Analysis and Calculation of DOF of Multi-loop Coupling Mechanism based on Constraint Normal Line

Guojun Luo; Xiaohui Wang; Xianguo Yan; Youli Wang

doi:10.16578/j.issn.1004.2539.2022.05.009

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Analysis and Calculation of DOF of Multi-loop Coupling Mechanism based on Constraint Normal Line

Design· Calculation | 更新时间：2022-09-24

- Analysis and Calculation of DOF of Multi-loop Coupling Mechanism based on Constraint Normal Line
- Journal of Mechanical Transmission Vol. 46, Issue 5, Pages: 62-68(2022)
- 作者机构：
  
  1.太原科技大学机械工程学院，山西太原 030024
  2.重型机械教育部工程研究中心，山西太原 030024
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2022.05.009
  CLC：
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罗国军,王晓慧,闫献国等.基于约束法线的多环耦合机构自由度分析计算[J].机械传动,2022,46(05):62-68.

Luo Guojun,Wang Xiaohui,Yan Xianguo,et al.Analysis and Calculation of DOF of Multi-loop Coupling Mechanism based on Constraint Normal Line[J].Journal of Mechanical Transmission,2022,46(05):62-68.
罗国军,王晓慧,闫献国等.基于约束法线的多环耦合机构自由度分析计算[J].机械传动,2022,46(05):62-68. DOI： 10.16578/j.issn.1004.2539.2022.05.009.

Luo Guojun,Wang Xiaohui,Yan Xianguo,et al.Analysis and Calculation of DOF of Multi-loop Coupling Mechanism based on Constraint Normal Line[J].Journal of Mechanical Transmission,2022,46(05):62-68. DOI： 10.16578/j.issn.1004.2539.2022.05.009.

摘要

针对空间多环耦合机构比空间并联机构更加复杂，运动链之间通过运动副作用于耦合构件产生了更多的约束作用，提出了一种适用于多环耦合机构的自由度计算新方法。首先，确定机构中的耦合构件，结合运动副约束法线分布，把机构中各构件之间通过运动副产生的约束，简化成约束点上法线的分布；然后，将耦合机构的自由度分析转化为分析各个耦合构件的约束法线几何关系，根据建立的约束法线几何关系对自由度的判定理论，分析判定耦合构件的自由度性质，并确定各耦合构件的过约束数目；最后，通过机构的连续性确定虚约束数目，代入自由度计算公式，得到多环耦合机构的自由度。结合实例分析可知，新方法不仅可以求得各耦合构件的自由度，还可准确计算耦合机构的自由度。新方法理论依据充分，物理意义明确，可有效应用于耦合机构的自由度分析。

Abstract

Since spatial multi-loop coupling mechanisms are more complicated than spatial parallel mechanisms， and the coupling members are more restrained by the side effects of motion between kinematic chains， a new method for calculating degrees of freedom （DOF） suitable for multi-loop coupling mechanisms is proposed. The idea is to firstly determine the coupling components in the mechanism， combine the constraint normal line distribution of the motion pairs， combine the constraints generated by the motion pairs between the various components in the mechanism， simplify into the distribution of normal lines on the constraint points， and then transform the degree of freedom analysis of the coupling mechanism into an analysis of the geometric relationship of the constraint normal lines of each coupling member. According to the established theory of determining the degrees of freedom of the constraint normal line geometric relationship， analyze and determine the nature of the degrees of freedom of the coupling member， determine the number of over-constraint of each coupling member.Finally，determine the number of virtual constraints through the continuity of the mechanism， and substitute the degrees of freedom calculation formula to obtain the degrees of freedom of the multi-loop coupling mechanism. Combined with example analysis， the method can not only obtain the degrees of freedom of each coupling member but also accurately calculate the degrees of freedom of the coupling mechanism. The new method has a sufficient theoretical basis and clear physical meaning， can be effectively applied to the analysis of the degrees of freedom of the coupling mechanism.

关键词

多环耦合机构约束法线几何定理自由度计算

Keywords

Multi-loop coupling mechanismConstraint normal lineGeometric theoremDegree of freedom calculation

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