Exploring Topological and Geometric Combination Indexfor Overhand Knot Formation

Chen Junrong; Hang Lubin; Huang Xiaobo; Wang Qiansheng; Liu Ziyu; Bai Lele

doi:10.13433/j.cnki.1003-8728.20190353

Volume 39 Issue 12

Dec. 2020

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Article Navigation > Mechanical Science and Technology for Aerospace Engineering > 2020 > 39(12): 1937-1943

Chen Junrong, Hang Lubin, Huang Xiaobo, Wang Qiansheng, Liu Ziyu, Bai Lele. Exploring Topological and Geometric Combination Indexfor Overhand Knot Formation[J]. Mechanical Science and Technology for Aerospace Engineering, 2020, 39(12): 1937-1943. doi: 10.13433/j.cnki.1003-8728.20190353

Citation:

Chen Junrong, Hang Lubin, Huang Xiaobo, Wang Qiansheng, Liu Ziyu, Bai Lele. Exploring Topological and Geometric Combination Indexfor Overhand Knot Formation[J]. Mechanical Science and Technology for Aerospace Engineering, 2020, 39(12): 1937-1943. doi: 10.13433/j.cnki.1003-8728.20190353

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Exploring Topological and Geometric Combination Indexfor Overhand Knot Formation

doi: 10.13433/j.cnki.1003-8728.20190353

School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

Received Date: 2019-10-24
Available Online: 2020-12-08
Publish Date: 2020-12-05

Abstract

Abstract

The topological and geometric control of the morphology of a rope belt in the knotting process iskeyto the development of a new knotting mechanism. Based on the Reidemeister fundamental transformation of the knot theory, the equivalent operation and formation principles of the rope beltduring the overhand knot forming process are proposed. A new knotting mechanism is built with the non-integral hollow gear disk that drives rope belt winding and the arc facade cam thatsupports the rope belt. The movable arm gripper picks up and fixes the rope belt. The topological and geometric combination index is constructed by using the cross-points of the rope belt and the extreme points of the catenary, and the knotting process is divided into four key stages. The geometric form of the boundary transient rope belt is solved by using the catenary theory. The experimental results show that the topological and geometriccontrol of the morphology of the boundary transient rope belt is realized and that the shape of the rope belt is maintained in the knotting process of the new knotting mechanism.
- knot theory,
- overhand knot,
- knotting mechanism,
- catenary theory,
- topological and geometric combination index

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References(17)

References

[1]	徐广明, 陶永红. 打结器的应用与发展简论[J]. 中国高新技术企业, 2007,(12): 97 doi: 10.3969/j.issn.1009-2374.2007.12.064 Xu G M, Tao Y H. A simple comment on application and development of knotter[J]. China High-Tech Enterprises, 2007,(12): 97 (in Chinese) doi: 10.3969/j.issn.1009-2374.2007.12.064
[2]	姜伯驹. 绳圈的数学[M]. 辽宁大连: 大连理工大学出版社, 2011. Jiang B J. Mathematics of string figures[M]. Liaoning Dalian: Dalian University of Technology Press, 2011 (in Chinese).
[3]	Chiodo M. An introduction to braid theory[D]. Melbourne: University of Melbourne, 2005.
[4]	Yamakawa Y, Namiki A, Ishikawa M, et al. Planning of knotting based on manipulation skills with consideration of robot mechanism/motion and its realization by a robot hand system[J]. Symmetry, 2017, 9(9): 194
[5]	Wang W F, Balkcom D. Knot grasping, folding, and re-grasping[J]. The International Journal of Robotics Research, 2018, 37(2-3): 378-399
[6]	Kudoh S, Gomi T, Katano R, et al. In-air knotting of rope by a dual-arm multi-finger robot[C]//2015 IEEE/RSJ International Conference on Intelligent Robots and Systems. Hamburg: IEEE, 2015: 6202-6207.
[7]	Wang W F, Bell M P, Balkcom D, et al. Towards arranging and tightening knots and unknots with fixtures[M]//Akin H L, Amato N M, Isler V, et al. Algorithmic Foundations of Robotics XI. Cham: Springer, 2015.
[8]	Van Vinh T, Tomizawa T, Kudoh S, et al. Knotting task execution based a hand-rope relation[J]. Advanced Robotics, 2017, 31(11): 570-579
[9]	黄松檀, 胡冲, 吕俊杰, 等. 新型打结装置打结过程的关键参数研究[J]. 机电工程, 2018, 35(3): 261-265 doi: 10.3969/j.issn.1001-4551.2018.03.009 Huang S T, Hu C, Lü J J, et al. Key parameters of knotting process of new knot tying device[J]. Journal of Mechanical & Electrical Engineering, 2018, 35(3): 261-265 (in Chinese) doi: 10.3969/j.issn.1001-4551.2018.03.009
[10]	He L, Zhang Q, Charvet H J, et al. A knot-tying end-effector for robotic hop twining[J]. Biosystems Engineering, 2013, 114(3): 344-350
[11]	Zhang Q, He L, Charvet H J. Knot-tying device and method: US, 8573656B1[P]. 2013-11-05.
[12]	Onda H, Kudoh S, Suehiro T, et al. Handling and describing string-tying operations based on metrics using segments between crossing sections[J]. IEEE Robotics and Automation Letters, 2016, 1(1): 375-382
[13]	Cella P. Reexamining the catenary[J]. The College Mathematics Journal, 1999, 30(5): 391-393
[14]	Cella P. Methodology for exact solution of catenary[J]. Journal of Structural Engineering, 1999, 125(12): 1451-1453
[15]	于凤军, 崔金玲, 李立新. 利用平衡原理导出悬链线方程[J]. 工科物理, 1998, 8(4): 14-16 Yu F J, Cui J L, Li L X. A method of obtaining the equation of the suspension chain[J]. Physics and Engineering, 1998, 8(4): 14-16 (in Chinese)
[16]	李哲, 王宇锐, 汤剑, 等. 基于悬链线理论的海带打结原理研究[J]. 工程设计学报, 2011, 18(4): 260-264 doi: 10.3785/j.issn.1006-754X.2011.04.006 Li Z, Wang Y R, Tang J, et al. Research of kelp-knot principle based on catenary theory[J]. Journal of Engineering Design, 2011, 18(4): 260-264 (in Chinese) doi: 10.3785/j.issn.1006-754X.2011.04.006
[17]	Such M, Jimenez-Octavio J R, Carnicero A, et al. An approach based on the catenary equation to deal with static analysis of three dimensional cable structures[J]. Engineering Structures, 2009, 31(9): 2162-2170