• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2017, Vol. 53 ›› Issue (23): 62-73.doi: 10.3901/JME.2017.23.062

• 机构学及机器人 • 上一篇    下一篇

张拉整体基本形体稳定构型理论

罗阿妮1, 刘贺平1, SKELTON R E2, 车士俊1   

  1. 1. 哈尔滨工程大学机电工程学院 哈尔滨 150001;
    2. 加州大学圣地亚哥分校机械与航空系 加州 92093 美国
  • 收稿日期:2016-12-15 修回日期:2017-06-05 出版日期:2017-12-05 发布日期:2017-12-05
  • 通讯作者: 刘贺平(通信作者),男,1975年出生,副教授。主要研究领域为大型空间可展结构、张拉整体结构、虚拟样机技术。E-mail:liuheping@hrbeu.edu.cn
  • 作者简介:罗阿妮,女,1978年出生,副教授。主要研究领域为大型空间可展结构、张拉整体结构、虚拟样机技术。E-mail:luoani@hrbeu.edu.cn;SKELTONRE,男,教授。主要研究领域为多体动力学控制、张拉整体结构。E-mail:bobskelton@ucsd.edu;车士俊,男,1992年出生,硕士研究生。主要研究领域为大型空间可展结构、张拉整体结构。E-mail:cheshijun1992@163.com。
  • 基金资助:
    国家自然科学基金(51605111,51675114)和黑龙江省自然基金(11202128)资助项目。

The Theory of Basic Tensegrity Unit Stable Forming

LUO Ani1, LIU Heping1, SKELTON R E2, CHE Shijun1   

  1. 1. College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001;
    2. Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA
  • Received:2016-12-15 Revised:2017-06-05 Online:2017-12-05 Published:2017-12-05

摘要: 提出用统一的几何参数描述一维、二维、三维不同空间维数结构,通过几何参数变化,实现不同维数结构的无缝演化。以基本形体结构的几何参数和分形参数为基础,提出应用节点力平衡法,构建张拉整体基本形体稳定构型理论。建立了主分形参数与辅助分形参数及构件空间位置、结构几何参数的数学分析模型。确立出主分形参数与辅助分形参数构建自应力稳定基本单元结构,必须满足的映射关系。分析得出自应力稳定状态下,各个构件力密度间的函数关系。应用节点广义坐标结合构件连接矩阵、构件内力密度、系统力平衡,编写Matlab程序;输入基本体包络几何参数和主分形参数,程序即可自动完成辅助分形参数确定及所有构件矢量计算及其空间布置方式,实现自应力稳定基本单元自动构型。对于不同的分形参数构建起的自应力稳定结构进行分析比较,给出分形参数与结构几何参数、力密度、辅助形体参数之间的函数关系及变化趋势。

关键词: 分形, 基本单元形体, 力密度, 连接矩阵, 张拉整体, 自动构型

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

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