- 學位論文
平板式和滾子式從動件之封閉式凸輪機構的充要設計條件
The Necessary and Sufficient Design Conditions for the FormClosed Cam Mechanisms with the Flat-Faced and Roller Follower
摘要
凸輪是一種將旋轉運動轉換成指定的輸出運動的機構，凸輪在現代工業中已經被廣泛使用，在實務上，已經有許多方法能夠用於分析與設計凸輪機構，然而，在理論上，凸輪機構是否可動這件事卻很少從數學上討論。本論文從數學上討論了要使四種凸輪機構(具有封閉式的平移平板從動件之凸輪機構、具有封閉式的平移滾子從動件之凸輪機構、具有封閉式的搖擺平板從動件之凸輪機構以及具有封閉式的搖擺滾子從動件之凸輪機構)可動的充分且必要的設計條件。對於前兩種凸輪機構，設計條件和凸輪機構的可動性之間的關係將透過證明由頂部和底部從動件所決定的凸輪輪廓需相等得出；對於第三種凸輪機構，該關係是透過將凸輪輪廓轉換為與正交曲線(orthoptic curve)相關的幾何圖形來得出；對於第四種凸輪機構，由於其從動件的臂長必須是可變的，因此為違反了剛體的基本性質，故在理論上無法設計。綜上所述，透過幾何方法，本文證明了前三種凸輪機構在且僅在它們滿足設計條件下，便會是可動的，而最後一種凸輪機構在理論上是永遠不可能被設計的。最後，本論文用數值範例展示了如何設計前三種凸輪機構以及第四種凸輪機構輪廓的誤差。
並列摘要
Cam, a mechanism usually used to transform a rotary motion into the desired output motion, has been commonly used in modern industry. In practice, a variety of practical methods have been discussed to analyze and synthesize the cam mechanism. In theory, however, the mobility of the cam mechanism is seldom mathematically addressed. This thesis mathematically discusses the necessary and sufficient design conditions for four kinds of cam mechanisms (a form-closed cam mechanism with a translating flat-faced follower, a form-closed cam mechanism with a translating roller follower, a form-closed cam mechanism with an oscillating flat-faced follower, and a form-closed cam with an oscillating roller follower) to be mobile. For the first two cam mechanisms, the relation between the design conditions and the mobility of the cam mechanism is derived by proving that the identical cam contour can be enveloped by the top and bottom follower faces. For the third cam mechanism, the relation is derived by transforming the cam contour into a geometric layout associated with an orthoptic curve. For the fourth cam mechanism, it is shown that the cam mechanism can not be theoretically designed due to its variable length of the follower arm, which does not obey the rigid body assumption. In conclusion, by means of these geometric methods, the first three kinds of cam mechanisms are proved to be mobile if and only if they satisfy the design conditions and the last cam mechanism is proved to be theoretically infeasible. Finally, numerical examples are given to demonstrate how to design the first three cam mechanisms and the error of the pitch curve of the fourth cam mechanism.