Dynamic Modeling and Dimensional Synthesis of a 4-DOF High-speed Parallel Robot with Two Limbs and a Single Moving Platform

doi:10.3901/JME.260452

Abstract

Abstract: Aiming at the sorting and grasping operations of light industry such as electronics, a 4-DOF high-speed parallel robot with two limbs and a single moving platform is proposed, and its dynamic modeling and design method is studied. Compared with other 4-DOF high-speed parallel robots, it only requires two limbs to achieve spatial 3T1R (three translations and one rotation) movement capabilities, and has the potential to be designed by balancing multiple performance indices, such as large workspace/mechanism volume ratio, high motion/force transmission efficiency, and excellent acceleration ability, etc. The kinematic and dynamic models are established based on the closed-loop vector equation and the principle of virtual work, respectively, leading to the definition of three dimensionless dynamic performance indices and two kinematic performance indices (pressure angle and workspace/mechanism volume ratio). On this basis, the influence of design parameters on the performance indices is determined by response surface modeling and contribution analysis. This is followed by a multi-objective dimensional optimization method by maximizing the diagonal dominance of the inertia matrix and acceleration capability subject to the geometrical and kinematic performance constraints. Decision of the optimized parameters are finally made by minimizing the maximum value of inertia term torque of the single motor shaft over the entire workspace. In this way, the kinematic and dynamic performance indices are balanced, laying a foundation for the development of engineering prototypes.

Key words: high speed parallel robot, kinematic and dynamic modeling, performance evaluation, dimensional synthesis

CLC Number:

TP242

MA Yue, PENG Dun, SUN Weihua, LI Bin, LIU Qi, CHEN Long, PENG Honggui, YANG Yuwei. Dynamic Modeling and Dimensional Synthesis of a 4-DOF High-speed Parallel Robot with Two Limbs and a Single Moving Platform[J]. Journal of Mechanical Engineering, 2026, 62(15): 366-381.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://www.cjmenet.com.cn/EN/10.3901/JME.260452

