Bennett机构交错角区间和机构类型的关系

doi:10.3901/JME.2020.09.009

机械工程学报 ›› 2020, Vol. 56 ›› Issue (9): 9-17.doi: 10.3901/JME.2020.09.009

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Bennett机构交错角区间和机构类型的关系

鹿玲^1,2, 张一同^1,3, 牟德君^1,3, 胡波^1,3, 卢文娟^1,3

1. 燕山大学机械工程学院秦皇岛 066004;
2. 燕山大学河北省重型智能制造装备技术创新中心秦皇岛 066004;
3. 燕山大学河北省并联机器人与机电系统实验室秦皇岛 066004

收稿日期:2019-06-12 修回日期:2019-11-24 出版日期:2020-05-05 发布日期:2020-05-29
通讯作者: 张一同(通信作者),男,1945年出生,教授。主要研究方向为机构结构理论。E-mail:ytzhang@ysu.edu.cn
作者简介:鹿玲,女,1964年出生,副教授。主要研究方向为先进制造工艺与机器人技术。E-mail:luling@ysu.edu.cn;牟德君,女,1967年出生,副教授。主要研究方向为机构结构理论。E-mail:djmu@ysu.edu.cn;胡波,男,1982年出生,教授,博士研究生导师。主要研究方向为机构结构理论和机器人技术。E-mail:hubo@ysu.edu.cn;卢文娟,女,1983年出生,副教授。主要研究方向为机构结构理论。E-mail:luwenjuan@ysu.edu.cn
基金资助:
河北省自然科学基金（E2011203193）和河北省杰出青年基金（E2017203094）资助项目。

Relationship between Stagger Angle Interval and Mechanism Type of the Bennett Mechanism

LU Ling^1,2, ZHANG Yitong^1,3, MU Dejun^1,3, HU Bo^1,3, LU Wenjuan^1,3

1. School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004;
2. Heavy-duty Intelligent Manufacturing Equipment Innovation Center of Hebei Province, Yanshan University, Qinhuangdao 066004;
3. Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System, Yanshan University, Qinhuangdao 066004

Received:2019-06-12 Revised:2019-11-24 Online:2020-05-05 Published:2020-05-29

摘要/Abstract

摘要： 目前Bennett（BNT）机构根据回转副轴线的方向，分成非对称安装和线性对称安装两类。为了研究这两类机构的共性和区别，在杆件交错角（0，2π）的区域内，用相邻象限组合为4个区间，由S₁₂（第1-2象限）区间和S₃₄（第3-4象限）区间各得到1组非对称安装的左旋和右旋BNT机构；由S₂₃（第2-3象限）和S₄₁（第4-1象限）区间各得到1组线性对称安装的左旋和右旋BNT机构。把前后2组机构进行对比，只有轴线方向是非对称的，机构结构本身都是对称的。由于S₁₂和S₃₄区间的非对称安装机构，通过交错角的设定，可以转换为S₄₁区间的线性对称机构，所以线性对称和非对称之间并无本质差别，4组机构本质是相同的1组。因为S₄₁区间机构的运动副的轴线方向指向相同，轴线的正方向与相邻杆内角逆时针的角位移方向一致，所以把S₄₁区间改用交错角锐角表示的R₄₁（第4-1象限）区间作为交错角的工作区间，就得到线性对称的右旋型和左旋型两种BNT机构基本类型，这两类机构的运动链是相同的，只是以不同构件为机架得到两种机构的形式。根据这些概念，左旋型和右旋型BNT机构，采用交错角锐角给出了统一的结构参数方程和含相邻杆内角表示的闭环位移方程。这种交错角为锐角的统一参数方程，简单，直观，便于应用。研究强调并补充了相邻杆的交错角不能在作用区间的同一象限选取的一个必要的约束条件。

关键词: Bennett机构, 约束条件, 交错角, 结构参数, 闭环位移方程

Abstract: At present, Bennett (BNT) mechanism can be divided into two types according to the direction of axis of revolute joints:Asymmetrical and linear symmetrical installation. In order to study the similarities and differences between these two types of mechanisms, using adjacent quadrants were used to form four intervals in the region of link stagger angle (0, 2π). Then, a group of asymmetrically installed left-handed and right-handed BNT mechanisms are obtained based on the S₁₂(quadrant I and II) and S₃₄(quadrant III and IV)intervals, and a group of linearly symmetrically installed left-handed and right-handed BNT mechanisms are obtained based on the S₂₃(quadrant II and III)and S₄₁(quadrant IV and I)intervals. Comparing these two groups of mechanisms, only the axis is asymmetrical while the structure itself is symmetrical. Since the asymmetrical installation mechanisms in the regions of S₁₂ and S₃₄ can be transformed into linear symmetrical mechanisms in the region of S₄₁ by setting the stagger angle, there is no essential difference between linear symmetrical and asymmetrical mechanisms, and these two groups of mechanisms are essentially the same one. Because the joints within the mechanism in the region of S₄₁ have the same axial direction, and the positive direction of the axis is the same as the anti-clockwise angular displacement direction of the inner angle of the adjacent links, so the interval of R₄₁(quadrant IV and I)represented by the sharp angle of the stagger angle is used as the working interval of the stagger angle, then two basic types of BNT linear symmetrical mechanisms, i.e., right-handed and left-handed, are obtained. The kinematic chains of these two types of mechanisms are the same, but they are obtained by taking different components as the frame. According to these concepts, aiming to the left-handed and right-handed BNT mechanisms, the uniform structural parameter equations and the closed-loop displacement equations with the inner angles of adjacent links are given by using the stagger sharp angles. This unified parametric equation with sharp angles is simple, intuitive and easy to apply. A necessary constraint condition that the stagger angles of adjacent links cannot be selected in the same quadrant of the action region is emphasized and supplemented.

Key words: Bennett mechanism, constraint condition, stagger angle, structural parameters, closed-loop displacement equation

中图分类号:

TH112

鹿玲, 张一同, 牟德君, 胡波, 卢文娟. Bennett机构交错角区间和机构类型的关系[J]. 机械工程学报, 2020, 56(9): 9-17.

LU Ling, ZHANG Yitong, MU Dejun, HU Bo, LU Wenjuan. Relationship between Stagger Angle Interval and Mechanism Type of the Bennett Mechanism[J]. Journal of Mechanical Engineering, 2020, 56(9): 9-17.

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Bennett机构交错角区间和机构类型的关系

Relationship between Stagger Angle Interval and Mechanism Type of the Bennett Mechanism

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