球面四杆Bricard-like机构的设计与研究

doi:10.3901/JME.2025.07.338

机械工程学报 ›› 2025, Vol. 61 ›› Issue (7): 338-348.doi: 10.3901/JME.2025.07.338

扫码分享

球面四杆Bricard-like机构的设计与研究

孙学敏¹, 李锐明², 荀致远³, 姚燕安²

1. 山东管理学院智能工程学院济南 250357;
2. 北京交通大学机械与电子控制工程学院北京 100044;
3. 暨南大学信息科学技术学院/网络空间安全学院广州 510632

收稿日期:2024-05-01 修回日期:2024-09-15 发布日期:2025-05-12
作者简介:孙学敏，女，1988年出生，博士。主要研究方向为机构学与机器人学。E-mail：xmsun@sdmu.edu.cn
李锐明(通信作者)，男，1985年出生，博士，副教授。主要研究方向为机构学与机器人学。E-mail：lirm@bjtu.edu.cn荀致远，男，1988年出生，博士。主要研究方向为机构学与机器人学。E-mail：xzyxun@126.com
姚燕安，男，1972年出生，博士，教授，博士研究生导师。主要研究方向为机构学与机器人学。E-mail：yayao@bjtu.edu.cn
基金资助:
山东管理学院博士科研启动基金资助项目(SDMUD202123)。

Design and Research of Spherical Four-bar Bricard-like Mechanism

SUN Xuemin¹, LI Ruiming², XUN Zhiyuan³, YAO Yanan²

1. School of Intelligent Engineering, Shandong Management University, Jinan 250357;
2. School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044;
3. College of Information Science and Technology/College of Cyber Security, Jinan University, Guangzhou 510632

Received:2024-05-01 Revised:2024-09-15 Published:2025-05-12

摘要/Abstract

摘要： 折展机构具有良好的折叠与展开性能，因此广泛应用于航空航天等领域，而构造单元创新设计一直是设计折展机构的关键问题。针对该问题，设计和研究一类由三个球面四杆机构组成的新型Bricard-like机构，并研究其运动特性与组网。通过分析球面四杆机构与Bricard机构的约束条件，得到球面四杆Bricard-like机构的设计方法以及其约束条件，得到三类球面四杆Bricard-like机构，即面对称、一般化三边形以及三对称类型。详细分析三对称Bricard-like机构的运动特点，设计圆弧和直杆两款三对称Bricard-like机构，通过分析球面剪叉机构和Bricard-like机构的特点，得到四类剪叉式Bricard-like机构的设计方法并分析其各自运动特点。此外，设计一系列的具有大折展比、可折叠为一束等特点的组网单元，选择球面Bricard-like机构及剪叉式Bricard-like机构进行组网。最后，设计与制作球面Bricard-like机构、剪叉式Bricard-like机构及组网单元的3D打印样机模型，验证设计方法的正确性与运动的可行性。

关键词: 球面四杆, 回环连接, Bricard, 折展机构, 剪叉机构

Abstract: Deployable mechanism has good folding and unfolding performance, so it is widely used in aerospace and other fields, and the innovative design of construction unit has always been the key problem in the design of deployable mechanism. In order to solve this problem, a new type of Bricard-like mechanism (BM) composed of three spherical four-bar mechanisms is designed and studied, and its motion characteristics and network are studied. By analyzing the constraint conditions of spherical four-bar mechanism and BM, the design method and constraint conditions of spherical four-bar BM are obtained, and three kinds of BM are obtained, that is, plane-symmetric, generalized trihedral and three-fold symmetric. The motion characteristics of the three-fold symmetric BM are analyzed in detail, and two kinds of three-fold symmetric BM are designed, namely arc and straight bar. By analyzing the characteristics of the spherical scissors mechanism and the BM, the design methods of four kinds of scissors Bricard-like mechanism(SBM) are obtained and their respective motion characteristics are analyzed. In addition, a series of network units with large deployable ratio and can be folded into a bundle are designed, and the BM and SBM are selected for designing the network. Finally, the 3D printing prototype models of BM, scissors BM and network unit are designed and made to verify the correctness of the design method and the feasibility of movement.

Key words: spherical four-bar, loop-connected, Bricard, deployable mechanism, scissors mechanism

中图分类号:

TH112

孙学敏, 李锐明, 荀致远, 姚燕安. 球面四杆Bricard-like机构的设计与研究[J]. 机械工程学报, 2025, 61(7): 338-348.

SUN Xuemin, LI Ruiming, XUN Zhiyuan, YAO Yanan. Design and Research of Spherical Four-bar Bricard-like Mechanism[J]. Journal of Mechanical Engineering, 2025, 61(7): 338-348.