http://www.cjmenet.com.cn/EN/Y2026/V62/I15/366

References

[1] 周济. 智能制造——“中国制造2025”的主攻方向[J]. 中国机械工程，2015，26(17)：2273-2284. ZHOU Ji. Intelligent manufacturing-the main direction of “Made in China 2025”[J]. China Mechanical Engineering，2015，26(17)：2273-2284.
[2] 董凯. “十四五”智能制造发展规划解读及趋势研判[J]. 中国工业和信息化，2022(1)：24-29. DONG Kai. “Fourteen Five” intelligent manufacturing development planning interpretation and trend judgment[J]. China Industry & Information Technology，2022(1)：24-29.
[3] 刘辛军，谢福贵，汪劲松. 当前中国机构学面临的机遇[J]. 机械工程学报，2015，50(13)：2-12. LIU Xinjun，XIE Fugui，WANG Jinsong. Current opportunities in the field of mechanisms in China[J]. Journal of Mechanical Engineering，2015，50(13)：2-12.
[4] 孟齐志，谢福贵，张赛，等. 高速高加速并联机器人构型与尺度参数设计[J]. 机械工程学报，2022，58(13)：36-49. MENG Qizhi，XIE Fugui，ZHANG Sai，et al. Type synthesis and dimensional optimization of a high-speed and high-acceleration parallel robot[J]. Journal of Mechanical Engineering，2022，58(13)：36-49.
[5] CLAVEL R. Device for the movement and positioning of an element in space：USA，US4976582[P]. 1990-12-11.
[6] 李玉航，梅江平，刘松涛，等. 一种新型4 自由度高速并联机械手动力尺度综合[J]. 机械工程学报，2015，50(19)：32-40. LI Yuhang，MEI Jiangping，LIU Songtao，et al. Dynamic dimensional synthesis of a 4-DOF high-speed parallel manipulator[J]. Journal of Mechanical Engineering，2015，50(19)：32-40.
[7] COMPANY O，MARQUET F，PIERROT F. A new high-speed 4-DOF parallel robot synthesis and modeling issues[J]. IEEE Transactions on Robotics and Automation，2003，19(3)：411-420.
[8] NABAT V，MIJANGOS M，COMPANY O，et al. Par4：Very high speed parallel robot for pick-and-place[C]// Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems，Center Edmont，Alberta，Canada，2005：553-558.
[9] KRUT S，COMPANY O，NABAT V，et al. Heli4：A parallel robot for scara motions with a very compact traveling plate and a symmetrical design[C]// Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems，Beijing，China，2006：1656-1661.
[10] LI Yuhang，MA Yue，LIU Songtao，et al. Integrated design of a 4-DOF high-speed pick-and-place parallel robot[J]. CIRP Annals-Manufacturing Technology，2014，63(1)：185-188.
[11] 吴存存，杨桂林，陈庆盈，等. 四自由度2PPPaR并联机构运动学及性能分析[J]. 机械工程学报，2018，54(3)：36-45. WU Cuncun，YANG Guilin，CHEN Qingying，et al. Kinematic and performance analysis of a 4-DOF 2PPPaR parallel manipulator[J]. Journal of Mechanical Engineering，2018，54(3)：36-45.
[12] ESKANDARY P K，ANGELES J. The dynamics of a parallel Schönflies-motion generator[J]. Mechanism and Machine Theory，2018，119：119-129.
[13] ZHANG Shuai，LI Wei，ZHOU Songlin，et al. Kinematics and workspace analysis of a 3-CR(Pa)(Pa)R parallel mechanism with an orthogonal layout[J]. Mechanism and Machine Theory，2024，195：105616.
[14] JOSHI S A，TSAI L W. Jacobian analysis of limited-DOF parallel manipulators[J]. ASME Journal of Mechanical Design 2002，124(2)：254-258.
[15] HOEVENAARS A G L，GOSSELIN C，LAMBERT P，et al. A systematic approach for the Jacobian analysis of parallel manipulators with two end-effectors[J]. Mechanism and Machine Theory，2017，109：171-194.
[16] LIU Haitao，HUANG Tian，KECSKEMETHY A，et al. A generalized approach for computing the transmission index of parallel mechanisms.[J]. Mechanism and Machine Theory，2014，74：245-256.
[17] SHEN Xudong，XU Lingmin，LI Qinchuan. Motion/Force constraint indices of redundantly actuated parallel manipulators with over constraints[J]. Mechanism and Machine Theory，2021，165104427.
[18] DASGUPTA B，MRUTHYUNJAYA T S. A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator[J]. Mechanism and Machine Theory，1998，33(8)：1135-1152.
[19] ABDELLATIF H，HEIMANN B. Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism[J]. Mechanism and Machine Theory，2009，44(1)：192-207.
[20] 梁栋，庞书康，宋轶民，等. 一类新型末端铰接高速并联机器人建模与动力尺度综合[J]. 机械工程学报，2024，60(21)：38-55. LIANG Dong，PANG Shukang，SONG Yimin，et al. Modeling and dynamic dimension synthesis for a novel class of high-speed parallel robot with articulated end structure[J]. Journal of Mechanical Engineering，2024，60(21)：38-55.
[21] 商德勇，黄欣怡，黄云山，等. 基于Kane方程的Delta并联机器人刚柔耦合动力学研究[J]. 机械工程学报，2024，60(07)：124-133. SHANG Deyong，HUANG Xinyi，HUANG Yunshan，et al. Research on rigid-flexible coupling dynamics of Delta parallel robot based on Kane equation[J]. Journal of Mechanical Engineering，2024，60(7)：124-133.
[22] ASADA H. Dynamic analysis and design of robot manipulators using inertia ellipsoids[C]// Proceedings of the IEEE International Conference on Robotics and Automation，Atlanta，Georgia，1984，1：94-102.
[23] WU Jun，GAO Ying，ZHANG Binbin，et al. Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment[J]. Robotics and Computer-Integrated Manufacturing，2017，44：199-207.
[26] 赵庆，王攀峰，黄田. 考虑链间耦合的高速并联机器人惯性参数预估方法[J]. 天津大学学报，2017，50(8)：868-876. ZHAO Qing，WANG Panfeng，HUANG Tian. An inertial parameter estimation method for high-speed parallel robots by considering inter-chain coupling[J]. Journal of Tianjin University，2017，50(8)：868-876.
[25] LIU Xinjun，HAN Gang，XIE Fugui，et al. A novel acceleration capacity index based on motion/force transmissibility for high-speed parallel robots[J]. Mechanism and Machine Theory，2018，126：155-170.
[26] LIU Songtao，HUANG Tian，MEI Jiangping，et al. Optimal design of a 4-DOF SCARA type parallel robot using dynamic performance indices and angular constraints[J]. ASME Journal of Mechanisms and Robotics，2012，4：031005.
[27] 张惠普，汪满新. 高速并联机器人动力尺度综合[J]. 机械工程学报，2022，58(1)：29-40. ZHANG Huipu，WANG Manxin. Dynamic dimension synthesis of 4-RR (SS)² high speed parallel robot[J]. Journal of Mechanical Engineering，2022，58(1)：29-40.
[28] DONG Chenglin，LIU Haitao，XIAO Juliang，et al. Dynamic modeling and design of a 5-DOF hybrid robot for machining[J]. Mechanism and Machine Theory，2021，165：104438.
[29] ZHAO Yanqin，MEI Jiangping，JIN Yan，et al. A new hierarchical approach for the optimal design of a 5-dof hybrid serial-parallel kinematic machine[J]. Mechanism and Machine Theory，2021，156：104160.
[30] BRIOT S，CARO S，GERMAIN C. Design procedure for a fast and accurate parallel manipulator[J]. ASME Journal of Mechanisms and Robotics，2017，9：061012.
[31] MA Jintao，LIAN Binbin，WANG Meng，et al. Optimal design of a parallel assembling robot with large payload-to-mass ratio[J]. Robotics and Computer-Integrated Manufacturing，2023，46：102474.