Research Papers

Automatic Structural Synthesis of the Whole Family of Planar 3-Degrees of Freedom Closed Loop Mechanisms

[+] Author and Article Information
Huafeng Ding

College of Mechanical Engineering and
Applied Electronics Technology,
Beijing University of Technology,
Beijing 100124, China
Hebei Provincial Key Laboratory of Parallel Robot
and Mechatronic System,
Yanshan University,
Qinhuangdao 066004, China
e-mail: dhf@ysu.edu.cn

Peng Huang

Hebei Provincial Key Laboratory of Parallel Robot
and Mechatronic System,
Yanshan University,
Qinhuangdao 066004, China
e-mail: h1985p@163.com

Jingfang Liu

College of Mechanical Engineering and
Applied Electronics Technology,
Beijing University of Technology,
Beijing 100124, China
e-mail: jfliu@bjut.edu.cn

Andrés Kecskeméthy

Chair for Mechanics and Robotics
University of Duisburg-Essen,
Duisburg 47057, Germany
e-mail: andres.kecskemethy@uni-due.de

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received August 28, 2011; final manuscript received April 18, 2013; published online September 11, 2013. Assoc. Editor: Qiaode Jeffrey Ge.

J. Mechanisms Robotics 5(4), 041006 (Sep 11, 2013) (10 pages) Paper No: JMR-11-1098; doi: 10.1115/1.4024919 History: Received August 28, 2011; Revised April 18, 2013

