Comparative Analysis of Stiffness Properties of Redundant/Non-redundant Over-constrained 2R1T PMs Based on the Mechanical Models of Limbs

doi:10.3969/j.issn.1004-132X.2026.08.010

Abstract

Abstract:

This paper presents a comparative stiffness performance analysis of two over-constrained parallel mechanisms （PMs） with redundant and non-redundant actuation， namely the 2RPU/2UPR and 2RPU/UPR configurations. First， the mechanical properties of the mechanism limbs are analyzed using the weighted generalized inverse method， yielding the distribution of limb forces within the prescribed workspace. Second， a simulation method for the dynamic mechanical properties at discrete interface point positions is proposed to emulate the motion of translational pairs， and the simulation results are mutually validated with theoretical analysis. Finally， based on the above findings， a comparative stiffness analysis of the two mechanisms is conducted from the perspective of the weakest limb components. The resistance and force conditions of the redundant limbs under external loads in different directions are obtained， providing guidance for the development of high-stiffness prototype structures.

Key words: redundant actuation, 2R1T parallel mechanism, mechanical property, stiffness analysis

摘要：

将冗余/非冗余驱动过约束并联机构2RPU/2UPR和2RPU/UPR进行对比分析。首先基于加权广义逆对机构支链的力学性能进行分析，得到支链在给定工作空间内的力学性能分布状况；然后提出一种离散界面点位置的动态力学性能仿真方法用于模拟移动副的运动过程，并与理论分析进行相互验证；最后基于上述力学分析结果，通过支链薄弱环节对两机构的刚度性能进行对比分析，得到冗余支链在受到不同方向外载荷时对机构形变的抵抗作用并判断支链约束的合理性，为后续高刚度样机的研制提供了方向。

关键词: 冗余驱动, 2R1T并联机构, 力学性能, 刚度分析

CLC Number:

TH112

XU Zhenghe, YANG Gaowei, LU Changheng, JIA Fuchun, MENG Jianguo, WANG Shaofeng. Comparative Analysis of Stiffness Properties of Redundant/Non-redundant Over-constrained 2R1T PMs Based on the Mechanical Models of Limbs[J]. China Mechanical Engineering, 2026, 37(8): 1909-1916.

徐郑和, 杨高炜, 卢昌亨, 贾富淳, 蒙建国, 王少锋. 基于支链力学模型的冗余/非冗余过约束2R1T并联机构刚度性能对比分析[J]. 中国机械工程, 2026, 37(8): 1909-1916.

Figures/Tables 15

Fig.1 2RPU/2UPR PM

Fig.2 2RPU/UPR PM

Tab.1 The parameters of mechanisms

参数名称	符号	数值
定平台Y方向长度	2a	0.18
动平台y方向长度	2h	0.3
动、定平台初始距离	Z	0.355
支链下连杆长度	l_i₁	0.14
支链上连杆半径	d_i₁	0.016
支链下连杆半径	d_i₂	0.02

Fig.3 Driving force distribution of 2RPU/2UPR PM

Fig.4 Simulation verification flowchart

Fig.5 Multi-interface point rod

Fig.6 Theoretical curves and simulation fitting curves

Fig.7 The rigid-flexible mixed model of 2RPU/2UPR PM

Fig.8 Comparison curve of the driving force theoryand the simulation fit

Fig.9 Design of the moving joint structure of PMs

Fig.10 The deformation diagram of PMs

Fig.11 Mechanical performance distribution diagram of 2RPU/UPR parallel mechanism under external load F1

Fig.12 Mechanical performance distribution diagram of 2RPU/2UPR parallel mechanism under external load F1

Fig.13 Mechanical performance distribution diagram of 2RPU/UPR parallel mechanism under external load F2

Fig.14 Mechanical performance distribution diagram of 2RPU/2UPR parallel mechanism under external load F2

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