Eversible duoprism mechanism

Abstract

In this study, a novel duoprism mechanism that demonstrates a fascinating eversion motion is developed. The mechanism comprises three scalable platforms and nine retractable limbs and is constructed by inserting prismatic and revolute joints into the edges and vertices of the duoprism, respectively. According to mobility and kinematic analyses, the mechanism has five degrees of freedom. Six inputs, including a redundant one, are required to overcome singularity and achieve an eversion motion. In the eversion motion, three platforms expand/contract synchronously, and the mechanism continuously turns inside out. The detailed gaits of eversion motion along an ellipse and a circle after a cycle are illustrated with two examples. A kinematic simulation is conducted, and a manual prototype is fabricated to verify the feasibility of the eversible duoprism mechanism.

Keywords

duoprism / eversion motion / singularity / over-constrained

References

[1] Kovács F, Tarnai T, Guest S D, Double-link expandohedra: A mechanical model for expansion of a virus. Proceedings: Mathematical, Physical and Engineering Sciences, 2004, 460(2051): 3191–3202

[2] Hoberman C. US Patent, 4942700, 1990-07-24

[3] Agrawal S K, Kumar S, Yim M. Polyhedral single degree-of-freedom expanding structures: Design and prototypes. Journal of Mechanical Design, 2002, 124(3): 473–478

[4] Hamlin G J, Sanderson A C. Tetrobot: A modular approach to parallel robotics. IEEE Robotics & Automation Magazine, 1997, 4(1): 42–50

[5] Clark P E, Curtis S A, Rilee M L. A new paradigm for robotic rovers. Physics Procedia, 2011, 20: 308–318

[6] Coxeter H S M. Regular Polytopes. New York: Dover Publications, 1973, 124

[7] Stalker R M U S. US Patent, 1997022, <Date>1935-04-09</Date>

[8] Rouse Ball W W, Coxeter H S M. Mathematical Recreations & Essays. 11th ed. New York: Macmillan Company, 1947, 153–154

[9] Fowler P W, Guest S D. A symmetry analysis of mechanisms in rotating rings of tetrahedra. Proceedings: Mathematical, Physical and Engineering Sciences, 2005, 461(2058): 1829–1846

[10] Hong D W, Ingram M, Lahr D. Whole skin locomotion inspired by amoeboid motility mechanisms. Journal of Mechanisms and Robotics, 2009, 1(1): 011015

[11] Festo, Inc. Smart Inversion, 2012,http://www.festo.com/cms/en_corp/12748.htm

[12] Li R, Miao Z, Yao Y, A novel hybrid 3-RPR mechanism with scalable platforms for self-crossing locomotion. In: ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014, V05AT08A084–V05AT08A084

[13] Hunt K H. Kinematic Geometry of Mechanisms. Oxford: Clarendon Press, 1990, 33–35

[14] Gosselin C, Angeles J. Singularity analysis of closed-loop kinematic chains. IEEE Transactions on Robotics and Automation, 1990, 6(3): 281–290

[15] Romdhane L. Design and analysis of a hybrid serial-parallel manipulator. Mechanism and Machine Theory, 1999, 34(7): 1037–1055

[16] Gallardo J, Lesso R, Rico J M, The kinematics of modular spatial hyper-redundant manipulators formed from RPS-type limbs. Robotics and Autonomous Systems, 2011, 59(1): 12–21

Acknowledgements

The authors thank Prof. Jian S Dai (Centre for Robotics Research, King’s College London) for suggesting the term “eversible duoprism mechanism”. The authors are also grateful to Dr. Xianwen Kong of Heriot-Watt University for his valuable discussions. This study was supported by the National “Climbing” Program of China (Grant No. 2015BAK04B02).

RIGHTS & PERMISSIONS

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg