KINEMATICS ANALYSIS IN TANGENTIAL PROBLEMS

In this paper, the tangential type problem in kinematics is analyzed. Firstly, the conclusion 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 given: 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 at the 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, and 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 for explaining the motion analysis method of "low pair replacing high pair" in the course of mechanical principles.