Skip to main content

Advertisement

SpringerLink
Log in

A mixed isomorphism approach for kinematic structure enumeration graphs based on intelligent design and manufacturing

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

When using graph theory for kinematic structure enumeration, the isomorphism identification of graphs is an important and complicated problem. The problem is known to be an NP-complete problem. This paper presents a mixed algorithm based on a mapping property, a genetic algorithm, and a simulated annealing algorithm for the isomorphism identification problem. A validity encoding scheme was developed by considering the mapping relationship between two graphs, and some reset measures for the crossover and mutation operators were developed based on the characteristics in which the encoding cell could not be reiterated. A simulated annealing algorithm was introduced into the mixed algorithm to prevent premature convergence in resolution, and some other measures were developed for improving the efficiency, based on the parameter selection. An example shows that the mixed algorithm is a valid algorithm for the isomorphism identification of kinematic structure graphs in mechanism design. It will be a reliable isomorphism identification algorithm for intelligent computer-aided design (CAD) and manufacturing (CAM).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

V(G):

The vertex set of graph G

E(G):

The line set of graph G

σ :

One-to-one mapping function

u, v :

Elements of V(G)

f :

Fitness function

y :

Objective function

c max :

The artificial maximum value of y

\( f\prime _{a} \) :

The fitness function value at the current solution

\( f\prime _{b} \) :

The fitness function value at the new solution

t 0 :

Initial temperature in simulated annealing process

t :

Temperature in simulated annealing process

a :

Parameter for deciding t

g :

Generation number

p k :

The probabilistic rate from old individual to new individual by introducing the simulated annealing algorithm

References

  1. Tsai LW (2001) Mechanism design: enumeration of kinematic structures according to function. CRC Press, Boca Raton, Florida

    Google Scholar 

  2. Hsu Cheng-Ho (2002) An analytic methodology for the kinematic synthesis of epicyclic gear mechanisms. J Mech Des—Trans ASME 124(3):574–576

    Article  Google Scholar 

  3. Chen L (2000) A selected tour of the theory of identification matrices. Theor Comp Sci 240(2):299–318

    Article  MATH  Google Scholar 

  4. Rao AC (2003) A genetic algorithm for epicyclic gear trains. Mech Mach Theory 38(2):135–147

    Article  MATH  Google Scholar 

  5. Hart RPS, Larcombe MT, Sherlock RA, Smith LA (1998) Optimisation techniques for a computer simulation of a pastoral dairy farm. Comput Electron Agric 19(2):129–153

    Article  Google Scholar 

  6. Bruzzone A, Signorile R (1998) Simulation and genetic algorithms for ship planning and shipyard layout. Simulation 71(2):74–83

    Article  Google Scholar 

  7. McHaney R (1999) Integration of the genetic algorithm and discrete-event computer simulation for decision support. Simulation 72(6):401–411

    Article  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the support of the National Natural Science Foundation of China, the Natural Science Foundation of Guangxi Province of China, the Natural Science Foundation for Qualified Personnel of JiangSu University, and the support program for Young and Middle-aged Disciplinary Leaders at the Guangxi Higher Education Institution, and Innovative Science Foundation of Jiangsu University during the course of this work.

Author information

Authors and Affiliations

  1. Research Center of Micro–Nano Science and Technology, JiangSu University, Zhenjiang, 212013, People’s Republic of China

    Yang Ping, Liao NingBo, Ding JianNing & Yang Jichang

  2. Department of Computer, Huihua Vocational and Technical College, Huihua, 41800, People’s Republic of China

    Yang Bin

Authors
  1. Yang Ping
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liao NingBo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang Bin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ding JianNing
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yang Jichang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Ping.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ping, Y., NingBo, L., Bin, Y. et al. A mixed isomorphism approach for kinematic structure enumeration graphs based on intelligent design and manufacturing. Int J Adv Manuf Technol 31, 841–845 (2007). https://doi.org/10.1007/s00170-005-0263-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-005-0263-y

Keywords

Search

Navigation