Topology Design Method for Parallel Mechanisms with Symbolic Forward Position Solution and Motion Decoupling Based on the Minimum Sub-kinematic-chain

doi:10.3901/JME.2025.23.041

Abstract

Abstract: The parallel mechanisms (PMs) with symbolic forward position solutions and motion decoupling characteristic are very beneficial to the subsequent dimension synthesis, error analysis, motion trajectory planning and real-time control, dynamic balance and dynamic analysis. A topological structure design (type synthesis) method for PM is proposed that degree of freedom (DOF) and position and orientation characteristics (POC) are guided, and symbolic forward position solutions (SFP) and motion decoupling (MD) as the performance indexes. First of all, 10 practical and simple low coupling degree (k=0, 1) minimum sub-kinematic-chains (SKC_min) (among which, 4 SKC_min are the new design) are proposed as the composition units of PMs. Secondly, two methods of PM design based on SKC_min are proposed. The first method, i.e, when the basic functions (DOF and POC) are known, a hybrid branch consisting of SKC_min with sub-DOF (DOF₀) and the terminal POC is designed, and then a PM consisting of the hybrid branch and (DOF-DOF₀) unconstraint branches is designed. The second method, i.e, when the basic functions (DOF and POC) are unknown, hybrid branches consisting of SKC_min and other constraint branches are first designed, then assembling them to form various types of PMs. Through topological analysis, the DOF and POC of these PMs are determined and categorized for application. Finally, the application of these two methods is illustrated by designing generally over-constrained PMs with limited-DOF. Additionally, the main topological characteristics of some of these PMs are analyzed and verified.

Key words: parallel mechanism, symbolic forward position solution, motion decoupling, minimum sub-kinematic-chain, topology design

CLC Number:

TH112

LI Ju, SHE Junjie, SHEN Huiping, ZENG Boxiong, YANG Tingli. Topology Design Method for Parallel Mechanisms with Symbolic Forward Position Solution and Motion Decoupling Based on the Minimum Sub-kinematic-chain[J]. Journal of Mechanical Engineering, 2025, 61(23): 41-57.

