绳牵引并联机器人悬链线优化解算方法  

Optimal solution method for the cable catenary between cable-driven parallel robots

作　　者：韦慧玲 仇原鹰[2] 盛英[2] 陈海初 卢清华 WEI Huiling;QIU Yuanying;SHENG Ying;CHEN Haichu;LU Qinghua(College of Mechanical and Electrical Engineering,Foshan University,Foshan 528225,China;School of Mechanical-Electrical Engineering,Xidian University,Xi'an 710071,China)

机构地区：[1]佛山科学技术学院机电工程学院,佛山528225 [2]西安电子科技大学机电工程学院,西安710071

出　　处：《清华大学学报（自然科学版）》2021年第3期224-229,共6页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(61973294,51175397);国家重点研发计划课题项目(2018YFB1308000);佛山科学技术学院高层次人才科研启动项目(099/CGG07219).

摘　　要：针对大跨度绳牵引并联机器人难以建立精确动力学模型的问题,该文提出一种绳索非线性悬链线模型降维优化解算方法。该方法首先通过柔索微分单元和积分法推导绳索悬链线模型的差分方程并确定其边界条件;根据系数矩阵行列式为零的方法对悬链线模型的超越方程进行降维;进一步通过换元法和Taylor展开方法求出悬链线模型的解析解;接着基于Newton迭代方法得出悬链线模型的精确数值解,分析数值解的取值范围确定其正确符号;最后,对降维优化解算方法的合理性和有效性通过实例计算进行了验证。研究成果可为绳牵引并联机构的动力学精确建模和稳定运动实时控制提供理论依据。Accurate dynamic models are difficult to develop for long-span cable-driven parallel robots. This paper presents a reduced dimension optimization method for designing nonlinear cable catenaries. This paper gives the differential equation for the catenary and its boundary conditions. The dimension of the transcendental equation of the catenary model was then reduced according to the boundary conditions with the analytical solution obtained using the substitution method and the Taylor expansion method. Then, the Newton method was used to numerically solve the catenary model to study the range and characteristics of the numerical solution. Finally, the effectiveness of the reduced dimension optimization method are verified by examples. This research provides a theoretical basis for accurate dynamic modeling and real-time motion stability control strategies for cable-driven parallel mechanisms.

关 键 词：绳牵引并联机器人 柔索 悬链线模型 解析解 数值解 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]