可轮换用动平台的三自由度并联机构的拓扑设计与性能分析

doi:10.3901/JME.2025.21.286

摘要/Abstract

摘要： 提出并设计了一种具有可轮换用动平台且部分运动解耦的并联机构，不需改变机构本身的拓扑结构，仅通过驱动副的控制就可实现其固有的三平移(3T)、两平移一转动(2T1R)两种运动输出模式。分别分析该机构在两种输出模式下的：① 拓扑学层面上的方位特征(POC)、自由度(DOF)、耦合度(k)；② 运动学层面上的符号式位置正反解、基于正解的工作空间求解、采用差分进化算法的机构几何尺寸参数优化设计、基于位置逆解的雅可比矩阵求解及其导出的机构奇异性；③ 动力学层面上的基于虚功原理序单开链法的机构三个驱动力的变化曲线；阐述了该机构两种模式下应用场景的概念设计；讨论了可轮换用动平台并联机构的优势和特点。研究拓展了多模式(可重构)机构的设计理念和方法，也拓宽了并联机构的设计思路与应用前景。

关键词: 并联机构, 可轮换用动平台, 拓扑学, 运动学, 动力学

Abstract: A novel parallel mechanism is proposed and designed. This mechanism featured a replaceable moving platform and partially decoupled motion. Without modifying its inherent topological structure, it achieved two natural motion output modes—three translations (3T) and two translations with one rotation (2T1R)—through control of its actuated joints. Analyses are conducted for both output modes in the following aspects: ① Topological properties: position and orientation characteristics (POC), degree of freedom (DOF), and coupling degree (k). ② Kinematic properties: symbolic forward and inverse position solutions, workspace determination based on forward solutions, geometric parameter optimization using a differential evolution algorithm, Jacobian matrix derivation via inverse solutions, and singularity analysis. ③ Dynamic properties: variation curves of three driving forces calculated using the virtual work principle-based sequential single-open-chain method. Conceptual designs for application scenarios under both modes are elaborated. The advantages and features of the parallel mechanism with alternately used moving platform are discussed. The study extended the design concepts and methodologies for multi-mode (reconfigurable) mechanisms and broadened the design approaches and application prospects of parallel mechanisms.

Key words: parallel mechanism, alternately used moving platform, topology, kinematics, dynamics

中图分类号:

TG112

沈惠平, 佘星宇, 李菊, 叶鹏达, 朱小蓉, 朱伟. 可轮换用动平台的三自由度并联机构的拓扑设计与性能分析[J]. 机械工程学报, 2025, 61(21): 286-301.

SHEN Huiping, SHE Xingyu, LI Ju, YE Pengda, ZHU Xiaorong, ZHU Wei. 3-DOF Parallel Mechanism with Alternately Used Moving Platform— Topology, Kinematics and Dynamics[J]. Journal of Mechanical Engineering, 2025, 61(21): 286-301.