References

[1] MERLET J P. Parallel robots[M]. 2nd ed. New York:Springer-Verlag New York Inc.,2005.
[2] HUANG Tian,WANG Manxin,YANG Shuofei,et al. Force/Motion transmissibility analysis of six degree of freedom parallel mechanisms[J]. ASME Journal of Mechanisms and Robotics,2014,6:031010
[3] DONG Chenglin,LIU Haitao,YUE Wei,et al. Stiffness modeling and analysis of a novel 5-DOF hybrid robot[J]. Mechanism and Machine Theory,2018,125:80-93.
[4] 刘辛军,谢福贵,汪劲松. 并联机器人机构学基础[M].北京:高等教育出版社,2018. LIU Xinjun,XIE Fugui,WANG Jinsong. Fundamental of parallel robotic mechanisms[M]. Beijing:Higher Education Press,2018.
[5] PAN Yang,GAO Feng. Position model computational complexity of walking robot with different parallel leg mechanism topology patterns[J]. Mechanism and Machine Theory,2017,107:324-337.
[6] HUANG Zhen,LI Qinchuan,DING Huafeng,Theory of parallel mechanisms[M]. Berlin:Springer,2013.
[7] LI Qinchuan,HERVÉ J M. 1T2R parallel mechanisms without parasitic motion[J]. IEEE Transactions on Robotics,2010,26(3):401-410.
[8] GOGU G. Structural Synthesis of Parallel Robots. Part 5:Basic over-constrained topologies with schonflies motions[M]. Berlin:Springer,2014.
[9] 杨廷力,刘安心,罗玉峰,等. 机器人机构拓扑结构设计[M]. 北京:科学出版社,2012. YANG Tingli,LIU Anxin,LUO Yufeng,et al. Theory and application of robot mechanism topology[M]. Beijing:Science Press,2012.
[10] 于靖军,裴旭,宗光华. 机械装置的图谱化创新设计[M]. 北京:科学出版社,2014. YU Jingjun,PEI Xu,ZONG Guanghua. Graphical approach to creative design of mechanical devices[M]. Beijing:Science Press,2014.
[11] 高峰,杨加伦,葛巧德. 并联机器人型综合的GF集理论[M]. 北京:科学出版社,2011. GAO Feng,YANG Jialun,GE Qiaode. Type synthesis of GF set theory of parallel robot[M]. Beijing:Science Press,2011.
[12] KONG Xianwen,GOSSELIN C. Type synthesis of parallel mechanisms[M]. Berlin:Springer Verlag,2007.
[13] ZENG Qiang,FANG Yuefa. Algorithm for topological design of multi-loop hybrid mechanisms via logical proposition[J]. Robotica,2012,30(4):599-612.
[14] LIU Xinjun,WANG Jinsong. Parallel kinematics-type,kinematics,and optimal design[M]. Berlin:Springer,2014.
[15] 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 mechanisms[M]. Beijing:Higher Education Press,2021.
[16] 沈惠平,李菊,王振,等. 基于结构降耦和运动解耦的并联机构拓扑结构优化及其性能改善研究[J]. 机械工程学报,2017,53(19):176-186. SHEN Huiping,LI Ju,WANG Zhen,et al. Topology structure optimization and performance improvement for parallel mechanisms based on structure coupling-reducing and motion decoupling[J]. Journal of Mechanism Engineering,2017,53(19):176-186.
[17] KUO C,DAI Jiansheng. Task-oriented structure synthesis of a class of parallel manipulators using motion constraint generator[J]. Mechanism and Machine Theory,2013,70:394-406.
[18] YI B,KIM S,KWAK H,KIM W. Multi-task oriented design of an asymmetric 3T1R type 4-DOF parallel mechanism[J]. Proceedings of Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2013,227(10):2236-2255.
[19] KUMAR N,PICCIN O,BAYLE B. A task-based type synthesis of novel 2T2R parallel mechanisms[J]. Mechanism and Machine Theory,2014,77:59-72.
[20] WU Guanglei,BAI Shaoping,HJØRNET P. Architecture optimization of a parallel Schönflies-motion robot for pick-and-place applications in a predefined workspace[J]. Mechanism and Machine Theory,2016,106:148-165.
[21] GAN Dongming,DAI Jiansheng,DIAS J. Singularity-free workspace aimed optimal design of a 2T2R parallel mechanism for automated fiber placement[J]. Journal of Mechanisms and Robotics,2015,7(4):041022.
[22] GLAZUNOV V. Design of decoupled parallel manipulators by means of the theory of screws[J]. Mechanism and Machine Theory,2010,45(2):239-250.
[23] JIN Xiaodong,FANG Yuefa,QU Haibo,et al. A class of novel 2T2R and 3T2R parallel mechanisms with large decoupled output rotational angles[J]. Mechanism and Machine Theory,2017,114:156-169.
[24] ZENG Daxing,JING Guodong,SU Yonglin,et al. A novel decoupled parallel mechanism with two translational and one rotational degree of freedom and its performance indices analysis[J]. Advances in Mechanical Engineering,2016,8(5):1-10.
[25] LEGNANI G,FASSI I,GIBERTI H,et al. A new isotropic and decoupled 6-DOF parallel manipulator[J]. Mechanism and Machine Theory,2012,58:64-81.
[26] SHEN Huiping,ZHU Xiaorong,ZHANG Dan,et al. The design methodology for fewer input-more output parallel mechanisms[J]. Mechanism and Machine Theory,2016,104:43-58.
[27] 沈惠平,邓嘉鸣,孟庆梅,等. 少输入-多输出并联机构的设计方法及其应用[J]. 机械工程学报,2018,54(1):223-232. SHEN Huiping,DENG Jiaming,MENG Qingmei,et al. Design methods and applications for the fewer input-more output parallel mechanisms[J]. Journal of Mechanism Engineering,2018,54(1):223-232.
[28] ESSOMBA T,NGUYEN V L. Kinematic analysis of a new five-bar spherical decoupled mechanism with two-degrees of freedom remote center of motion[J]. Mechanism and Machine Theory,2018,119:184-197.
[29] 沈惠平,尹洪波,杨廷力,等. 基于方位特征方法的范例并联机构的拓扑特征分析及其启示与应用[J]. 机械工程学报,2015,51(13):101-115. SHEN Huiping,YIN Hongbo,YANG Tingli,et al. Position and orientation characteristic based method and enlightenment for topology characteristic analysis of typical parallel mechanisms and its application[J]. Journal of Mechanism Engineering,2015,51(13):101-115.
[30] 沈惠平,曾博雄,尤晶晶,等. 具有解析式位置正解的三平移并联机构设计与分析[J]. 农业机械学报,2020,51(2):383-391. SHEN Huiping,ZENG Boxiong,YOU Jingjing,et al. Topology design and analysis of three-translation parallel mechanism with analytical direct position solutions[J]. Transactions of the Chinese Society of Agricultural Machinery,2020,51(2):383-391.
[31] SHEN Huiping,MENG Qinmei,LI Ju,et al. Kinematic sensitivity,parameter identification and calibration of a non-fully symmetric parallel Delta robot[J]. Mechanism and Machine Theory,2021,161:104311.
[32] SHEN Huiping,ZHAO Yinan,LI Ju,et al. A novel partially-decoupled translational parallel manipulator with symbolic kinematics,singularity identification and workspace determination[J]. Mechanism and Machine Theory,2021,164:104388.
[33] 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:Phoenix Education Publishing Ltd.,2025.
[34] YANG Tingli,LIU Anxin,SHEN Huiping,et al. Topology design of robot mechanisms[M]. Berlin:Springer,2018.
[35] 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):42-50.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):42-50.