一系列特殊的超6阶机构

doi:10.3901/JME.2021.05.031

机械工程学报 ›› 2021, Vol. 57 ›› Issue (5): 31-39.doi: 10.3901/JME.2021.05.031

扫码分享

一系列特殊的超6阶机构

张一同^1,2, 李艳文^1,2, 胡波^1,2, 牟德君^1,2, 赵美欣²

1. 燕山大学河北省并联机器人与机电系统实验室秦皇岛 066004;
2. 燕山大学机械工程学院秦皇岛 066004

收稿日期:2020-04-27 修回日期:2020-08-15 出版日期:2021-03-05 发布日期:2021-04-28
通讯作者: 李艳文(通信作者),女,1966年出生,博士,教授,硕士研究生导师。主要研究方向为机器人技术。E-mail:ywl@ysu.edu.cn
作者简介:张一同,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;胡波,男,1982年出生,博士,教授,博士研究生导师。主要研究方向为机构结构理论。E-mail:hubo@ysu.edu.cn;牟德君,女,1967年出生,博士,副教授,硕士研究生导师。主要研究方向为机构结构理论。E-mail:djmu@ysu.edu.cn;赵美欣,女,1996年出生,硕士研究生。主要研究方向为机构结构理论。E-mail:1322808962@qq.com
基金资助:
河北自然科技计划（19221909D）、河北省自然科学基金（E2020203197）和江苏省重点实验室（HGAMTL-1708）资助项目。

A Series of Special Mechanism with Rank More than Six

ZHANG Yitong^1,2, LI Yanwen^1,2, HU Bo^1,2, MU Dejun^1,2, ZHAO Meixin²

1. Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004;
2. School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004

Received:2020-04-27 Revised:2020-08-15 Online:2021-03-05 Published:2021-04-28

摘要/Abstract

摘要： 从机架共线的五环、六环、…、九环BNT（Bennett）机构中，拆去相邻环路公用的连架杆和它们两端的回转副，分别得到单环路的8杆、9杆、…、12杆机构。对拆杆前和拆杆后连杆铰链点轨迹圆的分析，发现铰链点的轨迹圆完全相同，证实了两种机构的运动学性能完全等效。得出单环路的8杆、…、12杆机构都符合BNT约束条件，机构自由度为1，它们的环路阶，分别为7、…、11，它们是一族新型的超6阶GBG（Goldberg）机构。这一发现，突破了现有环路阶小于等于6的传统观点。得出N杆GBG机构与机架共线的N□3环BNT机构的自由度相等，其值为1，N杆GBG机构的环路阶d是N□1的重要结论。通过对8杆GBG机构所有从动件的角位移θ_i（i=2，3，…，8）都是原动件角位移θ₁的一元函数的分析，证明了该机构的自由度为1。在Solidworks中，对8杆GBG机构的各杆角位移进行了检测，其结果和拆杆前的5环BNT机构对应的角位移检测值完全相同，精确地证明了两种机构运动学性能是完全等效的。充分证明了8杆GBG机构是自由度为1，环路阶为7的超6阶机构，也证明了用轨迹圆判断BNT约束条件的实用性和可靠性。这一研究成果拓宽了机构环路阶的使用区间，也使人们对机械系统约束性质的多样性有了更新的认识。

关键词: Bennett机构, Goldberg机构, 超6阶Goldberg机构, 轨迹圆

Abstract: The single loop 8-, 9-, …, 12-bar mechanism can be obtained by removing each of the public side links of the adjacent loops and the rotary pairs at their two ends from the 5-loop, 6-loop, …, 9-loop BNT (Bennett) mechanisms collinear with the rack, respectively. Through the analysis of the track circle of the hinge point of the link before and after the removal of the side link, it can be found that the locus circles of their hinge points are identical, which proves that the kinematic performance in the two mechanisms is completely equivalent. We can summarize that the 8-bar to the 12-bar mechanisms meet the BNT constraints, and the degree of freedom is 1, and their loop ranks are 7 to 11, they are in a family consisting of new GBG (Goldberg) mechanism with more than six ranks. This discovery breaks through the traditional view that the existing loop rank with less than or equal to 6. It is concluded that the degree of freedom of N-bar GBG mechanism is equal to N-3 ring BNT mechanism with collinear frame, and the value is 1. The loop rank of N-bar GBG mechanism is d=N-1. Taking 8-bar GBG mechanism as an example, the angular displacement is θ_i(i=2, 3, …, 8), it is proved that the angular displacement are all univariate functions of the angular displacement θ₁ of the original moving parts. The angular displacement of 8-bar GBG mechanism is measured with solidworks, and the result is identical with the corresponding angular displacement of 5-loop BNT mechanism before dismantling the bar. It is proved that the kinematic performance of the two mechanisms is completely equivalent. It is also proved that the 8-bar GBG mechanism is a mechanism with more than six ranks, the degree of freedom is 1, and the loop rank is 7, the practicability and reliability of BNT constraints are judged by trajectory circle. This research findings widens the use range of the loop rank in the mechanism, it makes people have a new understanding about the diversity of constraint properties in mechanical systems.

