the moving platform[M]. Springer，Dordrecht，2010.
[69] GOGU G. Structural synthesis of parallel robots：part 4：other topologies with two and three degrees of freedom [M]. Dordrecht：Springer，2012.
[70] HERVE J. Analyse structurelle des mécanismes par groupe des déplacements[J]. Mech Mach Theory，1978，13：437-450. HERVE J. Structural analysis of mechanisms by the groupe of displacements[J]. Mech Mach Theory，1978，13：437-450.
[71] HERVE J. Design of parallel manipulators via the displacement group[C]// Proc. of the 9th World Congress on the Theory of Machines and Mechanisms：Milan，Italy，1995：2079-2082.
[72] FANGHELLA P，GALLETTI C. Metric relations and displacement groups in mechanism and robot kinematics[J]. ASME Journal of Mechanical Design，1995，117：470-478.
[73] HERVE J. The Lie group of rigid body displacements，a fundamental tool for mechanism design[J]. Mech Mach Theory，1999，34：719-730.
[74] LI Q C，HUANG Z，HERVE J. Type synthesis of 3R2T 5-DOF parallel mechanisms using the Lie group of displacements[J]. IEEE Trans. Rob. Autom.，2004，20：173-180.
[75] RICO J，AGUILERA L，GALLARDO J，et al. A more general mobility criterion for parallel platforms [J]. ASME Journal of Mechanical Design，128：207-219，2006.
[76] SÁ NCHEZ-GARCIÁ A J，RICO J M，CERVANTES-SÁNCHEZ J J. A mobility determination method for parallel platforms based on the Lie algebra of SE(3) and its subspaces[J]. Journal of Mechanisms and Robotics，2021，13：031015-1-11.
[77] MENG J，LIU G F，LI Z X. A geometric theory for analysis and synthesis of sub-6 DOF parallel manipulators[J]. IEEE Trans. Rob.，2007，23：625-649.
[78] LI Q，HERVE J，YE W. Geometric method for type synthesis of parallel manipulators[M]. Springer，2020.
[79] 杨廷力，金琼，刘安心，等. 基于单开链单元的欠秩并联机器人机构型综合的一般方法[J]. 机械科学与技术，2001，20(3)：321-325. YANG Tingli，JIN Qiong，LIU Anxin，et al. General method for mechanism type synthesis of under-rank parallel robot based on single open chain element[J]. Mechanical Science and Technology，2001，20(3)：321-325.
[80] 杨廷力，金琼，刘安心，等，基于单开链单元的三平移并联机器人机构型综合及其分类[J]. 机械工程学报，2002，38(8)：31-36. YANG Tingli，JIN Qiong，LIU Anxin，et al. Mechanism type synthesis and classification of three-translation parallel robot based on single open chain element[J]. Journal of Mechanical Engineering，2002，38(8)：31-36.
[81] JIN Q，YANG T L. Theory for topology synthesis of parallel manipulators and its application to three dimension translation parallel manipulators[J]. Transactions of the ASME J. of Mechanical Design，2004，126：625-639.
[82] JIN Q，YANG T L. Synthesis and analysis of a group of 3-degree-of-freedom partially decoupled parallel manipulators[J]. ASME J. of Mechanical Design，2004，126：301-306.
[83] 杨廷力. 机器人机构拓扑结构学[M]. 北京：机械工业出版社，2004. YANG Tingli. Topological structure of robot mechanism[M]. Beijing：China Machine Press，2004.
[84] YANG T L，LIU A X，LUO Y F，et al. Position and orientation characteristic equation for topological design of robot mechanisms[J]. ASME Journal of Mechanical Design，2009，131：021001-1-17.
[85] YANG T L，SUN D J. A general DOF formula for parallel mechanisms and multi-loop spatial mechanisms[J]. ASME Journal of Mechanisms and Robotics，2012，4(1)：011001-1-17.
[86] 杨廷力，刘安心，罗玉峰，等. 机器人机构拓扑结构设计[M]. 北京：科学出版社，2012. YANG Tingli，LIU Anxin，LUO Yufeng，et al. Topology design of robot mechanism[M]. Beijing：Science Press，2012.
[87] YANG T L，LIU A X，SHEN H P，et al. On the correctness and strictness of the POC equation for topological structure design of robot mechanisms[J]. ASME Journal of Mechanisms and Robotics，2013，5(2)：021009-1-18.
[88] SHEN C W，HANG L B，YANG T L. Position and orientation characteristics of robot mechanisms based on geometric algebra[J]. Mechanism and Machine Theory，2017(108)：231-243.
[89] YANG T L，LIU A X，SHEN H P，et al. Composition principle based on single open chain unit for general spatial mechanisms and its application—in conjunction with a review of development of mechanism composition principles[J]. ASME Journal of Mechanisms and Robotics，2018，10：051005-1-16.
[90] YANG T L，LIU A X，SHEN H P，et al. Topology design of robot mechanisms[M]. Singapore：Springer，2018.
[91] 杨廷力，沈惠平，刘安心，等. 机构拓扑学理论的基本思想与数学方法—从方法论角度回顾几种原创性理论与方法[J]. 机械工程学报，2020，56(3)：1-15. YANG Tingli，SHEN Huiping，LIU Anxin，et al. The basic ideas and mathematical methods of institutional topology theory：a review of several original theories and methods from the perspective of methodology[J]. Journal of Mechanical Engineering，2020，56(3)：1-15.
[92] SHEN H P，YANG T L，LI J，et al. Evaluation of topological properties of parallel manipulators based on the topological characteristic indexes[J]. Robotic，2020，38(8)：1381- 1399.
[93] LI J，WU G L，SHEN H P，et al. Topology of robotic mechanisms：framework and mathematics methods—in conjunction with a review of four original theories[J]. Mechanism and Machine Theory，2022(175)：1-25.
[94] 杨廷力. 机器人机构拓扑学及其创建历程[M]. 北京：高等教育出版社，2022. YANG Tingli. Topology of robot mechanism and its creation process[M]. Beijing：Higher Education Press，2022.
[95] 沈惠平，李菊，朱小蓉，等. 基于最优路径的并联机构自由度计算方法及其新公式[J]. 机械工程学报，2024，60(19)：40-52. SHEN Huiping，LI Ju，ZHU Xiaorong，et al. New method and formula for degree-of-freedom calculation of parallel mechanism based on optimal paths[J]. Journal of Mechanical Engineering，2024，60(19)：40-52.