绳牵引并联机器人悬链线优化解算方法

韦慧玲; 仇原鹰; 盛英; 陈海初; 卢清华

doi:10.16511/j.cnki.qhdxxb.2020.26.019

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清华大学学报（自然科学版） ›› 2021, Vol. 61 ›› Issue (3) : 224-229. DOI: 10.16511/j.cnki.qhdxxb.2020.26.019

索驱动机器人

绳牵引并联机器人悬链线优化解算方法

韦慧玲¹, 仇原鹰², 盛英², 陈海初¹, 卢清华¹

作者信息 +

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

WEI Huiling¹, QIU Yuanying², SHENG Ying², CHEN Haichu¹, LU Qinghua¹

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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。

Abstract

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.

导出引用

韦慧玲, 仇原鹰, 盛英, 陈海初, 卢清华. 绳牵引并联机器人悬链线优化解算方法[J]. 清华大学学报（自然科学版）. 2021, 61(3): 224-229 https://doi.org/10.16511/j.cnki.qhdxxb.2020.26.019

WEI Huiling, QIU Yuanying, SHENG Ying, CHEN Haichu, LU Qinghua. Optimal solution method for the cable catenary between cable-driven parallel robots[J]. Journal of Tsinghua University(Science and Technology). 2021, 61(3): 224-229 https://doi.org/10.16511/j.cnki.qhdxxb.2020.26.019

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收稿日期	出版日期
2020-03-17	2021-03-15
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2021-03-06

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