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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2013, Vol. 8 Issue (1) : 3-9
Polyhedral linkages obtained as assemblies of planar link groups
1. Department of Mechanical Engineering, Izmir Institute of Technology, Izmir 35430, Turkey; 2. Department of Mechanical Engineering, Middle East Technical University, Ankara 06531, Turkey
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The study aims to devise means of obtaining polyhedral linkages for homothetic deployment of polyhedral shapes by embedding planar link groups in faces of the polyhedral shape of interest. The questions of which polyhedral shapes may be suitable for such a purpose and what are the compatibility conditions for spatially assembling planar link groups are addressed. Homohedral and tangential polyhedral shapes are found to be suitable for the task and some examples of linkages are worked out.

Keywords polyhedral linkages      homothety      homohedra      tangential polyhedra     
Corresponding Author(s): KİPER GÖkhan,   
Issue Date: 05 March 2013
 Cite this article:   
GÖ,khan Kİ,PER, et al. Polyhedral linkages obtained as assemblies of planar link groups[J]. Front. Mech. Eng., 2013, 8(1): 3-9.
Fig.1  Polygonal kinematic chain
Fig.2  (a) Variable+ fixed length example; (b) fixed+ variable length example;(c) variable+ variable length example
Fig.3  Octahedral linkage in compact, deployed and further actuated forms
Fig.4  Octahedral linkage with different dimensioning in compact and deployed forms
Fig.5  Adjacent faces of a tangential polyhedron
Fig.6  Tetrahedral linkage in compact and deployed forms
Fig.7  Hexahedral linkage in compact and deployed forms
Fig.8  Cubic linkage in compact and deployed forms
1 Bricard R. Mémoire sur la théorie de l’octaèdre articulé. Journal de Mathématiques Pures et Appliquées , 1897, 3: 113–150
2 Bennett G T. Deformable octahedra. In: Proceedings London Mathematical Society, 2nd Series , 1911, 10: 309–343
3 Goldberg M. Polyhedral linkages. National Mathematics Magazine , 1942, 16(7): 323–332
doi: 10.2307/3028440
4 Fuller R B, Krausse J, Lichtenstein C. Your Private Sky: The Art of Design Science . Lars Müller, 1999
5 Fuller R B. Synergetics: Explorations in the Geometry of Thinking. Macmillan , 1975
6 Verheyen H F. The complete set of Jitterbug transformers and the analysis of their motion. Computers & Mathematics with Applications, 1989, 17(1–3): 203–250
doi: 10.1016/0898-1221(89)90160-0
7 Wohlhart K. Heureka octahedron and Brussels folding cube as special cases of the turning tower. In: Proceedings of the 6th IFToMM International Symposium on Linkages and Computer Aided Design Methods , Bucharest, 1993, 325–332
8 Wohlhart K. The screwtower, an overconstrained multi-loop space mechanism. In: Proceedings of the International Conference on Spatial Mechanisms and High-Class Mechanisms , Almaty, 1994, 38–45
9 Wohlhart K. New overconstrained spheroidal linkages. In: Proceedings of the 9th IFToMM Congress , Milano, 1995, 149–155
10 R?schel O. Zwangl?ufig bewegliche Polyedermodelle I. Math Pann , 1995, 6: 267–284
11 R?schel O. Zwangl?ufig bewegliche Polyedermodelle II. Studia Scientiarum Mathematicarum Hungarica , 1996, 32: 383–393
12 R?schel O. Zwangl?ufig bewegliche Polyedermodelle III. Math Pann , 2001, 12: 55–68
13 Kiper G, S?ylemez E. Homothetic Jitterbug-like linkages. Mechanism and Machine Theory , 2012, 51: 145–158
doi: 10.1016/j.mechmachtheory.2011.11.014
14 Gosselin C M, Gagnon-Lachance D. Expandable polyhedral mechanisms based on polygonal one-degree-of-freedom faces. Proceedings of the Institution of Mechanical Engineers Part C: Mechanical Engineering Science , 2006, 220(7): 1011–1018
doi: 10.1243/09544062JMES174
15 Kiper G, S?ylemez E, Ki?isel A U ?. A family of deployable polygons and polyhedra. Mechanism and Machine Theory , 2008, 43(5): 627–640
doi: 10.1016/j.mechmachtheory.2007.04.011
16 Kiper G, S?ylemez E. Irregular polygonal and polyhedral linkages comprising scissor and angulated elements. In: Proceedings of the 1st IFToMM Asian Conference on Mechanism and Machine Science , Taipei, 2010
17 Wohlhart K. Regular polyhedral linkages. In: Proceedings of the 2nd Workshop on Computational Kinematics , Seoul, 2001, 239–248
18 Wohlhart K. New regular polyhedral linkages. In: Proceedings of the SYROM 2001 , Bucharest, 2001, 365–370
19 Wohlhart K. Irregular polyhedral linkages. In: Proceedings of the 11th World Congress in Mechanism and Machine Sciences , Tianjin, 2004, 1083–1087
20 Wohlhart K. Double pyramidal linkages. In: Proccegings of the 11th International Symposium on Theory of Machines and Mechanisms , Bucharest, 2005, 293–300
21 Wohlhart K. Double-ring polyhedral linkages. In: Proceedings of the Conference on Interdisciplinary Applications of Kinematics , Lima, 2008,1–17
22 Kiper G, S?ylemez E. Obtaining new linkages from Jitterbug-like polyhedral linkages. In: Proceedings of the AzC IFToMM 2010 International Symposium of Mechanism and Machine Science , ?zmir, 2010, 137–143
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