基于约束线的瞬轴求解方法

doi:10.3969/j.issn.1004-132X.2026.01.008

摘要/Abstract

摘要：

目前，空间瞬轴的主流求解方法为代数法，但机构稍复杂时代数法难以应用。从机构自由度本质为约束的观点出发，将机构运动副的约束用构件间的约束线来等效，研究了构件约束线数量及几何关系与构件自由度之间的关系。研究了构件约束线的性质与传递规律，证明了构件两条约束线的交点为构件的瞬心，两个约束面的交线为瞬轴，并从几何学角度论证了构件瞬心和瞬轴存在的充要条件。对构件约束线进行几何绘图和几何解析可确定机构构件的瞬心或瞬轴的位置。通过对Bennett机构连杆约束线的几何绘图和几何解析，求解了Bennett机构连杆的自由度和瞬轴，证明了从约束线出发求解构件瞬心和瞬轴方法的可行性。

关键词: 约束线, 瞬心, 瞬轴, Bennett机构

Abstract:

At present， the mainstream solution of spatial instantaneous axes was algebraic method， which was difficult to apply when the mechanisms were slightly complex. Starting from the perspective that the degrees of freedom of a mechanism were essentially constraints， the constraints of the motion pairs in the mechanisms were equivalent to the constraint lines between components， and the relationship between the number and geometric relationship of constraint lines on components and the degrees of freedom of components were studied. The properties and transmission laws of constraint lines on components were studied. It is proved that the intersection point of two constraint lines of a certain component is the instantaneous center， and the intersection line of two constraint surfaces is the instantaneous axis. The necessary and sufficient conditions for the existence of instantaneous centers and axes of components were demonstrated from a geometric perspective. Through geometric drawing and geometric analysis of constraint lines on components， the position of the instantaneous center or axis of each component in the mechanisms might be determined. The positions of instantaneous centers and axes were obtained through geometric drawing and analysis of the constraint lines on components. By geometric drawing and analysis of the constraint lines of the connecting rods in Bennett mechanisms， the degrees of freedom and instantaneous axis of the connecting rods in the Bennett mechanisms were solved， and the feasibility of using constraint lines to solve the instantaneous centers and axes was demonstrated．

Key words: constraint line, instantaneous center, instantaneous axis, Bennett mechanism

中图分类号:

TH122

王友利, 郭佳程, 王晓慧. 基于约束线的瞬轴求解方法[J]. 中国机械工程, 2026, 37(1): 66-72.

WANG Youli, GUO Jiacheng, WANG Xiaohui. A Method for Solving Instantaneous Axes Based on Constraint Line[J]. China Mechanical Engineering, 2026, 37(1): 66-72.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.01.008

https://www.cmemo.org.cn/CN/Y2026/V37/I1/66

图/表 12

图1 两条相交约束线的关系及等效

Fig.1 The relationship and equivalence of two intersecting constraint lines

图2 刚体在平面内全约束的约束线分布

Fig.2 The distribution of constraint lines for a rigid body fully constrained in a plane

图3 两条异面约束线关系及等效结果

Fig.3 The relationship and equivalence of two constraint lines in different planes

图4 平行面内的约束线关系及等效结果

Fig.4 The relationship and equivalence of constraint lines in parallel planes

图5 平面机构瞬心求解

Fig.5 The solution of instantaneous center of planar mechanisms

图6 基于约束线求解构件瞬轴的第一种情况

Fig.6 The first scenario of solving the instantaneous axes of components based on constraint line

图7 对图6基于约束线求解构件瞬轴

Fig.7 Solution of component instantaneous axis based on constraint line in Fig.6

图8 基于约束线求解构件瞬轴的第二种情况

Fig.8 The second scenario of solving the instantaneous axes of components based on constraint line

图9 基于约束线求解构件瞬轴的第三种情况

Fig.9 The third scenario of solving the instantaneous axes of components based on constraint line

图10 Bennett机构

Fig.10 Bennett mechanism

图11 Bennett机构中连杆的瞬轴分析

Fig.11 Analysis of the instantaneous axis of the connecting rod in a Bennett mechanism

图12 连杆瞬轴方程求解

Fig.12 Solution of the instantaneous axis equation of the connecting rod

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