Key words: Bennett mechanism, Goldberg mechanism, Goldberg mechanism with ranks more than six, locus circle

中图分类号:

TH112

张一同, 李艳文, 胡波, 牟德君, 赵美欣. 一系列特殊的超6阶机构[J]. 机械工程学报, 2021, 57(5): 31-39.

ZHANG Yitong, LI Yanwen, HU Bo, MU Dejun, ZHAO Meixin. A Series of Special Mechanism with Rank More than Six[J]. Journal of Mechanical Engineering, 2021, 57(5): 31-39.

参考文献

[1] GRÜBLER M. Allgemeine eigenschaften der zwangläufigen ebenen kinematische kette:I[J]. Civilingenieur,1883,29(1):167-200. GRÜBLER M. General characteristics of the two-tier kinematic chain:I[J]. Civilingenieur,1883,29(1):167-200.
[2] BAGCI C. Degrees of freedom of motion in mechanisms[J]. Trans. ASME J. Engi. Industry,1971,93B:140-148.
[3] HUNT K H. Kinematic geometry of mechanisms[M]. Oxford:Oxford University Press,1978.
[4] 黄真,赵永生,赵铁石. 高等空间机构学[M]. 北京:高等教育出版社,2006. HUANG Zhen,ZHAO Yongsheng,ZHAO Tieshi. Advanced spatial mechanism[M]. Beijing:Higher Education Press,2006.
[5] LU W J,ZENG D X,HUANG Z. Over-constraints and a unified mobility method for general spatial mechanisms. Part 2:Application of the principle[J]. Chinese Journal of Mechanical Engineering,2016,29(1):1-10.
[6] GOGU G. Chebychev-Grübler-Kutzbach's criterion for mobility calculation of multi-loop mechanisms revisited via theory of linear transformations[J]. European J. Mechanics-A/Solids,2005,24(3):427-441.
[7] GOGU G. Structural synthesis of parallel robots:Part 1:Methodology[M]. Dordrecht:Springer,2008.
[8] YANG Tingli,SUN Dongjin. A general DOF formula for parallel mechanisms and multi-loop spatial mechanisms[J]. ASME Journal of Mechanisms and Robotics,2012,4(1):011001-1-17.
[9] ZHANG Y T,MU D J. New concept and new theory of mobility calculation for multi-loop mechanisms[J]. Sci. China Tech. Sci.,2010,53(6):1598-1604.
[10] ZHANG Y T,LI Y W,WANG L Y. A new formula of mechanism mobility based on virtual constraint loop[J]. Sci. China Tech. Sci.,2011,54(10):2768-2775.
[11] ZHANG Y T,LU W J,MU D J,et al. Novel mobility formula for parallel mechanisms expressed with mobility of general link group[J]. Chinese Journal of Mechanical Engineering,2013,26(6):1082-1090.
[12] MOROSKINE Y F. General analysis of the theory of mechanisms[J]. Moscow:Akad. Nauk,SSSR,1954,1:1.
[13] 张启先. 机构组成学的新探讨[J]. 机械工程学报,1961,9(1):7-32. ZHANG Qixian. Study on structural theory of spatial mechanisms[J]. Chinese Journal of Mechanical Engineering,1961,9(1):7-32.
[14] BENNETT G T. A new mechanism[J]. Engineering,1903,76:777-778.
[15] MYARD F E. Contribution à la géométrie des systèmes articulés[J]. ociete Mathématiques de France,1931,59,183-210. MYARD F E. Contribution to joint system geometry[J]. ociete Mathématiques de France,1931,59,183-210.
[16] GOLDBERG M. New 5-bar and 6-bar linkages in three dimensions[J]. SME J. Mech.,1943,65:649-661.
[17] BAKER J E. The Bennett,Goldberg and Myard linkages in perspective[J]. Mech. Mach. Theory,1979,14:239-253.
[18] BAKER J E. An analysis of Goldberg's anconoidal linkage[J]. Mech. Mach. Theory,1983,18(5):371-376.
[19] CHEN Yan,YOU Zhong. Spatial 6R linkages based on the combination of two Goldberg 5R linkages[J]. Mech. Mach. Theory,2007,42:1484-1498.
[20] 鹿玲,张一同,牟德君,等. 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,et al. Relationship between stagger angle interval and mechanism type of the Bennett mechanism[J]. Journal of Mechanical Engineering,2020,56(9):9-17.

一系列特殊的超6阶机构

A Series of Special Mechanism with Rank More than Six

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价

[1]	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.
[2]	牟德君, 张一同, 李艳文, 胡波, 卢文娟. 7杆Goldberg机构的结构参数和位移方程[J]. 机械工程学报, 2020, 56(17): 82-90.