参考文献

[1] CLAVEL R. DELTA，A fast robot with parallel geometry[C]//Symposium on Industrial Robots. Proceedings of the 18th Int，1988：91-100
[2] TIANXU L，MINGDE G，KONGMING H，et al. A novel 3-DOF translational parallel robot and its fuzzy controller design[J]. Journal of Intelligent and Fuzzy Systems，2021：1-14.
[3] KONG X，GOSSELIN C M. Kinematics and singularity analysis of a novel type of 3-CRR 3-DOF translational parallel manipulator[J]. The International Journal of Robotics Research，2002，21(9)：791-798.
[4] 马履中，郭宗和，马晓丽，等. 三平移弱耦合并联机器人机构机型及位置精度分析[J]. 中国机械工程，2006，17(15)：1541-1545. MA Lüzhong，GUO Zonghe，MA Xiaoli，et al. Type synthesis of kinematic structures of 3-DOF weakly-coupled parallel robot mechanism and precision analysis[J]. Journal of Mechanical Engineering，2006，17(15)：1541-1545.
[5] LI S，HUANG Z，ZUO R. Kinematics of a special 3-DOF 3-UPU parallel manipulator[C]//American Society of Mechanical Engineers. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference，September 29–October 2，2002，Montreal，Quebec，Canada：ASME，2002：1035-1040.
[6] 尹小琴，马履中. 三平移并联机构3-RRC的工作空间分析[J]. 中国机械工程，2003，14(18)：1531-1533. YIN Xiaoqin，MA Lüzhong. Workspace analysis of a 3-DOF translational parallel mechanism 3-RRC[J]. Journal of Mechanical Engineering，2003，14(18)：1531-1533.
[7] ZHANG J，WANG D B，SONG Z M，et al. Workspace analysis and size optimization of planar 3-DOF redundantly actuated parallel mechanism[J]. Journal of Mechanical Science and Technology，2024，38(2)：957-967.
[8] 郭宗和，马履中，尹小琴，等. 非对称三平移并联机构的运动条件设计[J]. 农业机械学报，2006，37(10)：112-115. GUO Zonghe，MA Lüzhong，YIN Xiaoqin，et al. Design of dissymmetrical 3-DOF pare translational parallel manipulator based on the kinematic conditions[J]. Transactions of the Chinese Society for Agricultural Machinery，2006，37(10)：112-115.
[9] SHEN H，TANG Y，WU G，et al. Design and analysis of a class of two-limb non-parasitic 2T1R parallel mechanism with decoupled motion and symbolic forward position solution - influence of optimal arrangement of limbs onto the kinematics，dynamics and stiffness[J]. Mechanism and Machine Theory，2022，172：104815.
[10] XIE F，LIU X J，YOU Z，et al. Type synthesis of 2T1R-type parallel kinematic mechanisms and the application in manufacturing[J]. Robotics & Computer Integrated Manufacturing，2014，30(1)：1-10.
[11] 张帆，杨建国，李蓓智. 避免瞬时运动2T1R并联机构的拓扑综合[J]. 机械设计，2010(9)：48-51. ZHANG Fan，YANG Jianguo，LI Beizhi. Topological synthesis of instantaneous motion-free 2T1R parallel mechanism[J]. Journal of Machine Design，2010(9)：48-51.
[12] SHAO H，ZHANG H，YAN W. Dynamic modeling and performance optimization of a 2-PRU-PPRC 2T1R redundant parallel manipulator[C]//Institute of Electrical and Electronics Engineers. 2019 IEEE 9th Annual International Conference on CYBER Technology in Automation，Control，and Intelligent Systems (CYBER)，July 29–August 2，2019，Suzhou，China： IEEE，2019：951-956.
[13] 汤耀，沈惠平，曾博雄，等. 一种零耦合度及部分运动解耦的空间2T1R并联机构动力学建模[J]. 常州大学学报：自然科学版，2022，34(1)：48-59.TANG Yao，SHEN Huiping，ZENG Boxiong，et al. Dynamics modeling of a spatial 2T1R parallel mechanism with zero coupling degree and partial motion decoupling[J]. Journal of Jiangsu Polytechnic University (Nat. Sci. Ed.)，2022，34(1)：48-59.
[14] LEE C C，HERVE J M. Discontinuously movable seven-link mechanisms via group-algebraic approach[J]. Proceedings of the Institution of Mechanical Engineers- Part C，2005，219(6)：577-587.
[15] GALLETTI C，FANGHELLA P. Single-loop kinematotropic mechanisms[J]. Mechanism and Machine Theory，2001，36(6)：743-761.
[16] CARROLl D W，MAGLEBY S P，Howell L L，et al. Simplified manufacturing through a metamorphic process for compliant ortho-Planar mechanisms[C]//American Society of Mechanical Engineers. International Mechanical Engineering Congress and Exposition，November 5-11，2005，Orlando，Florida，USA：ASME，2005，42150：389-399.
