引用本文: 占旺龙, 方燕飞. 点的复合运动中任意相切型问题速度分析的一种特殊解法. 力学与实践, 2023, 45(6): 1393-1398.
Zhan Wanglong, Fang Yanfei. A special solution approach for velocity analysis of arbitrary tangential problems of the motion composition for moving points. Mechanics in Engineering, 2023, 45(6): 1393-1398.
 Citation: Zhan Wanglong, Fang Yanfei. A special solution approach for velocity analysis of arbitrary tangential problems of the motion composition for moving points. Mechanics in Engineering, 2023, 45(6): 1393-1398.

## A SPECIAL SOLUTION APPROACH FOR VELOCITY ANALYSIS OF ARBITRARY TANGENTIAL PROBLEMS OF THE MOTION COMPOSITION FOR MOVING POINTS

• 摘要: 对于相切型问题，实际作定轴转动刚体外形可能为任意封闭曲线，传统利用圆心到接触点距离保持不变特性选择动点的方法无法求解。针对这类问题，在教学中采用瞬时运动学分析方法，即找一特殊动点。该瞬时相对速度为零，从而得到所需要求解的运动学量，方法简单且直观。本文首先证明该特殊动点的存在性和唯一性，然后给出特殊动点的确定方法，最后给出3个求解实例。该方法在本校理论力学教学中得以实践，学生反映容易掌握和理解。

Abstract: For tangency type problems, the actual shape of the rigid body undergoing rotational motion can be any closed curve. The traditional method of selecting a moving point based on the characteristic that the distance between the center and the contact point remains constant is insufficient for solving these problems. In order to address this type of problem, the instantaneous kinematic analysis method is utilized in teaching, which involves finding a special moving point. This point has an instantaneous relative velocity of zero, allowing us to obtain the required kinematic quantities easily and intuitively. This paper first proves the existence and uniqueness of this special moving point, then provides a method for determining this point, and finally presents three examples of solving such problems. This method has been applied in the teaching of theoretical mechanics at our university and has been well received by students due to its easy grasp and understanding.

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