Topological Design and Performance Analysis of 3-DOF Parallel Mechanisms with Alternately Used Moving Platforms

doi:10.3969/j.issn.1004-132X.2026.01.013

Abstract

Abstract:

According to the theory and method of topological design for parallel mechanisms based on azimuthal characteristic equations， a 3-DOF parallel mechanism with alternately used moving platforms was designed. The mechanism generated two output motion modes by swapping the moving platform. The characteristics of the mechanism such as topological characteristics， kinematics performance， and dynamics performance were analyzed and calculated under two different modes. Topological characteristics were composed of position and orientation characteristics， degrees of freedom， and coupling degree. Kinematics performances were composed of symbolic forward and inverse position solutions， workspace， and singularity. Dynamics performances were composed of driving force variations. Then， the dimensional parameters of the mechanisms were subjected to an optimal design with the goal of achieving a reachable workspace. Finally， a conceptual design was conducted for the application scenario of using the mechanisms in automated object packaging productions.

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

摘要：

根据基于方位特征方程的并联机构拓扑设计理论和方法，设计了一种通过轮换使用动平台产生两种输出运动的三自由度并联机构。分析计算了该机构在两种模式下的以下特性：包括方位特征、自由度和耦合度的拓扑特征；符号式位置正反解、工作空间和奇异性的运动学性能；驱动力变化的动力学性能。然后，以可达工作空间为目标对机构尺寸进行了优化设计。最后对该机构在自动包装物件生产的应用场景进行了概念设计。

关键词: 并联机构, 拓扑学, 可轮换用动平台, 运动学, 动力学, 优化设计

CLC Number:

TH12

ZHU Xiao, SHEN Huiping, LI Ju, LI Tao, YE Pengda, ZHU Wei. Topological Design and Performance Analysis of 3-DOF Parallel Mechanisms with Alternately Used Moving Platforms[J]. China Mechanical Engineering, 2026, 37(1): 114-125.

朱潇, 沈惠平, 李菊, 李涛, 叶鹏达, 朱伟. 可轮换用动平台三自由度并联机构的拓扑设计及其性能分析[J]. 中国机械工程, 2026, 37(1): 114-125.

Figures/Tables 19

Fig.1 Schematic diagram of the PM in 3T1R output mode

Fig.2 Schematic diagram of the PM in 3T output mode

Fig.3 Kinematic modeling of 3-DOF APM-PM

Fig.4 Displacement curves of moving platform 1 in 3T1R mode

Fig.5 Displacement curves of moving platform 2 in 3T mode

Fig.6 3D workspaces at the centroids of moving platforms 1 and 2

Fig.7 Motion curve of moving platform mode

Fig.8 Input singular position

Tab.1 Parameters of rotational inertia of each bar kg·mm2

名称	I_XX	I_YY	I_ZZ
杆件B₁C₁	185 518.3	314 549.1	261 395.8
杆件B₂C₂	257 012.5	169 818.5	196 233.8
杆件B₃C₃	100 552.4	271 593.9	171 441.8
杆件C₁D₁	448 544.8	527 994.4	261 925.3
杆件C₂D₂	481 678.6	424 287.5	207 711.1
T型杆D₁D₂E₃（动平台2）	187 919.2	242 926.1	562 211.3
杆件E₃D₃（动平台1）	226 360.8	270 871.4	484 048.2

Fig.9 The motion trajectory and law of moving platform 1 in 3T1R mode

Fig.10 Curves of driving force in 3T1R mode

Fig.11 The motion trajectory and law of moving platform 2 in 3T mode

Tab. 2 Constraint ranges for design variables

设计变量	约束范围	设计变量	约束范围
l₁	［70，170］	l₆	［110，210］
l₄	［130，230］	d	［102，152］
l₅	［75，175］	e	［250，350］

Tab.3 Parameter settings

维度	随机数	迭代次数	缩放因子	交叉概率
7	100	20	0.5	0.9

Fig.10 Curve of the objective function with the number of iterations

Tab.4 Parameter values of optimized mechanism components

变量	优化前	优化后	变量	优化前	优化后
l₁	120	105.437	l₆	160	205.031
l₄	180	227.425	d	152	177.401
l₅	125	94.118	e	300	278.112

