Research Papers

Autogenerating/Drawing Valid Arrays and Contracted Graphs With Pentagonal Links for Type Synthesis of Mechanism by Computer Aided Design

[+] Author and Article Information
Yi Lu

College of Mechanical Engineering,
Yanshan University,
Qinhuangdao, Hebei 066004, China;
Parallel Robot and Mechatronic
System Laboratory of Hebei province,
Key Laboratory of Advanced Forging and
Stamping Technology and
Science of Ministry of National Education,
Yanshan University,
Qinhuangdao, Hebei 066004, China
e-mail: luyi@ysu.edu.cn

Hui Huang

College of Mechanical Engineering,
Yanshan University,
Qinhuangdao, Hebei 066004, China
e-mail: xiaobao1810@163.com

Yang Lu

e-mail: deersheepxn@163.com

Nijia Ye

e-mail: nijiareborn@163.com
Harbin Electric Corporation (QHD),
Heavy Equipment Company Limited,
Qinhuangdao, Hebei 066206, China

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 14, 2012; final manuscript received January 6, 2013; published online September 11, 2013. Assoc. Editor: Delun Wang.

J. Mechanisms Robotics 5(4), 041007 (Sep 11, 2013) (8 pages) Paper No: JMR-12-1029; doi: 10.1115/1.4024920 History: Received March 14, 2012; Revised January 06, 2013

A method for autogeneration/draw of valid arrays and contracted graphs by cad is studied in this paper. First, the concepts and relative new criteria of arrays and contracted graphs (CGs) are explained for the representation/generation of the CGs and the identification of the isomorphic/invalid CGs using the arrays. Second, a software is created in Visual Basic for automatically generating the arrays of the CGs with pentagonal links, identifying the isomorphic/invalid arrays, generating the valid arrays, and automatically drawing their CGs. Third, the interface of the software and the main functions of the compiled programs are explained. Finally, some examples are given to illustrate this software and method.

