相切型问题的运动分析  

KINEMATIC ANALYSIS IN TANGENTIAL PROBLEMS

作　　者：吴泽艳[1] 叶永[1] 郑保敬[1] 罗威[1] 彭辉[1] WU Zeyan;YE Yong;ZHENG Baojing;LUO Wei;PENG Hui(College of Hydraulic&Environmental Engineering,China Three Gorges University,Yichang 443002,Hubei,China)

机构地区：[1]三峡大学水利与环境学院,湖北宜昌443002

出　　处：《力学与实践》2025年第2期426-434,共9页Mechanics in Engineering

基　　金：三峡大学研究生课程建设培育项目(SDKC202301);三峡大学一般教研项目(J2023079)资助。

摘　　要：对运动学中相切型问题进行了分析。首先利用刚体间滚动兼滑动的运动条件和速度投影定理,解释了文献中动点必然落在过切点的公法线上的结论,然后直接利用刚体间滚动兼滑动的运动条件,分析机构的运动过程,讨论速度和加速度的计算方法,并给出结论:对于平底从动件凸轮机构,取凸轮切点处曲率圆圆心为动点,则动点的相对速度和相对加速度的方向与切点处切向平行;对于任意曲线轮廓从动件凸轮机构,取凸轮切点处曲率圆圆心为动点,则动点的相对速度方向与切点处切向平行,相对加速度的方向未定;对本文研究的3种机构,均存在对应的瞬时替代机构,求解该瞬时替代机构,可得到原问题的解答。本文的结果既便于用来计算相切型问题的速度和加速度,又可用来解释机械原理课程中“高副低代”的运动分析方法。In this paper,the tangential type problem in kinematics is analyzed.Firstly,the conclusion,which states that the moving point must fall on the common normal between the tangential points in the literature,is explained by using the motion condition of rolling and sliding between two rigid bodies and the velocity projection theorem.Then,the calculation methods of velocity and acceleration are discussed directly by using the motion condition.The following conclusions are drawn:for the cam mechanism with flat bottom follower,if the center of the curvature circle at the tangential point of the cam is taken as the moving point,the relative velocity and acceleration of the moving point are parallel to the tangential direction of the tangential point;for the cam mechanism with arbitrary curved follower,if the center of the curvature circle atthe tangential point of the cam is taken as the moving point,the relative velocity of the moving point is parallel to the tangential direction of the tangential point,while the direction of the relative acceleration is undetermined;for the three kinds of mechanisms studied in this paper,there exists a corresponding instantaneous substitute mechanism,and the solution of the original problem can be obtained by solving the instantaneous substitute mechanism.The results of this paper are not only convenient for calculating the velocity and acceleration of the tangential type problem,but also aid in explaining the motion analysis method of"low pair replacing high pair"in the course of mechanical principles.

关 键 词：相切型问题 速度 加速度 高副低代 

分 类 号：O311.1[理学—一般力学与力学基础]