基于螺旋理论的四面体可展机构运动特性与动力学分析  

Kinematic Characteristics and Dynamics Analysis of the Tetrahedral Deployable Mechanism Based on the Screw Theory

作　　者：韩博[1,2] 韩媛媛[3] 许允斗[1,2] 郑东 姚建涛[1,2] 赵永生[1,2] HAN Bo;HAN Yuanyuan;XU Yundou;ZHENG Dong;YAO Jiantao;ZHAO Yongsheng(Parallel Robot and Mechatronic System Laboratory of Hebei Province,Yanshan University,Qinhuangdao 066004.China;Key Laboratory of Advanced Forging&Stamping Technology and Science of Ministry of Education,Yanshan University,Qinhuangdao 066004,China;Department of Mathematics and Computer Science,Hengshui University,Hengshui 053000,China)

机构地区：[1]燕山大学河北省并联机器人与机电系统实验室,河北秦皇岛066004 [2]燕山大学先进锻压成形技术与科学教育部重点实验室,河北秦皇岛066004 [3]衡水学院数学与计算机科学系,河北衡水053000

出　　处：《机器人》2020年第1期21-28,38,共9页Robot

基　　金：国家自然科学基金(51675458);河北省自然科学基金重点项目(E2017203335);河北省高等学校青年拔尖人才计划(BJ2017060)。

摘　　要：为了解决星载四面体构架式可展开天线运动学和动力学建模分析困难的问题,建立了一种基于螺旋理论的运动学和动力学特性分析方法.首先分析了3RR-3RRR四面体可展机构的构型机理及几何特征,基于螺旋理论绘制了旋量约束拓扑图,计算了机构的自由度,结果表明其只有1个自由度.然后对其进行了运动学分析,通过运动旋量的组合运算分析了各个构件的速度,并推导得到了机构的雅可比矩阵,采用旋量导数表示构件的6维加速度,推导得到了各个花盘和杆件的角加速度与质心线加速度.最后基于牛顿-欧拉方程和虚功原理建立了动力学方程,并进行了数值计算与仿真验证,数值计算结果与仿真结果完全一致,验证了基于螺旋理论的运动学和动力学特性分析方法的正确性.本文的研究方法在分析过程中各参数物理意义明确,分析过程较为程式化,易于编程,适合应用于此类空间可展开机构的分析中.In order to solve the modeling and analysis problems of the kinematics and dynamics of the spaceborne tetrahedral space deployable antenna, a kinematics and dynamics characteristics analysis method based on screw theory is established. Firstly, configuration and geometric characteristics of the 3RR-3RRR tetrahedral deployable mechanism are analyzed,its screw constrained topology diagram is obtained based on screw theory, and its degree of freedom(DOF) is calculated to be only one. Then, the kinematics analysis of the mechanism is conducted, the velocities of the components are obtained through the combinatorial operation of kinematic twists, and the Jacobian matrix of this mechanism is also obtained. The 6-dimensional acceleration of each component is expressed by the screw derivative, and the angular accelerations and centroid linear accelerations of the node disks and rods are deduced. Finally, the dynamic equation is established based on the Newton-Euler equation and the principle of virtual work, and the numerical calculation and simulation verification are carried out. The simulation results are completely consistent with the numerical results, which verifies the correctness of the kinematics and dynamics characteristics analysis method based on screw theory. Every parameter has clear physical meanings in the analysis based on the proposed method, and the analysis process is easy to program due to its stylization and is suitable for the analysis of such spatial deployable mechanisms.

关 键 词：螺旋理论 四面体可展机构 自由度 运动学 动力学 

分 类 号：TH112[机械工程—机械设计及理论]