Conception of the kinematic structures with better performance has been a challenging, yet pivotal issue, since the beginning of the design of mechanisms or robots. This paper proposes a systematic method to synthesize and classify automatically all the valid kinematic structures of planar 3-DOF closed loop mechanisms or robots. First, after the structure representation graphs of planar mechanisms or robots are addressed, the unique representation of both contracted graphs and topological graphs is proposed and used to detect isomorphism in the synthesis process. Then the valid atlas database of the contracted graphs for planar 3-DOF closed loop mechanisms or robots up to 16-link is built. Based on the atlas database, an automatic synthesis method is proposed to synthesize all the kinematic structures of planar 3-DOF closed loop mechanisms or robots, and the complete atlas database with all the valid kinematic structures classified for planar 3-DOF closed loop mechanisms or robots up to 16-link is established. The creative design of 3-DOF heavy-load hydraulic robots is conducted to show the usefulness of the established atlas database.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Yan, H. S., 1998, Creative Design of Mechanical Devices, Springer-Verlag, Singapore.
Döring, U., Brix, T., and Reeßing, M., 2006, “Application of Computational Kinematics in the Digital Mechanism and Gear Library DMG-Lib,” Mech. Mach. Theory, 41(8) pp. 1003–1015. [CrossRef]
Al-Dweiri, A. F., Dweiri, F. T., and Ashour, O. M., 2010, “A Novice-Centered Decision-Support System for Type Synthesis of Function-Generation Mechanisms,” Mech. Mach. Theory, 45(9), pp. 1252–1268. [CrossRef]
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, II,” Bull. Petrograd Polytech. Inst., 20, pp. 329–386; 21, pp. 187–283 (1914); 21–23 (1914–1916).
Manolescu, N. I., 1968, “For a United Point of View in the Study of the Structural Analysis of Robots and Mechanisms,” J. Mech., 3(3), pp. 149–169. [CrossRef]
Manolescu, N. I., 1973, “A Method Based on Baranov Trusses and Using Graph Theory to Find the set of Planar Jointed Robots and Mechanisms,” Mech. Mach. Theory, 8(1), pp. 3–22. [CrossRef]
Davies, T. H., and Crossley, F. R. E., 1966, “Structural Analysis of Plane Linkages by Franke’s Condensed Notation,” J. Mech., 1, pp. 171–183. [CrossRef]
Crossley, F. R. E., 1965, “The Permutations of Robots of Eight Members or Less From the Graph-Theoretic View Point,” Developments in Theoretical and Applied Mechanics, Vol. 2, Pergamon, Oxford, pp. 467–486.
Woo, L. S., 1967, “Type Synthesis of Plane Linkages,” ASME J. Eng. Ind., 89B, pp. 159–172. [CrossRef]
Dobrjanskyj, L., and Freudenstein, F., 1967, “Some Applications of Graph Theory to the Structural Analysis of Mechanisms,” ASME J. Eng. Ind., 89B, pp. 153–158. [CrossRef]
Mruthyunjaya, T. S., 1979, “Structural Synthesis by Transformation of Binary Chains,” Mech. Mach. Theory, 14(4), pp. 221–231. [CrossRef]
Yan, H. S., and Hwang, Y. W., 1990, “Number Synthesis of Robots Based on Permutation Groups,” Math. Comput. Modell., 13(8), pp. 29–42. [CrossRef]
Yan, H. S., 1992, “A Methodology for Creative Mechanism Design,” Mech. Mach. Theory, 27(3), pp. 235–242. [CrossRef]
Hwang, W. M., and Hwang, Y. W., 1992, “Computer-Aided Structural Synthesis of Planar Robots With Simple Joints,” Mech. Mach. Theory, 27(2), pp. 189–199. [CrossRef]
Dai, J. S., and Rees Jones, J., 1999, “Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds,” ASME J. Mech. Des., 121(3), pp. 375–382. [CrossRef]
Li, D., Zhang, Z., and McCarthy, J. M., 2011, “A Constraint Graph Representation of Metamorphic Linkages,” Mech. Mach. Theory, 46(2), pp. 228–238. [CrossRef]
Gan, D. M., Dai, J. S., and Liao, Q. Z., 2010, “Constraint Analysis on Mobility Change of a Novel Metamorphic Parallel Mechanism,” Mech. Mach. Theory, 45(12), pp. 1864–1876. [CrossRef]
Johnson, R. C., 1987, Mechanical Design Synthesis-Creative Design and Optimize, 2nd ed., Huntington, New York.
Gogu, G., 2008, Structural Synthesis of Parallel Robots: Part 1: Methodology, Springer, New York.
Liu, X-J., Wang, J., and Pritschow, G., 2005, “A New Family of Spatial 3-DOF Fully-Parallel Manipulators With High Rotational Capability,” Mech. Mach. Theory, 40(4), pp. 475–494. [CrossRef]
Huang, Z., and Li, Q. C., 2002, “General Methodology for Type Synthesis of Lower-Mobility Symmetrical Parallel Manipulators and Several Novel manipulators,” Int. J. Robot. Res., 21(2), pp. 131–145. [CrossRef]
Kong, X. W., and Gosselin, C. M., 2004, “Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Screw Theory,” ASME J. Mech. Des., 126(1), pp. 83–92. [CrossRef]
Hess-Coelho, T. A., 2006, “Topological Synthesis of a Parallel Wrist Mechanism,” ASME J. Mech. Des., 128(1), pp. 230–235. [CrossRef]
Yan, H. S., and Kang, C. H., 2009, “Configuration Synthesis of Mechanisms With Variable Topologies,” Mech. Mach. Theory, 44(5), pp. 896–911. [CrossRef]
Herve, J. H., 1999, “The Lie Group of Rigid Displacements, A Fundamental Tool for Mechanical Design,” Mech. Mach. Theory, 34, pp. 719–730. [CrossRef]
Li, Q. C., and Herve, J. M., 2009, “Parallel Mechanisms With Bifurcation of Schoenflies Motion,” IEEE Trans. Robot., 25(1), pp. 158–164. [CrossRef]
Pucheta, M. A., and Cardona, A., 2007, “An Automated Method for Type Synthesis of Planar Linkages Based on a Constrained Subgraph Isomorphism Detection,” Multibody Syst. Dyn., 18(2), pp. 233–258. [CrossRef]
Pucheta, M. A., and Cardona, A., 2008, “Synthesis of Planar Multiloop Linkages Starting From Existing Parts or Mechanisms: Enumeration and Initial Sizing,” Mech. Based Des. Struct. Mach., 36(4), pp. 364–391. [CrossRef]
Wang, X. Y., Baron, L., and Cloutier, G., 2008, “Topological and Geometrical Synthesis of Three-Degree-Of-Freedom Fully Parallel Manipulators by Instantaneous Kinematics,” ASME J. Mech. Des., 130(3), p. 032301. [CrossRef]
Lu, Y., and Ding, L., 2010, “Autoderivation of Topological Graphs for Type Synthesis of Planar 3DOF Parallel Mechanisms,” ASME J. Mech. Robot., 2(1), p. 011002. [CrossRef]
Ding, H. F., Hou, F. M., Kecskeméthy, A., and Huang, Z., 2011, “Synthesis of a Complete Set of Contracted Graphs for Planar Non-Fractionated Simple-Jointed Kinematic Chains With All Possible DOFs,” Mech. Mach. Theory, 46(11), pp. 1588–1600. [CrossRef]
Ding, H. F., Hou, F. M., Kecskeméthy, A., and Huang, Z., 2012, “Synthesis of the Whole Family of Planar 1-DOF Kinematic Chains and Creation of their Atlas Databases,” Mech. Mach. Theory, 47(1), pp. 1–15. [CrossRef]
Ding, H. F., and Huang, Z., 2009, “Isomorphism Identification of Graphs: Especially for the Graphs of Kinematic Chains,” Mech. Mach. Theory, 44(1), pp. 122–139. [CrossRef]
Ding, H. F., Huang, Z., Mu, D. J., 2008, “Computer-Aided Structure Decomposition Theory of Kinematic Chains and its Applications,” Mech. Mach. Theory, 43(12), pp. 1596–1609. [CrossRef]


Grahic Jump Location
Fig. 2

A contracted graph for 3-DOF mechanisms with 16 links

Grahic Jump Location
Fig. 1

(a) A hydraulic excavator, (b) the main mechanism, (c) its kinematic chain, (d) its topological graph, and (e) its contracted graph

Grahic Jump Location
Fig. 4

Unique labeling of edges for the contracted graph in Fig. 1(e)

Grahic Jump Location
Fig. 11

Other 24 feasible kinematic structures of 3-DOF heavy-load hydraulic robots

Grahic Jump Location

The contracted graph corresponding to “[8,3,0,1]”




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