﻿ 基于移动补偿的绳驱动关节运动解耦方法
 机器人 2022, Vol. 44 Issue (2): 195-202 0

HE Leiying, CHEN Jianguo, WU Tianci, YANG Liangliang. A Motion Decoupling Method for Cable-driven Joint Based on Movement Compensation[J]. ROBOT, 2022, 44(2): 195-202.

1. 浙江理工大学机械与自动控制学院, 浙江 杭州 310018;
2. 浙江省种植装备技术重点实验室, 浙江 杭州 310018

A Motion Decoupling Method for Cable-driven Joint Based on Movement Compensation
HE Leiying1,2 , CHEN Jianguo1 , WU Tianci1 , YANG Liangliang1
1. Faculty of Mechanical Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China;
2. Key Laboratory of Transplanting Equipment and Technology of Zhejiang Province, Hangzhou 310018, China
Abstract: A method is presented to solve the motion coupling of cable-driven joints through movement compensation.Firstly, the constraint conditions for decoupling are deduced according to the principle of motion coupling, and a 2-DOF (degree-of-freedom) cable-driven manipulator is designed correspondingly.To analyze the influence of elastic deformation of the cable on the effectiveness of decoupling, a theoretical model of the relationship between the cable tension and the joint angle offset is established by applying the capstan equation.Finally, some corresponding experiments are carried out.Results show that the maximum angular offset of the joint is 0.72° when no external torque is loaded on the joint, and the difference between the calculated angular offset and the experimental one is less than 0.02° when a certain torque is loaded on the joint.In addition, the angular offset of the joint decreases with the increase of the preload, and the dynamic decoupling performance of the joint is still good.Therefore, the effectiveness of the proposed decoupling method and the accuracy of the joint angle offset model are verified.
Keywords: cable-driven    motion decoupling    elastic deformation    joint angle offset

1 引言（Introduction）

2 绳驱动关节运动解耦方法（Motion decoupling method for cable-driven joints） 2.1 绳驱动关节运动耦合现象

2.2 解耦原理

 图 2 解耦机构的原理图及绕线方式 Fig.2 Principle of the decoupling mechanism and its winding way

(1) 关节$i$上解耦轮的直径和过渡轮的直径相等；

(2) 所有绕经动滑轮的自由段绳索都必须相互平行。

3 2自由度绳驱动机械臂的设计与分析（Design and analysis on the 2-DOF cable-driven manipulator） 3.1 结构设计

 图 3 2自由度绳驱动解耦机械臂模型 Fig.3 Model of the 2-DOF cable-driven decoupling manipulator

3.2 关节转角偏移分析

 图 4 绳索受力、形变图 Fig.4 Force and deformation of the cable

 $$${\rm \Delta} l=\frac{ \left({T_{i} -T_{\rm p}} \right)l_{{\rm free}} }{E}, \; \; i={\rm a}, {\rm b}$$$ (1)

 $$${\Delta} s_{{\rm a}} =\frac{r}{E\mu} \left({T_{{\rm a}} -T_{\rm p} -T_{\rm p} \ln \frac{T_{{\rm a}}} {T_{\rm p}}} \right)$$$ (2)

 \begin{align} {\rm \Delta} s_{{\rm b}} =\frac{r}{E\mu} \left({T_{\rm p} -T_{{\rm b}} +T_{\rm p} \ln \frac{T_{{\rm b}}} {T_{\rm p}}} \right) \end{align} (3)

 \begin{aligned} T_{{\rm a}}&=\max (T_{1}, T_{2}) \\ T_{{\rm b}}& =\min (T_{1}, T_{2}) \end{aligned} (15)

4.3 试验及结果分析 4.3.1 无外力矩时关节解耦效果测试

 图 8 无外力矩时的关节解耦效果 Fig.8 Result of joint decoupling effect without external torque

4.3.2 解耦关节转角偏移模型验证

 图 9 关节2的转角偏移试验结果 Fig.9 Experimental results of the angle offset of joint-2
4.3.3 机械臂关节的动态解耦效果测试

 图 10 关节2动态解耦效果 Fig.10 Results of the dynamic decoupling effect of joint-2

(1) 机械臂关节1运动过程中关节2的转角偏移量会发生明显的变化，但是偏移量不超过3.0$^{\circ}$，表明关节2的动态解耦性能良好；

(2) 关节2的转角偏移量会发生周期性的抖动，尤其是匀速运行阶段，这是由于关节2的动态弹性形变导致的；

(3) 随着预紧力增大，机械臂关节2的转角偏移量减小；

(4) 在A、B区域，关节2的转角偏移量发生明显突变，此时对应的$q_{1} \approx$ 90$^{\circ}$，这是因为机械臂在转过竖直位形时，关节2所受重力力矩方向突然改变，使得关节由于行星齿轮减速器的齿隙产生角度跳动。

5 结论（Conclusion）

(1) 本文对绳驱动机械臂关节运动耦合现象进行了分析，提出了一种采用通过动滑轮补偿关节运动耦合量，从而实现绳驱动关节运动解耦的方法。

(2) 基于解耦原理，研制了一种2自由度绳驱动机械臂。进而分析了绳索的弹性形变对关节解耦效果的影响，建立了关节转角偏移理论模型。

(3) 通过试验验证了提出的解耦机构的有效性，以及关节转角偏移模型的准确性，同时显示关节转角偏移量同紧边拉力$T_{\rm a}$之间近似呈线性关系，预紧力越大，关节转角偏移量越小。

(4) 机械臂的动态测试试验结果表明机械臂关节的动态解耦性能良好，但为了实现高精度定位，后续需要应用鲁棒的减振控制算法。

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