平面二自由度冗余驱动并联机构动力学建模与驱动力优化  

Dynamics Modeling and Actuating-force Optimization of a Planar 2-DOF Redundantly-actuated Parallel Mechanism

作　　者：王耀军[1,2] 徐国辉 WANG Yaojun;XU Guohui(School of Automation,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,China;Faculty of Mechanical Engineering and Automation,Zhejiang Sci-Tech University,Hangzhou 310018,China;The Ningbo Branch,Ordnance Science Institute of China,Ningbo 315103,China)

机构地区：[1]浙江机电职业技术学院自动化学院,浙江杭州310053 [2]浙江理工大学机械与自动控制学院,浙江杭州310018 [3]中国兵器科学研究院宁波分院,浙江宁波315103

出　　处：《新技术新工艺》2023年第4期33-40,共8页New Technology & New Process

基　　金：国家留学基金资助项目(201708330573);浙江省自然科学基金资助项目(LQ19E050015)。

摘　　要：针对并联机构引入冗余驱动造成驱动力求解不唯一、可能引起内力对抗问题,对冗余驱动并联机构的动力学建模和驱动力优化进行了研究。首先,基于闭环矢量法得到了机构运动学关系;接着引入螺旋理论,采用与系统运动螺旋成线性关系的约束矩阵之正交补来消除约束力螺旋,扩展自然正交补(Natural Orthogonal Complement,NOC)方法到冗余驱动并联机构,建立了平面二自由度冗余驱动机构的动力学模型;此外,建立了机构的驱动力模型,并基于最小范数法进行了驱动力静不定问题的约束优化求解,进一步采用Householder矩阵应用QR分解提高求解效率,得到了物理意义明确、求解快速的驱动力优化方法;最后通过平面轨迹跟踪仿真,对提出的建模和驱动力优化方法进行了验证。研究结果表明:基于螺旋理论的自然正交补方法推导动力学模型具有系统高效、中间变量少等优点;采用最小范数法的QR分解法求解各驱动器驱动力矩物理意义明确,速度快。该建模和驱动力优化方法不仅适用于冗余驱动的平面机构,也适用于空间机构以及超冗余机构。Aimed at the problem of non-unique solutions of actuating forces(or torques)and potentially antagonistic internal forces,it was studied that a dynamic modeling and ensuing internal forces distribution and optimization of redundantly-actuated parallel mechanisms.Firstly,the kinematic relationship of the mechanism was obtained based on the closed-loop-vector method.Then the screw theory was introduced,the natural orthogonal complement(NOC)was included to derive the dynamics modeling of the redundantly-actuated parallel mechanism,with the benefit of eliminating the constraint wrenches by resorting to the orthogonal relations of the screws and the wrenches.Furthermore,the actuating-force model of the mechanism was established,and the non-uniqueness constrained optimization was solved by a minimum-norm method,and then the solving efficiency was improved by relying on the QR-decomposition of Householder matrices,an efficient and robust method was gotten to compute explicitly the optimized solution.Finally,the proposed modeling and optimization method were verified by trajectory-tracking simulation.The research results showed that the NOC method offered a simple,systematic alternative to the modeling of redundantly-actuated mechanical systems,with less intermediate variables.The minimum-norm method had clear physical meaning and proposed QR-decomposition was of greater efficiency,which could be applied to varied redundant system,and was suitable for super redundant mechanisms as well.

关 键 词：冗余驱动 并联机构 螺旋理论 驱动力优化 动力学 建模 

分 类 号：TH113[机械工程—机械设计及理论]