0
Research Papers

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

[+] Author and Article Information
Ting-Li Yang

School of Mechanical Engineering,
Changzhou University,
Changzhou 213164, China
e-mail: yangtl@126.com

Anxin Liu

School of Air Transportation and Engineering,
Nanhang Jingcheng College,
Nanjing 211156, China
e-mail: liuanxinn@163.com

Huiping Shen

School of Mechanical Engineering,
Changzhou University,
Changzhou 213164, China
e-mail: shp65@126.com

Lubin Hang

School of Mechanical Engineering,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: hanglb@126.com

Qiaode Jeffery Ge

Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794-2300a
e-mail: qiaode.ge@stonybrook.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received May 10, 2017; final manuscript received May 30, 2018; published online July 9, 2018. Editor: Venkat Krovi.

J. Mechanisms Robotics 10(5), 051005 (Jul 09, 2018) (16 pages) Paper No: JMR-17-1143; doi: 10.1115/1.4040488 History: Received May 10, 2017; Revised May 30, 2018

Based on the general degree-of-freedom (DOF) formula for spatial mechanisms proposed by the author in 2012, the early single open chain (SOC)-based composition principle for planar mechanisms is extended to general spatial mechanisms in this paper. First, three types of existing mechanism composition principle and their characteristics are briefly discussed. Then, the SOC-based composition principle for general spatial mechanisms is introduced. According to this composition principle, a spatial mechanism is first decomposed into Assur kinematic chains (AKCs) and an AKC is then further decomposed into a group of ordered SOCs. Kinematic (dynamic) analysis of a spatial mechanism can then be reduced to kinematic (dynamic) analysis of AKCs and finally to kinematic (dynamic) analysis of ordered SOCs. The general procedure for decomposing the mechanism into ordered SOCs and the general method for determining AKC(s) contained in the mechanism are also given. Mechanism's kinematic (dynamic) analysis can be reduced to the lowest dimension (number of unknowns) directly at the topological structure level using the SOC-based composition principle. The SOC-based composition principle provides a theoretical basis for the establishment of a unified SOC-based method for structure synthesis and kinematic (dynamic) analysis of general spatial mechanisms.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Assur, L. V. , 1913, “ Investigation of Plane Hinged Mechanisms With Lower Pairs From the Point of View of Their Structure and Classification (in Russian)—Part I,” Bull. Petrograd Polytech. Inst., 20, pp. 329–386.
Assur, L. V. , 1914, “ Investigation of Plane Hinged Mechanisms With Lower Pairs From the Point of View of Their Structure and Classification (in Russian)—Part II,” Bull. Petrograd Polytech. Inst, 21, pp. 187–283.
Dobrovolskii, V. V. , 1939, “ Main Principles of Rational Classification,” AS USSR.
Verho, A. , 1973, “ An Extension of the Concept of the Group,” Mech. Mach. Theory, 8(2), pp. 249–256. [CrossRef]
Manolescu, N. I. , 1979, “ A Unified Method for the Formation of All Planar Jointed Kinematic Chains and Baranov Trusses,” Environ. Plann. B, 6(4), pp. 447–454. [CrossRef]
Galletti, C. , 1986, “ A Note on Modular Approaches to Planar Linkage Kinematic Analysis,” Mech. Mach. Theory, 21(5), pp. 385–391. [CrossRef]
Fanghella, P. , 1988, “ Kinematics of Spatial Linkages by Group Algebra: A Structure-Based Approach,” Mech. Mach. Theory, 23(3), pp. 171–183. [CrossRef]
Ceresole, E. , Fanghella, P. , and Galletti, C. , 1996, “ Assur's Groups, AKCs, Basic Trusses, SOCs, etc.: Modular Kinematics of Planar Linkages,” ASME Paper No. 96-DETC/MECH-1027.
Mruthyunjaya, T. S. , 2003, “ Kinematic Structure of Mechanisms Revisited,” Mech. Mach. Theory, 38(4), pp. 279–320. [CrossRef]
Servatius, B. , Shai, O. , and Whiteley, W. , 2010, “ Combinatorial Characterization of the Assur Graphs From Engineering,” Eur. J. Combinatorics, 31(4), pp. 1091–1104. [CrossRef]
Shai, O. , Sljoka, A. , and Whiteley, W. , 2013, “ Directed Graphs, Decompositions, and Spatial Rigidity,” Discrete Appl. Math., 161(18), pp. 3028–3047. [CrossRef]
Reuleaux, F. , 1876, Theoretische Kinematic, Fridrich Vieweg, Braunschweig, Germany (English Translation by A. B. W. Kennedy, The Kinematics of Machinery, Dover, Mineola, NY).
Franke, R. , 1951, Vom Aufbau der Getriebe, 2nd ed., Vol. 1, Beuthvertrieb, Berlin.
Beyer, R. , 1963, The Kinematic Synthesis of Mechanisms, McGraw-Hill, London.
Hain, K. , 1967, Applied Kinematics, 2nd ed., McGraw-Hill, New York.
Woo, L. S. , 1967, “ Type Synthesis of Plane Linkages,” ASME J. Eng. Ind., 89(1), pp. 159–172. [CrossRef]
Tischler, C. , Samuel, A. , and Hunt, K. H. , 1995, “ Kinematic Chains for Robot Hands—I: Orderly Number-Synthesis,” Mech. Mach. Theory, 30(8), pp. 1193–1215. [CrossRef]
Wittenburg, J. , 1977, Dynamics of Systems of Rigid Bodies, Teubner, Stuttgart, Germany. [CrossRef]
Dobrjanskyj, L. , and Freudenstein, F. , 1967, “ Some Applications of Graph Theory to the Structural Analysis of Mechanisms,” J. Eng. Ind., 89(1), pp. 153–158. [CrossRef]
Paul, B. , 1979, Kinematics and Dynamics of Planar Machinery, Prentice Hall, Englewood Cliffs, NJ.
Kinzel, G. L. , and Chang, C. H. , 1984, “ The Analysis of Planar Linkages Using a Modular Approach,” Mech. Mach. Theory, 19(1), pp. 165–172. [CrossRef]
Sohn, W. J. , and 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), pp. 494–497. [CrossRef]
Tuttle, E. R. , Peterson, S. W. , and Titus, J. E. , 1989, “ Enumeration of Basic Kinematic Chains Using the Theory of Finite Groups,” ASME J. Mech. Trans. Autom. Des., 111(4), pp. 498–503. [CrossRef]