参考文献

[1] ZHAO J，CHU F，FENG Z. The mechanism theory and application of deployable structures based on SLE[J]. Mechanism and Machine Theory，2009，44(2)：324-335.
[2] LI R，YAO Y，KONG X. Reconfigurable deployable polyhedral mechanism based on extended parallelogram mechanism[J]. Mechanism and Machine Theory，2017，116：467-480.
[3] LI R，YAO Y，DING X. A family of reconfigurable deployable polyhedral mechanisms based on semiregular and Johnson polyhedra[J]. Mechanism and Machine Theory，2018，126：344-358.
[4] 孙学敏，姚燕安，李锐明，等. 一类平面对心折展机构的构造方法[J]. 机械工程学报，2019，55(11)：176-185. SUN Xuemin，YAO Yanan，LI Ruiming，et al. A method for constructing planar center-coincident deployable mechanisms[J]. Journal of Mechanical Engineering，2019，55(11)：176-185.
[5] SUN X，YAO Y，LI R. Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes[J]. Frontiers of Mechanical Engineering，2020，15(1)：89-99.
[6] 郝艳玲，李锐明，孙学敏，等. 可重构立方体机构的设计与运动模式分析[J]. 机械工程学报，2020，56(13)：120-127. HAO Yanling，LI Ruiming，SUN Xuemin，et al. Design and motion pattern analysis of reconfigurable cube mechanism[J]. Journal of Mechanical Engineering，2020，56(13)：120-127.
[7] KANG X，LEI H，LI B. Multiple bifurcated reconfiguration of double-loop metamorphic mechanisms with prismatic joints[J]. Mechanism and Machine Theory，2022，178：105081.
[8] 贾广鲁，李兵，戴建生. 变胞折块机构：圆柱体/圆锥体切割链接而成的变胞折块机构设计与运动学分析[J]. 机械工程学报，2023，59(13)：24-35. JIA Guanglu，LI Bing，DAI Jiansheng. Metamorphic oriblocks：design and kinematic analysis of metamorphic oriblocks constructed by cutting and linking cylinders/cones[J]. Journal of Mechanical Engineering，2023，59(13)：24-35.
[9] GUO J，ZHAO Y，XU Y，et al. Mechanics analysis and structural design of a truss deployable antenna mechanism based on 3RR-3URU tetrahedral unit[J]. Mechanism and Machine Theory，2022，171：104749.
[10] 田大可，高海明，金路，等. 多构型组合式模块化可展开天线机构设计与分析[J]. 机械工程学报，2023，59(13)：36-48. TIAN Dake，GAO Haiming，JIN Lu，et al. Design and analysis of multi-configuration combined modular deployable antenna mechanism[J]. Journal of Mechanical Engineering，2023，59(13)：36-48.
[11] 张树新，于亦奇，曹政，等. 可重复展收单折伞状天线机构创新设计与实验验证[J]. 机械工程学报，2023，59(3)：13-21. ZHANG Shuxin，YU Yiqi，CAO Zheng，et al. Novel mechanism design and prototype verification of a single folding umbrella antenna for repeatable deploying and furling function[J]. Journal of Mechanical Engineering，2023，59(3)：13-21.
[12] HUANG H，LI B，ZHANG T，et al. Design of large single-mobility surface-deployable mechanism using irregularly shaped triangular prismoid modules[J]. Journal of Mechanical Design，2019，141(1)：012301.
[13] CHENG P，DING H，CAO W，et al. A novel family of umbrella-shaped deployable mechanisms constructed by multi-layer and multi-loop spatial linkage units[J]. Mechanism and Machine Theory，2021，161：104169.
[14] GAO C，KANG X，LEI H，et al. Design and analysis of a novel large-span two-fold deployable mechanism[J]. Mechanism and Machine Theory，2023，186：105352.
[15] MENG Q，XIE F，TANG R，et al. Deployable polyhedral mechanisms with radially reciprocating motion based on novel basic units and an additive-then-subtractive design strategy[J]. Mechanism and Machine Theory，2023，181：105174.
[16] YANG T，LI P，SHEN Y，et al. Center-driven planar closed-loop mechanisms based on an angulated four-bar linkage[J]. Mechanism and Machine Theory，2023，180：105130.
[17] 李端玲，张忠海，于振. 球面剪叉可展机构的运动特性分析[J]. 机械工程学报，2013，49(13)：1-7. LI Duanling，ZHANG Zhonghai，YU Zhen. Kinematic characteristic analysis of spherical scissors deployable mechanisms[J]. Journal of Mechanical Engineering，2013，49(13)：1-7.
[18] CASTRO M，RASMUSSEN J，ANDERSEN M，et al. A compact 3-DOF shoulder mechanism constructed with scissors linkages for exoskeleton applications[J]. Mechanism and Machine Theory，2019，132：264-278.
[19] LI J，WANG J，ZHAO J，et al. Design，dimensional synthesis and evaluation of a novel two-degrees-of-freedom spherical remote center of motion mechanism for minimally invasive surgery[J]. Journal of Mechanisms and Robotics，2024，16(5)：051005.
[20] BRICARD R. Mémoire sur la théorie de l'octaèdre articulé[J]. Journal de Mathématiques pures et appliquées，1897，3：113-148. BRICARD R. Memoir on the theory of articulated octahedra[J]. Journal of Pure and Applied Mathematics，1897，3：113-148.
[21] BRICARD R. Leçons de Cinématique，T. II[M]. Paris：Gauthier-Villars，1927. BRICARD R. Kinematics Lessons，T. II[M]. Paris：Gauthier-Villars，1927.
[22] WOHLHART K. Merging two general goldberg 5R linkages to obtain a new 6R space mechanism[J]. Mechanism and Machine Theory，1991，26(7)：659-668.
[23] CHEN Y，YOU Z，TARNAI T. Threefold-symmetric Bricard linkages for deployable structures[J]. International Journal of Solids and Structures，2005，42(8)：2287-2301.
[24] QI X，HUANG H，MIAO Z，et al. Design and mobility analysis of large deployable mechanisms based on plane-symmetric Bricard linkage[J]. Journal of Mechanical Design，2017，139(2)：022302.
[25] WANG J，KONG X. Deployable mechanisms constructed by connecting orthogonal Bricard linkages，8R or 10R single-loop linkages using S joints[J]. Mechanism and Machine Theory，2018，120：178-191.
[26] LÜ S，ZLATANOV D，ZOPPI M，et al. Bundle folding type III Bricard linkages[J]. Mechanism and Machine Theory，2020，144：103663.
[27] LÜ S，YAO P，XIAO H，et al. Approximating cylinders with bundle-folding plane-symmetric Bricard linkages[J]. International Journal of Mechanical Sciences，2022，221：107231.
[28] SUN X，LI R，XUN Z，et al. A new Bricard-like mechanism with anti-parallelogram units[J]. Mechanism and Machine Theory，2020，147：103753.
[29] SUN X，LI R，XUN Z，et al. A multiple-mode mechanism composed of four antiparallelogram units and four revolute joints[J]. Mechanism and Machine Theory，2021，155：104106.
[30] 孙学敏，李锐明，姚燕安. 面对称Bricard-like机构的设计与研究[J]. 机械工程学报，2021，57(21)：78-87. SUN Xuemin，LI Ruiming，YAO Yanan. Design and research of plane-symmetric Bricard-like mechanism[J]. Journal of Mechanical Engineering，2021，57(21)：78-87.
[31] SUN X，LI R，YAO Y. Loop-construction mechanism and its network based on quadrilateral mechanisms[J]. Mechanism and Machine Theory，2023，181：105181.