[17] YAN H S，KUO C H. Topological Representations and characteristics of variable kinematic joints[J]. Journal of Mechanical Design，2006，128(2)：384-391.
[18] KONG X，GOSSELIN C M，RICHARD P L. Type synthesis of parallel mechanisms with multiple operation modes[J]. Journal of Mechanical Design，2007，129(6)：595-601.
[19] 于靖军，刘凯，孔宪文. 多模式机构研究进展[J]. 机械工程学报，2020，56(19)：14-27. YU Jingjun，LIU Kai，KONG Xianwen. State of the art of multi-mode mechanisms[J]. Journal of Mechanical Engineering，2020，56(19)：14-27.
[20] NURAHMI L，CARO S，WENGER P，et al. Reconfiguration analysis of a 4-RUU parallel manipulator[J]. Mechanism and Machine Theory，2016，96：269-289.
[21] 刘川禾，杨廷力，刘毅. 变拓扑机构理论的基本问题[J]. 机械工程学报，2005，41(8)：56-62. LIU Chuanhe，YANG Tingli，LIU Li. Basic problems of the theory for the variable topology mechanisms[J]. Journal of Mechanical Engineering，2005，41(8)：56-62.
[22] ZHANG L，DAI J S. Reconfiguration of spatial metamorphic mechanisms[J]. Journal of Mechanisms & Robotics，2009，1(1)：011012.
[23] YOON J，RYU J，LIM K B. Reconfigurable ankle rehabilitation robot for various exercises[J]. Journal of Field Robotics，2010，22(S1)：15-33.
[24] 杨廷力，刘安心，孙东锦. 变拓扑机构结构组成原理及其基本类型[C]//中国机械工程学会. 中国机构与机器科学国际学术会议. 2006：262-264. YANG Tingli，LIU Anxin，SUN Dongmian. Structure composition principles and basic types of variable topology mechanism[C]//Chinese Mechanical Engineering Society. IFToMM CCMMS，2006：262-264.
[25] 杨廷力. 机械系统基本理论，结构学、运动学、动力学[M]. 北京：机械工业出版社，1996. YANG Tingli. Basic theory of mechanical system, structical, kinematical, dynamics[M]. Beijing：China Machine Press，1996.
[26] 沈惠平. 机器人机构拓扑特征运动学[M]. 北京：高等教育出版社，2021. SHEN Huiping. Topological characteristics-based kinematics for robotic mechanism[M]. Beijing：Higher Education Press，2021.
[27] 沈惠平. 并联机器人机构拓扑分析——方法与技巧及应用[M]. 南京：江苏凤凰教育出版社，2025 SHEN Huiping. Topological analysis for parallel robotic mechanisms—Methods，techniques and applications[M]. Nanjing：Jiangsu Phoenix Education Publishing House Co.，Ltd，2025.
[28] 沈惠平，李菊，朱小蓉，等. 基于最优路径的并联机构自由度计算方法及其新公式[J]. 机械工程学报，2024，60(19)：40-52. SHEN Huiping，LI Ju，ZHU Xiaorong，et al. New method and formula for degree-of-freedom calculation of parallel mechanism based on optimal paths[J]. Journal of Mechanical Engineering，2024，60(19)：40-52.
[29] 沈惠平，潘海月，李菊，等. 运动解耦且位置正解符号化的三维平移操作手：中国，202310760734.9[P]. 2023-06-26. SHEN Huiping，PAN Haiyue，LI Ju，et al. 3D translational manipulator with decoupled motion and positive positional desymbolisation：China，202310760734.9[P]. 2023-06-26.
[30] 杜中秋，沈惠平，李菊，等. 一种位置正解符号化且运动部分解耦的新型2T1R并联机构动力学分析[J]. 机电工程，2023，40(8)：1231-1239. DU Zhongqiu，SHEN Huiping，LI Ju. Dynamics analysisi of a new 2T1R parallel mechanism with symbolic position solutions and partially motion decoupled[J]. Journal of Mechanical & Electrical Engineering，2023，40(8)：1231-1239.
[31] 张春美. 差分进化算法理论与应用[M]. 北京：北京理工大学出版社，2014. ZHANG Chunmei. Theory and applications of differential evolution algorithm[M]. Beijing：Beijing Institute of Technology Press，2014.
[32] 吴桂勇，唐昌悟，解玄. 激光加工技术在模具制造中的应用与展望[J]. 模具工业，2024，50(5)：1-5. WU Guiyong，TANG Changwu，XIE Xuan. Application and prospect of laser machining technology in die and mould manufacturing[J]. Die & Mould Industry，2024，50(5)：1-5.
[33] 刘洪俊. 汽车车门内板冲压成形及工艺分析[J]. 锻压装备与制造技术，2020，55(6)：123-126. LIU Hongjun. Stamping and process analysis of automobile door inner panel[J]. China Metalforming Equipment & Manufacturing Technology，2020，55(6)：123-126.
[34] 沈惠平，李菊，吴广磊，等. 并联机器人机构的拓扑结构优化[M]. 北京：高等教育出版社，2025.SHENHuiping，LIJu，WU Guanglei，et al. Topology optimization of parallel robot mechanisms[M]. Beijing：Higher Education Press，2025.