Fig.13 Workspace of the optimized mechanism

Fig.14 Conceptual design diagram of the application scenario

Fig.15 Workflow diagram of APM-PM

References 20

[1]	KRUT S， COMPANY O， BENOIT M， et al. A New Parallel Mechanism for Scara Motions［C］∥ Proceedings of the 2003 IEEE International Conference on Robotics and Automation（ICRA 2003）. New York， 2003：1875-1880.
[2]	GHAFFARI H， PAYEGANEH G， ARBABTAFTI M. Kinematic Design of a Novel 4-DOF Parallel Mechanism for Turbine Blade Machining［J］. The International Journal of Advanced Manufacturing Technology， 2014， 74（5）： 729-739.
[3]	贺磊盈，涂叶凯，叶伟，等. 一种可整周回转的新型3T1R并联机构运动学分析［J］. 机械工程学报， 2018， 54（11）： 151-160.
	HE Leiying， TU Yekai， YE Wei， et al. Kinematics Analysis of a Novel 3T1R Parallel Manipulator with Full Rotational Capability［J］. Journal of Mechanical Engineering， 2018， 54（11）： 151-160.
[4]	BOURI M， CLAVEL R. The Linear Delta： Developments and Applications［C］∥ISR 2010 （41st International Symposium on Robotics） and ROBOTIK 2010 （6th German Conference on Robotics）. Munich， 2010： 1-8.
[5]	PRAUSE I， CHARAF EDDINE S， et al. Comparison of Parallel Kinematic Machines with Three Translational Degrees of Freedom and Linear Actuation［J］. Chinese Journal of Mechanical Engineering， 2015， 28（4）： 841-850.
[6]	MAZARE M， TAGHIZADEH M， RASOOL NAJAFI M. Kinematic Analysis and Design of a 3-DOF Translational Parallel Robot［J］. International Journal of Automation and Computing， 2017， 14（4）： 432-441.
[7]	吴砚博. 多模式机构模式切换力平稳性分析与冗余驱动优选研究［D］. 秦皇岛：燕山大学， 2023.
	WU Yanbo. Study on The Stability Analysis of Mode Switching Force and Redundant Drive Optimization of Multimode Mechanism［D］. Qinhuangdao：Yanshan University， 2023.
[8]	HUNT K. Kinematic Geometry of Mechanism［M］. Oxford： Clarendon Press， 1990.
[9]	ZLATANOV D， BONEV I， GOSSELIN C. Constraint Singularities as C-space Singularities［M］∥Advances in Rokot Kinematics. Dordrecht： Springer， 2002.
[10]	YE Wei， FANG Yuefa， GUO Sheng， et al. Two Classes of Reconfigurable Parallel Mechanisms Constructed with Multi-diamond Kinematotropic Chain［J］. Proceedings of the Institution of Mechanical Engineers， Part C： Journal of Mechanical Engineering Science， 2016， 230（18）： 3319-3330
[11]	KONG Xianwen. Reconfiguration Analysis of a 4-DOF 3-RER Parallel Manipulator with Equilateral Triangular Base and Moving Platform［J］. Mechanism and Machine Theory， 2016， 98： 180-189.
[12]	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］. 2023-08-29.
	SHEN Huiping， PAN Haiyue， LI Ju， et al . A 3 -DOF Translational Manipulator with Motion Decoupling and Symbolic Forward Position Solutions：China， 202310760734.9［P］. 2023-08-29.
[13]	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
[14]	沈惠平，邓嘉鸣，李菊，等. 少维输入-多维期望运动输出并联机构及其应用［J］. 机械设计与制造工程， 2013， 42（6）： 1-4.
	SHEN Huiping， DENG Jiaming， LI Ju， et al. Fewer Inputs-more Expected Outputs Parallel Mechanisms and Application［J］. Machine Design and Manufacturing Engineering， 2013， 42（6）： 1-4.
[15]	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.
[16]	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.
	SHEN Huiping， LI Ju， WU Guanglei， et al. Topological Structure Optimization for Parallel Robotic Mechanisms［M］. Beijing： Higher Education Press， 2025.
[17]	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［M］. Nanjing：Jiangsu Phoenix Education Publishing， Ltd，， 2025.
[18]	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： Structure， Kinematics and Dynamics［M］. Beijing： China Machine Press， 1996.
[19]	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.
[20]	王佳睿，张德强. 包装机PVC夹持步进装置同步带传动机构建模与动态特性分析［J］. 机械设计与制造， 2024（10）： 203-208.
	WANG Jiarui， ZHANG Deqiang. Modeling and Dynamic Characteristics Analysis of Synchronous Belt Transmission Mechanism in PVC Clamping and Stepping Device for Packaging Machine［J］. Machinery Design & Manufacture， 2024（10）： 203-208.