球面四杆Bricard-like机构的设计与研究

Design and Research of Spherical Four-bar Bricard-like Mechanism

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

编辑推荐

Metrics

本文评价

[1]	范小东, 史创, 王治易, 刘天明, 郭宏伟, 刘荣强. 固面可展开天线机构设计及运动学分析[J]. 机械工程学报, 2025, 61(3): 237-250.
[2]	牟德君, 王雅静, 陆鹏程, 王童辉. 空间双层过约束可展机构的设计与分析[J]. 机械工程学报, 2024, 60(1): 274-283.
[3]	姚鹏飞, 吕胜男, 张武翔, 丁希仑. 基于正四棱台Bricard单元的双环可展开天线机构构型设计[J]. 机械工程学报, 2023, 59(21): 147-156.
[4]	杨富富, 林维炜, 杨飞雨, 张俊, 姚立纲. 基于二重对称剪纸的新型超材料胞元结构的设计与特性分析[J]. 机械工程学报, 2023, 59(17): 97-108.
[5]	杨慧, 冯健, 刘永斌, 刘荣强. 百米级多超弹性铰链抛物柱面天线折展机构设计与运动学分析[J]. 机械工程学报, 2022, 58(3): 75-83.
[6]	郭路瑶, 赵永生, 李明, 韩博, 路斯成, 崔琦峰, 许允斗. 基于旋量理论平板折展机构构型综合与分析[J]. 机械工程学报, 2021, 57(9): 28-38.
[7]	孙学敏, 李锐明, 姚燕安. 面对称Bricard-like机构的设计与研究[J]. 机械工程学报, 2021, 57(21): 78-87.
[8]	徐坤, 乔安伟, 丁希仑. 剪叉弯曲折展变胞机构的设计与分析[J]. 机械工程学报, 2020, 56(5): 55-62.
[9]	梁友鉴, 赵杰亮, 阎绍泽. 基于蜜蜂腹部变体机制的空天飞行器仿生变体头锥设计[J]. 机械工程学报, 2020, 56(5): 47-54.
[10]	朱佳龙, 黄志荣, 郑士昆, 许允斗, 段玉柱, 马小飞. 基于螺旋理论的三棱锥折展机构构型综合与组网[J]. 机械工程学报, 2020, 56(5): 29-38.
[11]	郭瑞峰, 连宾宾, 宋轶民, 齐杨, 孙涛. 基于FIS理论的Myard环形组网机构运动学分析[J]. 机械工程学报, 2020, 56(19): 132-142.
[12]	孙学敏, 姚燕安, 李锐明, 刘然, 魏超然. 一类平面对心折展机构的构造方法[J]. 机械工程学报, 2019, 55(11): 176-185.
[13]	车林仙，杜力，黄勇刚. 球面四杆机构函数综合的带修复策略可行性规则差分进化算法[J]. 机械工程学报, 2015, 51(11): 31-40.
[14]	李端玲;张忠海;于振. 球面剪叉可展机构的运动特性分析[J]. , 2013, 49(13): 1-7.