The Theory of Basic Tensegrity Unit Stable Forming

doi:10.3901/JME.2017.23.062

Abstract

Abstract: Unified geometric parameters are put forward to describe different one-dimensional, two-dimensional and threedimensional space dimension structure, and through geometric parameter changes, the seamless evolution of the different dimension structures can be realized. Based on basic form structure geometric parameters and fractal parameters, the method of application node force balance is put forward, and stable configuration theory of tensegrity basic form is built. The mathematical analysis model of the main fractal parameters and auxiliary fractal parameters and component spatial position and structure geometry parameter is established. The mapping relationship, which must be satisfied by the main fractal parameters and auxiliary fractal parameters to build the basic unit structure of self-stress stability, is established. The function relationship between each component force density under self-stress steady state is concluded after analysis. Application node generalized coordinates are combined with the component connection matrix, component internal force density and system force balance, write out the Matlab program. The input of basic body envelope geometric parameters can automatically complete vector calculation of all components and their spatial arrangement form, to implement the self-stress stable basic unit automatic configuration. Self-stress stable structure built by different fractal parameters is compared and analyzed, and the function relation between fractal parameters and structural geometrical parameters, force density, auxiliary shape parameter and its variation trend can be given.

Key words: auto-forming, basic unit, connectivity matrix, force density, fractal, tensegrity

CLC Number:

LUO Ani, LIU Heping, SKELTON R E, CHE Shijun. The Theory of Basic Tensegrity Unit Stable Forming[J]. Journal of Mechanical Engineering, 2017, 53(23): 62-73.

