基于违约稳定法的剪式可展机构展开过程分析与仿真  

Analysis and Simulation of the Deployment Process of the Scissor Deployable Mechanism Based on the Stabilization of Contract

作　　者：吴上生[1] 陈柘 兰侨 Wu Shangsheng;Chen Zhe;Lan Qiao(School of Mechanical and Automotive Engineering,South China University of Technology,Guangzhou 510630,China)

机构地区：[1]华南理工大学机械与汽车工程学院,广州510630

出　　处：《机电工程技术》2022年第5期1-5,25,共6页Mechanical & Electrical Engineering Technology

基　　金：国家自然科学基金委员会与英国爱丁堡皇家学会合作交流项目(编号:51911530245)。

摘　　要：为了研究由不同长度杆件组成并受力均匀的单自由度剪式单元可展机构的展开过程动力学特性,首先基于能量函数推导了单元质量矩阵,并按照叠加法组装系统整体质量矩阵,结合剪式单元杆长约束、铰接点约束和边界条件约束方程,利用拉格朗日乘子法建立其动力学模型。其次采用Baumgarte坐标违约和速度违约稳定法进行修正使结果稳定,通过多步长Runge-Kutta法进行数值计算,最后利用MATLAB仿真得到该机构展开过程中各节点位置坐标、速度、加速度随时间变化的关系,并对仿真结果进行了相应分析,得到驱动力一侧节点速度要低于非驱动力一侧的速度的结论,有利于对剪式单元可展机构进行精细化控制策略的研究,分析结果对不同杆件长度的剪式单元可展机构应用范围的扩展提供了理论基础。In order to study the dynamic characteristics of the deployment process of a single-degree-of-freedom scissor element deployable mechanism composed of different lengths and uniform force,the element mass matrix was first derived based on the energy function,and the overall mass matrix of the system was assembled according to the superposition method.The shear element rod length constraint,hinge point constraint and boundary condition constraint equations were used to establish its dynamic model by Lagrangian multiplier method.Secondly,the Baumgarte coordinate default and speed default stabilization methods were used to correct the results to stabilize the results,and the multistep Runge-Kutta method was used for numerical calculation.Finally,MATLAB simulation was used to obtain the position coordinates,speed,and acceleration of each node during the unfolding process of the mechanism with time.The simulation results were analyzed accordingly,and it was concluded that the speed of the node on the side of the driving force was lower than that on the side of the non-driving force,which was conducive to the study of the fine control strategy of the scissor unit deployable mechanism.The analysis results provides a theoretical basis for the extension of the application range of the scissor unit deployable mechanism with different bar lengths.

关 键 词：剪式单元 约束方程 动力学 拉格朗日乘子法 Baumgarte违约修正 

分 类 号：TH112[机械工程—机械设计及理论]