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Physically feasible decomposition of Engino® toy models: A graph-theoretic approach

Published online by Cambridge University Press:  04 March 2018

E. N. ANTONIOU ,
A. ARAÚJO ,
M. D. BUSTAMANTE  and
A. GIBALI
E. N. ANTONIOU
Affiliation:
Department of Information Technology, Alexander Technological Educational Institute of Thessaloniki, 57400, Thessaloniki, Greece email: [email protected]
A. ARAÚJO
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal email: [email protected]
M. D. BUSTAMANTE
Affiliation:
Institute for Discovery, School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland email: [email protected]
A. GIBALI
Affiliation:
Department of Mathematics, ORT Braude College, P.O. Box 78, Karmiel 2161002, Israel email: [email protected]
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Abstract

During the 125th European Study Group with Industry held in Limassol, Cyprus, 5–9 December 2016, one of the participating companies, Engino.net Ltd, posed a very interesting challenge to the members of the study group. Engino.net Ltd is a Cypriot company, founded in 2004, that produces a series of toy sets – the Engino® toy sets – consisting of a number of building blocks, which can be assembled by pupils to compose toy models. Depending on the contents of a particular toy set, the company has developed a number of models that can be built utilizing the blocks present in the set; however, the production of a step-by-step assembly manual for each model could only be done manually. The goal of the challenge posed by the company was to implement a procedure to automatically generate the assembly instructions for a given toy. In the present paper, we propose a graph-theoretic approach to model the problem and provide a series of results to solve it by employing modified versions of well-established algorithms in graph theory. An algorithmic procedure to obtain a hierarchical, physically feasible decomposition of a given toy model, from which a series of step-by-step assembly instructions can be recovered, is proposed.

Keywords

05C3805C9068R1094C15
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 2 , April 2019 , pp. 278 - 297
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

†MDB acknowledges support from Science Foundation Ireland under research Grant number 12/IP/1491.

References

[1] Agrawala, M. et al. (2003) Designing effective step-by-step assembly instructions. In: Proceedings of ACM SIGGRAPH 2003 ACM Transactions on Graphics (TOG), Vol. 22, pp. 828–837.Google Scholar
[2] Bang-Jensen, J. & Gutin, G. Z. (2009) Digraphs: Theory, Algorithms and Applications, 2nd ed., Springer-Verlag London.Google Scholar
[3] Bondy, J. A. & Murty, U. S. R. (1976) Graph Theory with Applications. Vol. 290. London: Macmillan.Google Scholar
[4] Cormen, T. H., Leiserson, C. E., Rivest, R. L. & Stein, C. (2001) Introduction to Algorithms, 2nd ed., The MIT Press, Cambridge, Massachusetts, and McGraw-Hill Book Company, Boston.Google Scholar
[5] Dijkstra, E. (1976) A Discipline of Programming, Prentice Hall, NJ.Google Scholar
[6] Hsu, Y.-Y., Tai, P.-H., Wang, M.-W. & Chen, W.-C. (2011) A knowledge-based engineering system for assembly sequence planning. Int. J. Adv. Manuf. Technol. 55, 763–782.Google Scholar
[7] Kassem, S., Lee, A. T., Leigh, D. A., Marcos, V., Palmer, L. I. & Pisano, S. (2017) Stereodivergent synthesis with a programmable molecular machine. Nature 549, 374–378.Google Scholar
[8] Lambert, A. J. D. (2003) Disassembly sequencing: A survey. Int. J. Prod. Res. 41, 3721–3759.Google Scholar
[9] Li, W., Agrawala, M., Curless, B. & Salesin, D. (2008) Automated generation of interactive 3D exploded view diagrams. In: Proceedings of ACM SIGGRAPH 2008 ACM Transactions on Graphics (TOG), Vol. 27, p. 101.Google Scholar
[10] Natarajan, B. K. (1988) On planning assemblies. In: Proceedings of the 4th Annual Symposium on Computational Geometry, ACM, pp. 299–308.Google Scholar
[11] Peysakhov, M., Galinskaya, V. & Regli, W. C. (2000) Representation and evolution of lego-based assemblies. In: Proceedings of the AAAI/IAAI, p. 1089.Google Scholar
[12] Sharir, M. (1981) A strong connectivity algorithm and its applications to data flow analysis. Comput. Math. Appl. 7, 67–72.Google Scholar
[13] Snoeyink, J. & Stolfi, J. (1994) Objects that cannot be taken apart with two hands. Discret. Comput. Geom. 12, 367–384.Google Scholar
[14] Tarjan, R. E. (1972) Depth-first search and linear graph algorithms. SIAM J. Comput. 1, 146–160.Google Scholar
[15] Wang, L., Keshavarzmanesh, S., Feng, H. Y. & Buchal, R. O. (2009) Assembly process planning and its future in collaborative manufacturing: A review. Int. J. Adv. Manuf. Technol. 41, 132–144.Google Scholar
[16] Wilson, R. H. & Latombe, J. C. (1994) Geometric reasoning about mechanical assembly. Artif. Intell. 71, 371–396.Google Scholar