Waldron, K. J. , and Sreenivasan, S. V. , 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. Des., 118(3), pp. 390–395. [CrossRef]
Tsai, L.-W. , 1999, Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley, New York.
McCarthy, J. M. , and Soh, G. S. , 2011, Geometric Design of Linkages, Springer, New York. [CrossRef]
Yang, T.-L. , and Yao, F.-H. , 1988, “ The Topological Characteristics and Automatic Generation of Structural Analysis and Synthesis of Plane Mechanisms—Part 1: Theory, Part 2: Application,” ASME Conference, Orlando, FL, pp. 179–190.
Yang, T.-L. , and 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,” ASME Conference, Phoenix, AZ, pp. 179–190.
Jin, Q. , and 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(4), pp. 625–639. [CrossRef]
Jin, Q. , and Yang, T.-L. , 2004, “ Synthesis and Analysis of a Group of 3-Degree-of-Freedom Partially Decoupled Parallel Manipulators,” ASME J. Mech. Des., 126(2), pp. 301–306. [CrossRef]
Yang, T.-L. , 2004, Theory and Application of Robot Mechanism Topology, China Machine Press, Beijing, China.
Yang, T.-L. , and Sun, D.-J. , 2012, “ A General DOF Formula for Parallel Mechanisms and Multi-Loop Spatial Mechanisms,” ASME J. Mech. Rob., 4(1), p. 011001. [CrossRef]
Yang, T.-L. , Liu, A.-X. , Luo, Y.-F. , Shen, H.-P. , Hang, L.-B. , and Jin, Q. , 2009, “ Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms,” ASME J. Mech. Des., 131(2), p. 021001. [CrossRef]
Yang, T.-L. , Liu, A.-X. , Shen, H.-P. , Luo, Y.-F. , Hang, L.-B. , and Shi, Z.-X. , 2013, “ On the Correctness and Strictness of the POC Equation for Topological Structure Design of Robot Mechanisms,” ASME J. Mech. Rob., 5(2), p. 021009. [CrossRef]
Yang, T.-L. , Liu, A.-X. , Shen, H.-P. , and Hang, L.-B. , 2016, “ Topological Structure Synthesis of 3T1R Parallel Mechanism Based on POC Equations,” Ninth International Conference on Intelligent Robotics and Applications (ICIRA), Tokyo, Japan, Aug. 22–24, pp. 147–161.
Huang, Z. , and Li, Q. C. , 2002, “ General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators,” Int. J. Rob. Res., 21(2), pp. 131–145. [CrossRef]
Kong, X. , and Gosselin, C. M. , 2007, Type Synthesis of Parallel Mechanisms (Springer Tracts in Advanced Robotics, Vol. 33), Springer, New York.
Hervé, J. M. , 1995, “ Design of Parallel Manipulators Via the Displacement Group,” Ninth World Congress on the Theory of Machines and Mechanisms, Milan, Italy, Aug. 29–Sept. 2, pp. 2079–2082.
Gogu, G. , 2008, Structural Synthesis of Parallel Robots—Part 1: Methodology, Springer, Dordrecht, The Netherlands. [CrossRef]
Meng, X. , Gao, F. , Wu, S. , and Ge, J. , 2014, “ Type Synthesis of Parallel Robotic Mechanisms: Framework and Brief Review,” Mech. Mach. Theory, 78, pp. 177–186. [CrossRef]
Yang, T.-L. , 1996, Basic Theory of Planar Mechanical System: Structure, Kinematic and Dynamic, China Machine Press, Beijing, China.
Yang, T.-L. , Yao, F.-H. , Zhang, M. , and Xu, Z. , 1998, “ A Comparative Study on Some Modular Approaches for Analysis and Synthesis of Planar Linkages—Part I: Modular Structural Analysis and Modular Kinematic Analysis,” ASME Paper No. DETC98/MECH-5920.
Yang, T.-L. , Yao, F.-H. , Zhang, M. , and Xu, Z. , 1998, “ A Comparative Study on Some Modular Approaches for Analysis and Synthesis of Planar Linkages—Part II: Modular Dynamic Analysis and Modular Structural Synthesis,” ASME Paper No. DETC98/MECH-6058.
Shen, H.-P. , Ting, K.-L. , and Yang, T.-L. , 2000, “ Configuration Analysis of Complex Multiloop Linkages and Manipulators,” Mech. Mach. Theory, 35(3), pp. 353–362. [CrossRef]
Yang, T.-L. , 1986, “ Structural Character of Planar Complex Mechanisms and Methods of Kinematic and Kinetostatic Analysis by Imaginary Unknown Parameters,” ASME Paper No. 86-DET-180.
Hang, L. B. , Jin, Q. , Jin, J. , Wu ., and Yang, T.-L. , 2000, “ A General Study of the Number of Assembly Configurations for Multi-Circuit Planar Linkages,” J. Southeast Univ., 16(1), pp. 46–51.
Nicolas, R. , and Federico, T. , 2012, “ On Closed-Form Solutions to the Position Analysis of Baranov Trusses,” Mech. Mach. Theory, 50(2), pp. 179–196. [CrossRef]
Hahn, E. , and Shai, O. , 2016, “ A Single Universal Construction Rule for the Structural Synthesis of Mechanisms,” ASME Paper No. IDETC/CIE 2016-59133.
Hahn, E. , and Shai, O. , 2016, “ Construction of Baranov Trusses Using a Single Universal Construction Rule,” ASME Paper No. IDETC/CIE 2016-59134.
Shi, Z.-X. , Luo, Y.-F. , Hang, L.-B. , and Yang, T.-L. , 2007, “ A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot,” ASME J. Mech. Des., 129(8), pp. 793–798. [CrossRef]
Jin, Q. , and Yang, T.-L. , 2002, “ Over-Constraint Analysis on Spatial 6-Link Loops,” Mech. Mach. Theory, 37(3), pp. 267–278. [CrossRef]
Feng, Z.-Y. , Zhang, C. , and Yang, T.-L. , 2006, “ Direct Displacement Solution of 4-DOF Spatial Parallel Mechanism Based on Ordered Single-Open-Chain,” Chin. J. Mech. Eng., 42(7), pp. 35–38. [CrossRef]
Shi, Z.-X. , Luo, Y.-F. , and Yang, T.-L. , 2006, “ Modular Method for Kinematic Analysis of Parallel Manipulators Based on Ordered SOCs,” ASME Paper No. DETC2006-99089.
Shen, H. , Shao, G. , Deng, J. , and Yang, T.-L. , 2017, “ A Novel 3T1R Parallel Robot 2 PaRSS: Design and Kinematics,” ASME Paper No. DETC2017-67265.
Zhang, J.-Q. , and Yang, T.-L. , 1994, “ A New Method and Automatic Generation for Dynamic Analysis of Complex Planar Mechanisms Based on the SOC,” ASME Design Technical Conference, pp. 215–220.
Yang, T.-L. , Li, H.-L. , and Luo, Y.-F. , 1991, “ On the Structure of Dynamic Equation of Any Mechanical System,” Chin. J. Mech. Eng., 27(4), pp. 1–15. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

