Design of a 3（rU）PU Metamorphic Parallel Mechanism Based on Variable Axis Kinematic Pairs

doi:10.3969/j.issn.1004-132X.2026.02.011

China Mechanical Engineering ›› 2026, Vol. 37 ›› Issue (2): 361-373.DOI: 10.3969/j.issn.1004-132X.2026.02.011

Design of a 3（rU）PU Metamorphic Parallel Mechanism Based on Variable Axis Kinematic Pairs

FENG Shengquan¹, QU Shuwei¹^,³(), LI Ruiqin¹, YAO Wei², MA Chunsheng¹

^1.School of Mechanical Engineering，North University of China，Taiyuan，030051
^2.North of England Robotic Innovation Centre （NERIC），University of Salford，Salford，M6 6AP，UK
^3.State Key Laboratory of Computer-Aided Design and Computer Graphics，Zhejiang University，Hangzhou，310058

Received:2024-08-15 Online:2026-02-25 Published:2026-03-13
Contact: QU Shuwei
Supported by:
］ DONG Changbin, LI Longkun, LIU Yongping, et al. Translation Torsion Coupling Dynamic Modeling and Nonlinearities Investigation of Non-circular Planetary Gear Systems［J］. Nonlinear Dynamics, 2024, 112（21）： 18931-18948

基于变轴线运动副3（rU）PU变胞并联机构设计

冯盛权¹, 屈淑维¹^,³(), 李瑞琴¹, 姚威², 马春生¹

^1.中北大学机械工程学院, 太原, 030051
^2.索尔福德大学英格兰北方机器人创新中心, 索尔福德, M6 6AP
^3.浙江大学计算机辅助设计与图形系统全国重点实验室, 杭州, 310058

通讯作者: 屈淑维
作者简介:冯盛权，男，1999年生，硕士研究生。研究方向为机构理论与机器人装备
屈淑维^*（通信作者），女，1978年生，副教授。研究方向为机构理论与机器人装备。E-mail：shuweiqu1222@ nuc.edu.cn。
基金资助:
中央引导地方科技发展项目(YDZJSX2025D042);山西省重点研发计划(202202150401018);山西省基础研究计划(20210302124220);山西省基础研究计划(202203021211101);山西省基础研究计划(202503021211112);浙江大学计算机辅助设计与图形系统全国重点实验室开放课题（A2325）

Abstract

Abstract:

The line geometric method of screw theory was used to analyze the geometric relationship among the axes of the kinematics pairs in the UPU limbs， it is found that the constraints of the limbs vary with different geometric relationships. Based on this law， a variable axis kinematics pair （rU） composed of a U pair， a slider， and a slideway was designed. By sliding the sliders on the slideway to drive the U-pair connected with the sliders to slide， a revolute pair axis direction was changed in the U-pair， thereby the geometric relationship among the axes was changed. By replacing the U-pair on the UPU limb with the variable axis kinematic pair （rU）， the 3（rU）PU metamorphic parallel mechanism may achieve both three rotations （3R） and three translations （3T）. An equivalent plane of the UPU limb was proposed， and the equivalence plane was applied to analyze the degrees of freedom （DOF） of the 3（rU）PU metamorphic mechanisms in motion. A retractable platform was designed to resize the lower platform based on the similarity of equilateral triangles. It was verified by simulation experiments that the metamorphic mechanisms may realize both 3R-3T motion modes. The mechanisms will be used in position and orientation adjustments.

Key words: 3（rU）PU metamorphic parallel mechanism, variable axis kinematic pair, 3R-3T motion mode, switching plan, position and orientation adjustment

摘要：

运用螺旋理论的线几何法分析UPU支链中运动副轴线之间的几何关系，发现几何关系不同，则支链的约束不同，根据这一规律设计了一种由U副、滑块和滑轨组成的变轴线运动副（rU）。通过滑块在滑轨上滑动来带动与滑块连接的U副滑动，实现U副中一个转动副轴线方向的变化，从而改变轴线之间的几何关系。用变轴线运动副（rU）代替UPU支链上的U副，使得3（rU）PU变胞并联机构可以实现三转动（3R）和三移动（3T）两种运动。提出UPU支链的等效平面，并将该等效平面应用于运动中3（rU）PU变胞机构自由度的分析。基于等边三角形的相似性设计了一种可伸缩平台，用于调整下平台的大小。通过仿真实验证明该变胞机构可实现3R-3T两种运动模式，该机构被应用于位姿调整中。

关键词: 3（rU）PU变胞并联机构, 变轴线运动副, 3R-3T运动模式, 切换方案, 位姿调整

CLC Number:

TH112

FENG Shengquan, QU Shuwei, LI Ruiqin, YAO Wei, MA Chunsheng. Design of a 3（rU）PU Metamorphic Parallel Mechanism Based on Variable Axis Kinematic Pairs[J]. China Mechanical Engineering, 2026, 37(2): 361-373.