References

[1] RICHARD B F. Tensile-integrity structures:U.S., 3, 063, 521[P]. 1962-11-13.
[2] EMMERICH D. Construction de reseaux autotendants:France, 1, 377, 290[P].1964-09-28.
[3] SNELSON K D. Continuous tension, discontinuous compression structures:U.S., 3, 169, 611[P]. 1965-02-16.
[4] MOTRO R. Tensegrity:Structural systems for the future[M]. USA:Kogan Page Science, 2003.
[5] SKELTON R E, de OLIVEIRA M C. Tensegrity systems[M]. New York:Springer, 2009.
[6] CONNELLY R. Convex geometry[M]. Amsterdam:Plenum Press, 1993.
[7] CONNELLY R. Tensegrity structures:Why are they stable[M]. Amsterdam:Plenum Press, 1999.
[8] ZHANG P, KAWAGUCHI K, FENG J. Prismatic tensegrity structures with additional cables:Integral symmetric states of self-stress and cable-controlled reconfiguration procedure[J]. International Journal of Solids and Structures, 2014, 51(25):4294-4306.
[9] SULTAN C, CORLESS M, SKELTON R E. Symmetrical reconfiguration of tensegrity structures[J]. International Journal of Solids and Structures, 2002, 39(8):2215-2234.
[10] ZHANG J Y, GUEST S D, OHSAKI M. Symmetric prismatic tensegrity structures[J]. Part I. Configuration and Stability. Int. J. Solids Struct., 2009, 46(1):1-14.
[11] CALLADINE C R. Buckminster fuller's "tensegrity" structures and clerk Maxwell's rules for the construction of stiff frames[J]. Int. J. Solids Structures, 1978, 14:161-172.
[12] PELLEGRINO S. Structural computations with the singular value decomposition of the equilibrium matrix[J]. International Journal of Solids and Structures, 1993, 30(21):3025-3035.
[13] GUEST S D. The stiffness of prestressed frameworks:A unifying approach[J]. International Journal of Solids and Structures, 2006, 43(3):842-854.
[14] GUEST S D. The stiffness of tensegrity structures[J]. IMA Journal of Applied Mathematics, 2011, 76(1):57-66.
[15] CONNELLY R, TERRELL M. Globally rigid symmetric tensegrities[J]. Structural Topology, 1995, 21:59-78.
[16] CONNELLY R, BACK A. Mathematics and tensegrity[J]. Amer. Sci., 1998, 86:142-151.
[17] ZANG Liyuan, LI Yue, CAO Yanping, et al. Stiffness matrix based form-finding method of tensegrity structures[J]. Engineering Structures, 2014, 58:36-48.
[18] 杨癸庚,杨东武,杜敬利,等. 一种基于力密度的网状可展开天线索网结构初始形态设计方法[J]. 机械工程学报, 2016, 52(11):34-41. YANG Guigeng, YANG Dongwu, DU Jingli, et al. Method for deployable mesh antenna cable network structures' form-finding design based on force density[J]. Journal of Mechanical Engineering, 2016, 52(11):34-41.
[19] 陈根良,王皓,来新民,等. 基于广义坐标形式牛顿-欧拉方法的空间并联机构动力学正问题分析[J]. 机械工程学报, 2009, 45(7):41-48. CHEN Genliang, WANG Hao, LAI Xinmin, et al. Forward dynamics analysis of spatial parallel mechanisms based on the Newton-Euler method with generalized coordinates[J]. Journal of Mechanical Engineering, 2009, 45(7):41-48.
[20] GONZÁLEZ A, LUO Ani, LIU Heping. Construction of a unit cell Tensegrity structure[C]//14th World Congress in Mechanism and Machine Science, Taipei, Taiwan, China, October 25-30, 2015. 2015:65-67.
[21] LI Bingyan, LUO Ani, LIU Rongqiang, et al.Configuration modeling and interior force analysis of deployable tensegrity[C]//14th World Congress in Mechanism and Machine Science, Taipei, Taiwan, China, October 25-30, 2015. 2015:126-131.
[22] LUO Ani, LI Quanhe, LIU Heping, et al. Establishment and mechanical properties analysis of spherical tensegrity structures[C]//Proceedings of the 5th Structural Engineers World Congress (SEWC), Singapore, October 19-22, 2015.
[23] LUO Ani, LI Quanhe, XIAO Te, et al. Cylindrical tensegrity deployable structure[C]//Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015, Houston, Texas, November 13-19, 2015.
[24] LIU Heping, LI Xu, CHENG Jianjun, et al. The folding course for the tensegrity basic unit[C]//Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015, Houston, Texas, November 13-19, 2015.
[25] LUO Ani, LIU Heping, WANG Yongfan, et al. Analysis of instability for the string-net structure in the deployable antenna[J]. Key Engineering Materials. Trans. Tech. Publications, 2014, 572:529-532.
[26] LUO Ani, LIU Heping, LI Cheng, et al. Study of a flowerlike deployable structure[J]. Strojniški vestnikJournal of Mechanical Engineering, 2013, 59(4):216-222.
[27] LUO Ani, SKELTON R E, LIU Heping, et al. Structure of the ball tensegrity robot[C]//Robotics and Biomimetics (ROBIO), 2014 IEEE International Conference on. IEEE, 2014:1781-1786.
[28] LIU Heping, MA Wentao, LUO Ani, et al. Analysis of the movement of the new wave-energy dynamoelectric equipment[C]//Applied Mechanics and Materials. Trans Tech Publications, August 19-20, 2014:1535-1539.
[29] LUO Ani, KUN Z, SONG J H, et al. Analysis of equilibrium and carrying capability of the octahedral truss structure[C]//Applied Mechanics and Materials. Trans. Tech. Publications, August 19-20, 2014:1797-1801.
[30] LUO Ani, LIU Heping, WANG Yongfan, et al. Researching on finding form and instability of the radial string-net structure on deployable antenna[C]//ASME 2013 International Mechanical Engineering Congress and Exposition, San Diego, CA, United States, November 15-21, 2013.
[31] LIU Heping, LUO Ani, LI Cheng, et al. Design method of octahedron deployable mast[C]//ASME 2013 International Mechanical Engineering Congress and Exposition, San Diego, CA, United States, November 15-21, 2013.
[32] 罗阿妮,王龙昆,曹鹏飞,等. 张拉整体基本单元自动构型理论[C]//第24届全国结构工程学术会议论文集(第Ⅰ册).2015. 10. 30福建,厦门. 2015:9. LUO Ani, WANG Longkun, CAO Pengfei, et al. Automatic configuration theory of tensegrity elements[C]//24th National Academic Conference on Structural Engineering. October 30, 2015, Fujian, Xiamen. 2015:9
[33] 刘仁志,宋志佳,高文杰,等.正八面体空间伸展臂的八面体单元结构分析[J]. 机械设计, 2013(6):72-75. LIU Renzhi, SONG Zhijia, GAO Wenjie, LUO Ani. Analysis of eight face element structure of eight dimensional spatial extended arm[J]. Machine Design, 2013(6):72-75.
[34] 罗阿妮,张庆华,刘贺平,等. 圆柱形张拉整体结构质量最小化方法[J]. 哈尔滨工业大学学报, 2016(1):120-125. LUO Ani, ZHANG Qinghua, LIU Heping, et al. Minimum mass approach of cylindrical tensegrity structure[J]. Journal of Harbin Institute of Technology, 2016(1):120-125.
[35] 罗阿妮,王龙昆,刘贺平,等. 张拉整体三棱柱构型和结构稳定性分析[J]. 哈尔滨工业大学学报, 2016(7):82-87. LUO Ani, WANG Longkun, LIU Heping, et al. Analysis of configuration and structural stability of 3-bar tensegrity prism[J]. Journal of Harbin Institute of Technology, 2016(7):82-87.
[36] 罗阿妮,李旭,李全贺,等. 三杆张拉整体折展过程动力学分析[J]. 哈尔滨工程大学学报, 2016(7):974-978. LUO Ani, LI Xu, LI Quanhe, et al. Dynamic analysis of the three-bar tensegrity deployable structure[J]. Journal of Harbin Engineering University, 2016(7):974-978.