平面索牵引机构工作空间解析求解与验证

doi:10.19665/j.issn1001-2400.2019.04.005

西安电子科技大学学报 ›› 2019, Vol. 46 ›› Issue (4): 28-34.doi: 10.19665/j.issn1001-2400.2019.04.005

平面索牵引机构工作空间解析求解与验证

何世凯,段清娟,李浩,赵萍

西安电子科技大学机电工程学院,陕西西安 710071

收稿日期:2019-02-22 出版日期:2019-08-20 发布日期:2019-08-15
作者简介:何世凯(1993—),男,西安电子科技大学硕士研究生,E-mail: 601332483@qq.com.
基金资助:
陕西省自然科学基础研究计划(2016JM5034)

Analytical solution and verification of the workspace of the planar cable-driven mechanism

HE Shikai,DUAN Qingjuan,LI Hao,ZHAO Ping

School of Mechano-electronic Engineering, Xidian Univ., Xi'an 710071, China

Received:2019-02-22 Online:2019-08-20 Published:2019-08-15

摘要/Abstract

摘要：

为求解平面索牵引多体机构的力旋量封闭工作空间边界,提出矩阵零空间的方法。该方法通过对力的雅克比矩阵分析,推导出保证索力的非负条件,并根据此条件求解出力旋量封闭工作空间边界,找到力旋量可行工作空间。使用蒙特卡罗方法优化电机的位置和杆上牵索点的位置,使得力旋量可行工作空间最大,并保证机构的运行轨迹在力旋量可行工作空间的范围内。对平面串联两杆机构的一种构型进行参数优化求解和实验验证,结果表明参数优化后的构型可以保证预期轨迹在力旋量可行工作空间内,解析法可以准确地推导出力旋量封闭工作空间的边界。

关键词: 索牵引, 零空间, 力旋量封闭工作空间, 力旋量可行工作空间

Abstract:

In order to find the wrench closed workspace boundary of the Planar Multibody Cable-Driven Mechanism, a matrix null space method is proposed. By analyzing the cable force Jacobian matrix, the condition for guaranteeing non-negative cable forces are derived, and the boundary of wrench closed workspace and wrench feasible workspace are solved according to the condition. The Monte Carlo method is used to optimize the the position of the motor and cable connection point to maximize the wrench feasible workspace and ensure that the trajectory of the mechanism is within the wrench feasible workspace. Parameter optimization and experimental verification of a configuration of the planar serial two-link mechanism show that the optimal configuration guarantees the desired trajectory in the wrench feasible workspace, and that the analytical method can accurately derive the boundary of the wrench closure workspace.

Key words: cable-driven, null space, wrench closure workspace, wrench feasible workspace

中图分类号:

TH122

何世凯,段清娟,李浩,赵萍. 平面索牵引机构工作空间解析求解与验证[J]. 西安电子科技大学学报, 2019, 46(4): 28-34.

HE Shikai,DUAN Qingjuan,LI Hao,ZHAO Ping. Analytical solution and verification of the workspace of the planar cable-driven mechanism[J]. Journal of Xidian University, 2019, 46(4): 28-34.

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参考文献 9

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参数	[1,2]配置	[0,3]配置
1杆长/m	0.5	0.5
2杆长/m	0.4	0.4
d₁/mm	380	250
d₂/mm	100	100
d₃/mm	382	382
M₁/m	(0.89,-0.38)	(0.89,-0.38)
M₂/m	(-0.895,-0.24)	(-0.895,-0.24)
M₃/m	(0.89,0.185)	(0.89,0.185)

平面索牵引机构工作空间解析求解与验证

Analytical solution and verification of the workspace of the planar cable-driven mechanism

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