Terminal Constraint Analysis of (3-RPS)+(2-RCR) Hybrid Mechanisms

doi:10.3969/j.issn.1004-132X.2024.09.004

Abstract

Abstract: In order to explore the particularity of terminal constraint form of “parallel+parallel” type lower mobility hybrid mechanisms, taking (3-RPS)+(2-RCR) mechanisms as research object, a method for solving the intersection of screw systems corresponding to terminal constraint issue was proposed. Firstly, the composition principle of terminal constraint/mobility of (3-RPS)+(2-RCR) mechanisms was introduced, and the calculation formula of terminal constraint/mobility was given. Secondly, the number of terminal mobility of the mechanisms was analyzed using line geometry under different geometric configurations. Then, the ruled surface and generatrix equation corresponding to sub-constrained screw systems were established by analytic geometry theory and screw theory, and the intersection analytic model of three-screw system and four-screw system was obtained, and the terminal constraint of the mechanisms was determined. Thirdly, the terminal constraint/mobility properties were discussed under different geometric configurations. Finally, numerical examples of the mechanisms were given to solve the terminal constraint under three different configurations. The results show that terminal constraint of the mechanisms is not a constraint force/couple, but the general form of wrench under the general configuration. The method of solving the intersection of screw systems provides an effective way to solve the terminal constraint problems of this kind of hybrid mechanisms.

Key words: terminal constraint, hybrid mechanism, screw system, intersection, line geometry, ruled surface

摘要： 为探索“并+并”型少自由度混联机构末端约束的特点，以(3-RPS)+(2-RCR)机构为研究对象，提出了求解其末端约束的螺旋系求交法。阐述了(3-RPS)+(2-RCR)机构末端约束/自由度组成原理，给出了末端约束/自由度计算公式；结合线几何分析了机构在不同几何位形下的末端自由度数目；应用解析几何理论和螺旋理论建立子约束螺旋系对应的直纹面和母线方程，得到了螺旋三系和四系的交集解析模型，确定了机构末端约束螺旋；讨论了不同几何位形下的末端约束/自由度性质，给出机构在3种不同位形下末端约束求解的数值算例。研究表明，在一般位形下，该机构末端约束并非约束力/力偶，而是一般形式的力螺旋。提出的螺旋系交集求解方法为此类混联机构末端约束问题研究提供了有效的解决方案。

关键词: 末端约束, 混联机构, 螺旋系, 交集, 线几何, 直纹面

CLC Number:

TH112

HU Bo1, 2, ZHAO Jinjun1, 2, LIU Jianzheng1, 2, ZONG Hongyi1, 2. Terminal Constraint Analysis of (3-RPS)+(2-RCR) Hybrid Mechanisms[J]. China Mechanical Engineering, 2024, 35(09): 1548-1558.

胡波1, 2, 赵金君1, 2, 刘建正1, 2, 宗洪意1, 2. (3-RPS)+(2-RCR)混联机构末端约束分析[J]. 中国机械工程, 2024, 35(09): 1548-1558.

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