Abstract
We proved several theorems about the Rubik’s snake toy, which has a chain-like structure with applications in robot design. These mathematical theories can guide people to design beautiful shapes using the Rubik’s snake. We presented an example for shape design to demonstrate the effectiveness of our approach.
Issue Section:
Technical Brief
References
1.
Fiore
, A.
, 1981
, Shaping Rubik’s Snake
, Penguin Books
, Harmondsworth, Middlesex, England
.2.
Korf
, R. E.
, 1982
, “A Program that Learns to Solve Rubik’s Cube.
,” AAAI-82 proceedings
, pp. 164
–167
.3.
Niblo
, G.
, and Roller
, M.
, 1998
, “Groups Acting on Cubes and Kazhdan’s Property (t)
,” Proc. Am. Math. Soc.
, 126
(3
), pp. 693
–699
. 10.1090/S0002-9939-98-04463-34.
Ding
, X.
, Lu
, S.
, and Yang
, Y.
, 2011
, “Configuration Transformation Theory From a Chain-type Reconfigurable Modular Mechanism-rubik’s Snake
,” The 13th World Congress in Mechanism and Machine Science
, Guanajuato, Mexico
, June
.5.
Ding
, X.
, and Lu
, S.
, 2013
, “Fundamental Reconfiguration Theory of Chain-Type Modular Reconfigurable Mechanisms
,” Mech. Mach. Theory.
, 70
, pp. 487
–507
. 10.1016/j.mechmachtheory.2013.08.0116.
Iguchi
, K.
, 1998
, “A Toy Model for Understanding the Conceptual Framework of Protein Folding: Rubik’s Magic Snake Model
,” Mod. Phys. Lett. B.
, 12
(13
), pp. 499
–506
. 10.1142/S02179849980006037.
Liu
, J.
, Zhang
, X.
, Zhang
, K.
, Dai
, J. S.
, Li
, S.
, and Sun
, Q.
, 2018
, “Configuration Analysis of a Reconfigurable Rubik’s Snake Robot
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 233
(9
), pp. 3137
–3154
. 10.1177/09544062188051128.
White
, P. J.
, Revzen
, S.
, Thorne
, C. E.
, and Yim
, M.
, 2011
, “A General Stiffness Model for Programmable Matter and Modular Robotic Structures
,” Robotica
, 29
(1 SPEC. ISSUE
), pp. 103
–121
. 10.1017/S02635747100007439.
Zhang
, X.
, and Liu
, J.
, 2016
, “Prototype Design of a Rubik Snake Robot
,” Mech. Mach. Sci.
, 36
, pp. 581
–591
.10.
Liu
, J.
, Zhang
, X.
, and Hao
, G.
, 2016
, “Survey on Research and Development of Reconfigurable Modular Robots
,” Adv. Mech. Eng.
, 8
(8
), pp. 1
–21
.11.
Liu
, J.
, Wang
, Y.
, Ma
, S.
, and Li
, Y.
, 2010
, “Enumeration of the Non-isomorphic Configurations for a Reconfigurable Modular Robot with Square-cubic-cell Modules
,” Int. J. Adv. Rob. Syst.
, 7
(4
), pp. 58
–68
.12.
Stoy
, K.
, and Brandt
, D.
, 2013
, “Efficient Enumeration of Modular Robot Configurations and Shapes
,” IEEE International Conference on Intelligent Robots and Systems
, Tokyo, Japan
, Nov. 3–7
, pp. 4296
–4301
.13.
Zhang
, X.
, Liu
, J.
, Feng
, J.
, Liu
, Y.
, and Ju
, Z.
, 2020
, “Effective Capture of Nongraspable Objects for Space Robots Using Geometric Cage Pairs
,” IEEE/ASME Trans. Mech.
, 25
(1
), pp. 95
–107
. 10.1109/TMECH.2019.295255214.
Yim
, M.
, Roufas
, K.
, Duff
, D.
, Zhang
, Y.
, Eldershaw
, C.
, and Homans
, S.
, 2003
, “Modular Reconfigurable Robots in Space Applications
,” Auto. Rob.
, 14
(2–3
), pp. 225
–237
. 10.1023/A:102228782080815.
Li
, Z.
, Hou
, S.
, and Bishop
, T.
, 2020
, “Computational Design and Analysis for a Magic Snake
,” ASME J. Mech. Rob.
, 12
(5
), p. 054501
. 10.1115/1.404635116.
Bondy
, J. A.
, and Murty
, U. S. R.
, 1976
, Graph Theory with Applications
, Elsevier Science Ltd.
, Oxford, UK
.17.
Adams
, C. C.
, and Franzosa
, R. D.
, 2008
, Introduction to Topology: Pure and Applied
, Pearson Prentice Hall
, Upper Saddle River, NJ
.Copyright © 2020 by ASME
You do not currently have access to this content.