Assur kinematic chain decomposed into links and kinematic pairs

Grahic Jump Location
Fig. 1

Four-branch parallel mechanism decomposed into four driving pairs and two AKCs: (a) KC[F = 4,ν = 3], (b) Jd[F = 4], (c) AKC1[ν1 =1], and (d) AKC2[ν2 = 2]

Grahic Jump Location
Fig. 3

Assur kinematic chain decomposed into loops: (a) AKC [ν = 2], (b) SLC1 {−USSU−}, and (c) SLC2{−U−S−R⊥R︷−}

Grahic Jump Location
Fig. 4

Mechanism composition principle based on SOC unit

Grahic Jump Location
Fig. 5

Assur kinematic chain decomposed into SOCs: (a) AKC [ν = 2], (b) SOC1{−U−S−R⊥R︷−}, and (c) SOC2 {−SU−}

Grahic Jump Location
Fig. 7

Three-SOC{−R∥R∥R−} spatial AKC

Grahic Jump Location
Fig. 6

A planar three-loop AKC

Grahic Jump Location
Fig. 8

Three-SOC{−R⊥P−S−} PM

Grahic Jump Location
Fig. 12

A (2T-2R) parallel mechanism

Grahic Jump Location
Fig. 9

The smallest group during structure decomposition

Grahic Jump Location
Fig. 10

A five-loop planar mechanism

Grahic Jump Location
Fig. 11

A (3T-1R) parallel mechanism [35]

Grahic Jump Location
Fig. 13

Assur kinematic chain displacement analysis

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In