冯盛权, 屈淑维, 李瑞琴, 姚威, 马春生. 基于变轴线运动副3（rU）PU变胞并联机构设计[J]. 中国机械工程, 2026, 37(2): 361-373.

Figures/Tables 33

Fig.1 The UPU limb

Fig.2 Diagram of UPU limb

Fig.3 The variable axis kinematic pair

Fig.4 Geometric conditions of the mechanism

Fig.5 Initial geometrical conditions of the mechanism

Fig.6 The 3（rU）PU metamorphic parallel mechanism

Fig.7 Diagram of 3R mode mechanism

Fig.8 Equivalent diagram of 3R mode

Fig.9 The 3R mode after rotating

Fig.10 The 3R mode after translating along Z axis

Fig.11 Diagram of 3T mode mechanism

Fig.12 Equivalent diagram of 3T mode

Fig.13 The 3T mode after translating

Fig.14 Geometric relationship of the retractable platform

Fig.15 The retractable platform

Fig.16 Overall configuration of 3（rU）PU metamorphic parallel mechanism

Fig.17 Model and state simulation of 3（rU）PU metamorphic parallel mechanisms

Fig.18 The 3R mode one-state simulation

Fig.19 The 3R mode two-state simulation

Fig.20 The 3T mode one-state simulation

Fig.21 The 3T mode two-state simulation

Fig.22 Constraints on the intersecting limbafter locked Si1

Fig.23 The 3R mode after locked Si1

Fig. 24 Model and state switching simulation of 3（rU）PU metamorphic parallel mechanisms