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Crossley, F. E., 1965, “The Permutations of Kinematic Chains of Eight Members or Less From the Graph Theoretic Viewpoint,” Developments in Theoretical and Applied Mechanisms, Vol. 2, W. A.Shaw, ed., Pergamon, Oxford, pp. 467–486.
Dobrjanskyj, L., and Freudenstein, F., 1967, “Some Applications of Graph Theory to the Structural Analysis of Mechanisms,” ASME J. Eng. Ind., 89, pp. 153–158. [CrossRef]
Sohn, W. J., and Freudenstein, F., 1986, “An Application of Dual Graphs to the Automatic Generation of the Kinematic Structures of Mechanisms,” ASME Design Engineering Technical Conference, Columbus, OH.
Vucina, D., and Freudenstein, F., 1991, “Application of Graph Theory and Nonlinear Programming to the Kinematic Synthesis of Mechanisms,” Mech. Mach. Theory, 26(6), pp. 553–563. [CrossRef]
Tsai, L. W., 2001, Mechanism Design: Enumeration of Kinematic Structures According to Function, CRC Press, Boca Raton, FL., pp. 102.
Yan, H. S., and Hsu, C. H., 1988, “Contracted Graphs of Kinematic Chains With Multiple Joints,” Math. Comput. Modell., 10(9), pp. 681–695. [CrossRef]
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]
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.
Gogu, G., 2005, “Mobility of Mechanisms: A Critical Review,” Mech. Mach. Theory, 40, pp. 1068–1097. [CrossRef]
Lu, Y., and Leinonen, T., 2005, “Type Synthesis of Unified Planar–Spatial Mechanisms by Systematic Linkage and Topology Matrix- Graph Technique,” Mech. Mach. Theory, 40(10), pp. 1145–1163. [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]
Yan, H. S., and Kuo, C. H., 2006, “Topological Representations and Characteristics of Variable Kinematic Joints,” ASME J. Mech. Des., 128(2), pp. 384–391. [CrossRef]
Hervé, J. M., 1999, “The Lie Group of Rigid Displacements, a Fundamental Tool for Mechanical Design,” Mech. Mach. Theory, 34(5), pp. 719–730. [CrossRef]
Pucheta, M. A., and Alberto, C., 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 Alberto, C., 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]
Saxena, A., and Ananthasuresh, G. K., 2003, “A Computational Approach to the Number of Synthesis of Linkages,” ASME J. Mech. Des., 125(1), pp. 110–118. [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]
Huang, Z., and Ding, H. F., 2007, “Theory of Loop Algebra on Multi-Loop Kinematic Chains and its Application,” Sci. China, Ser. E: Technol. Sci., 50(4), pp. 437–447. [CrossRef]
Kong, X. W., and Gosselin, C. M., 2007, “Type Synthesis of Parallel Mechanisms,” Springer Tracts in Advanced Robotics, Springer, Heidelberg.
Tuttle, E. R., Peterson, S. W., and Titus, J. E., 1989, “Further Applications of Group Theory to the Enumeration and Structural Analysis of Basic Kinematic Chains,” ASME J. Mech. Transm., Autom. Des., 111, pp. 494–497. [CrossRef]
Hess-Coelho, T. A., 2006, “Topological Synthesis of a Parallel Wrist Mechanism,” ASME J. Mech. Des., 128(1), pp. 230–235. [CrossRef]
Lu, Y., Mao, B. Y., and Yu, J. P., 2011, “Derivation of Valid Contracted Graphs With Pentagonal Links Plus Quaternary Links or Ternary Links for Closed Mechanisms by Arrays,” Proc. Inst. Mech. Eng., Part C (J. Mech. Eng. Sci.), 225(4), pp. 1001–1013. [CrossRef]
Schütz, D., and Wahl, F. M., 2011, “Robotic Systems for Handling and Assembly,” Springer Tracts in Advanced Robotics, Vol. 67, Springer, New York, pp. 17–37.
Chu, J. K., Zhang, R., and Chen, Z. P., 2011, “A Novel SU-8 Electrothermal Microgripper Based on the Type Synthesis of the Kinematic Chain Method and the Stiffness Matrix Method,” J. Micromech. Microeng., 21(5), p. 054030. [CrossRef]
Kong, X. W., 2011, “Type Synthesis of 3-DOF Parallel Manipulators With Both Planar and Translational Operation Modes,” Proceedings of the ASME Design Engineering Technical Conference, Vols. 6, A and B, pp. 1059–1067.
Yu, J., Li, S., Su, H.-J., and Culpepper, M. L., 2011, “Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms,” ASME J. Mech. Rob., 3(3), p. 03100. [CrossRef]
Huang, Z., Liu, Q. F., and Li, Y. W., 2011, Discussion on Degree of Freedom of Mechanism, Science Press, Bejing.


Grahic Jump Location
Fig. 1

Some CGs with 2P + 2Q, P + 5T

Grahic Jump Location
Fig. 2

A main interface of software (a, d), A subwindow (b, c)

Grahic Jump Location
Fig. 3

A subprogram flow of generating the whole queues

Grahic Jump Location
Fig. 4

A subprogram flow of generating array matrix

Grahic Jump Location
Fig. 5

A tree for generating the whole arrays of PQPQ

Grahic Jump Location
Fig. 6

A flow diagram of program for generating arrays in which the last digit of the jth string is the 1st digit of the (j + 1)th string (a) and its subprogram for j = 4 (b)

Grahic Jump Location
Fig. 7

and a flow diagram of its subprogram for j = 4

Grahic Jump Location
Fig. 8

A flow diagram of subprogram for removing arrays

Grahic Jump Location
Fig. 9

A subprogram flow for removing the nonpair arrays

Grahic Jump Location
Fig. 10

A flow diagram of subprogram for identifying ordering isomorphic arrays

Grahic Jump Location
Fig. 11

Four CGs and the PMs




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