Fig.25 Simulation of 3R mode state switching

Fig 26 Constraints on the parallel limb after locked Si1

Fig.27 The 3T mode after locked Si1

Fig.28 Simulation of 3T mode state switching

Fig.29 Constraints on the limb after locked Si3

Fig.30 The 3R mode after locked Si3

Fig.31 The 3T mode after locked Si3

Fig.32 The Mode switching simulation

Fig.33 Application of the metamorphic mechanisms

References 19

[1]	康熙，戴建生. 机构学中机构重构的理论难点与研究进展——变胞机构演变内涵、分岔机理、设计综合及其应用［J］. 中国机械工程， 2020， 31（1）： 57-71.
	KANG Xi， DAI Jiansheng. Theoretical Difficulties and Research Progresses of Mechanism Reconfiguration in Mechanisms—Evolution Connotation， Furcation Principle， Design Synthesis and Application of Metamorphic Mechanisms［J］. China Mechanical Engineering， 2020， 31（1）： 57-71.
[2]	张磊，王延杰，唐刚强，等. 基于变胞机构的移动机器人构型设计研究综述［J］. 信息与控制， 2022， 51（1）： 12-22.
	ZHANG Lei， WANG Yanjie， TANG Gangqiang， et al. Review of Configurational Design of Mobile Robot Based on Metamorphic Mechanism［J］. Information and Control， 2022， 51（1）： 12-22.
[3]	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.
[4]	LI Ju， WU Guanglei， SHEN Huiping， et al. Topology of Robotic Mechanisms： Framework and Mathematics Methods－in Conjunction with a Review of Four Original Theories［J］. Mechanism and Machine Theory， 2022， 175： 104895.
[5]	周杨，畅博彦，金国光，等. 面向变胞机构动力学建模的变拓扑构型数学描述方法［J］. 机械工程学报， 2022， 58（9）： 49-61.
	ZHOU Yang， CHANG Boyan， JIN Guoguang， et al. Mathematic Description Method of Variable Topology Configuration for Dynamic Modeling of Metamorphic Mechanism［J］. Journal of Mechanical Engineering， 2022， 58（9）： 49-61.
[6]	于红英，曾重元，郭震. 少自由度变胞并联机构综合设计方法［J］. 哈尔滨工业大学学报， 2018， 50（1）： 42-49.
	YU Hongying， ZENG Zhongyuan， GUO Zhen. Type Synthesis Method of Lower-mobility Metamorphic Parallel Mechanism［J］. Journal of Harbin Institute of Technology， 2018， 50（1）： 42-49.
[7]	王汝贵，孙家兴，戴建生. 基于遗传基因理论的变胞机构变胞方程研究［J］. 机械设计与研究， 2019， 35（1）： 75-80.
	WANG Rugui， SUN Jiaxing， DAI Jiansheng. Research on Metamorphic Equation of Metamorphic Mechanism Based on Genetic Gene Theory［J］. Machine Design & Research， 2019， 35（1）： 75-80.
[8]	GAN Dongming， DAI J S， DIAS J， et al. Reconfigurability and Unified Kinematics Modeling of a 3RTPS Metamorphic Parallel Mechanism with Perpendicular Constraint Screws［J］. Robotics and Computer-Integrated Manufacturing， 2013， 29（4）： 121-128.
[9]	YE Wei， CHAI Xinxue， ZHANG Ketao. Kinematic Modeling and Optimization of a New Reconfigurable Parallel Mechanism［J］. Mechanism and Machine Theory， 2020， 149： 103850.
[10]	贾璞，李端玲，雷志强，等. 一种3（Ra）PS变胞并联机构构型与运动学分析［J］. 农业机械学报， 2022， 53（2）： 443-450.
	JIA Pu， LI Duanling， LEI Zhiqiang， et al. Configuration and Kinematics Analysis of a 3（Ra）PS Metamorphic Parallel Mechanism［J］. Transactions of the Chinese Society for Agricultural Machinery， 2022， 53（2）： 443-450.
[11]	吴腾，张武翔，丁希仑. 一种新型并联变胞机构的设计与分析［J］. 机械工程学报， 2015， 51（7）： 30-37.
	WU Teng， ZHANG Wuxiang， DING Xilun. Design and Analysis of a Novel Parallel Metamorphic Mechanism［J］. Journal of Mechanical Engineering， 2015， 51（7）： 30-37.
[12]	GAN Dongming， DIAS J， SENEVIRATNE L. Unified Kinematics and Optimal Design of a 3rRPS Metamorphic Parallel Mechanism with a Reconfigurable Revolute Joint［J］. Mechanism and Machine Theory， 2016， 96： 239-254.
[13]	WANG Ruiqin， KANG Xi， DAI J S. A Novel Reconfigurable Spherical Joint Based on Linear Independence of Screws and Its Resultant Metamorphic Mechanisms［J］. Mechanism and Machine Theory， 2021， 164： 104351.
[14]	贾璞，李端玲，李海源，等. 基于变胞铰链的并联机构结构设计与构型分析［J］. 机械工程学报， 2020， 56（19）： 92-102.
	JIA Pu， LI Duanling， LI Haiyuan， et al. Structural Design and Configuration Analysis of Parallel Mechanism with Metamorphic Joint［J］. Journal of Mechanical Engineering， 2020， 56（19）： 92-102.
[15]	WEI Jun， DAI Jiansheng. Reconfiguration-aimed and Manifold-operation Based Type Synthesis of Metamorphic Parallel Mechanisms with Motion between 1R2T and 2R1T［J］. Mechanism and Machine Theory， 2019， 139： 66-80.
[16]	畅博彦，金国光，戴建生. 基于变约束旋量原理的变胞机构构型综合［J］. 机械工程学报，2014，50（5）： 17-25.
	CHANG Boyan， JIN Guoguang， DAI Jiansheng. Type Synthesis of Metamorphic Mechanism Based on Variable Constraint Screw Theory［J］. Journal of Mechanical Engineering， 2014， 50（5）： 17-25.
[17]	YE Wei， LI Qinchuan. Type Synthesis of Lower Mobility Parallel Mechanisms： a Review［J］. Chinese Journal of Mechanical Engineering， 2019， 32（1）： 13-23.
[18]	WEI Jun， YU Bin， LIU Chenglei， et al. Grassmann Line Geometry Based Configuration Synthesis of Equivalent UU Parallel Mechanisms with Two Virtual Center-of-motion［J］. Mechanism and Machine Theory， 2023， 181： 105208.
[19]	于靖军，刘辛军，丁希仑，等. 机器人机构学的数学基础［M］. 北京：机械工业出版社， 2008.
	YU Jingjun， LIU Xinjun， DING Xilun， et al. Mathematical Basis of Robot Mechanism［M］. Beijing： China Machine Press， 2008.

Design of a 3（rU）PU Metamorphic Parallel Mechanism Based on Variable Axis Kinematic Pairs

基于变轴线运动副3（rU）PU变胞并联机构设计

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Figures/Tables 33

References 19

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