對於輸入桿作角位移運動的機構而言，由於機構的動能會隨著輸入桿角位置的不同而改變，以致輸入扭矩常有波動的現象，造成驅動轉速也隨之而變動，而導致其動態特性不佳。為改善該問題，前人提出在該機構上加入一倒置凸輪機構，以平衡其輸入扭矩。本研究除了加入彈簧於該倒置凸輪機構以期增進其對輸入扭矩的平衡效果外，建立該倒置凸輪機構的設計及分析模式，並加入應有的設計限制而得更泛用之平衡輸入扭矩的最佳設計模式，亦為本文之主要研究目的。
本文首先應用包絡理論建立具彈簧之倒置凸輪機構的凸輪輪廓設計模式；且建立該凸輪機構之各項特性分析的數學模式，包括壓力角分析、曲率分析、運動靜力分析，及推導系統輸入扭矩表示式。再以此為基礎分別進行應用該倒置凸輪機構於連桿機構及凸輪機構之輸入扭矩的最佳平衡設計，以期平衡後整體系統能有較佳的動態特性。並各以實例設計與分析，分別顯示及討論其結果。
根據本文所得的結果可知，分別應用該倒置凸輪機構於連桿機構及凸輪機構之輸入扭矩的平衡，均得到良好的結果；應用加入彈簧的倒置凸輪機構進行輸入扭矩平衡時，應考慮凸輪及滾子保持接觸之限制條件；並且在滾子與凸輪不能分離的前提下，具彈簧之設計的平衡效果較無彈簧者佳，表示將彈簧加入設計模式可提升平衡輸入扭矩的效能。因此，本文所得成果於學術及應用上均有其參考價值。

For a mechanism with a rotating input in a steady state, if its kinetic energy and input torque vary during a cycle, then its input speed may change cyclically, which would induce the mechanism having poor dynamic performance. An inverted cam mechanism was proposed in a previous study, which could be added to reduce the input torque fluctuation. Consequently, the dynamic characteristics of the mechanism may be improved. Except proposing adding springs on the inverted cam mechanism to improve its balancing effects, develop the design and analysis models of this inverted cam mechanism, for the optimum input torque balance of mechanisms, is also the main object of this study.
Theory of envelope is applied to develop the model of the cam profile design of the mechanism. Furthermore, the models for the analyses, such as pressure angle, curvature, kinetostatics, and input torque, of the mechanism are built. Based on these, the design models of the inverted cam mechanism with springs for the optimal input torque balances of linkages and cam mechanisms, respectively, are developed. Several examples are included to illustrate the balancing effects of the mechanism.
Based on the results, the inverted cam mechanism has good effects on balancing linkages and cam mechanisms. Subject to the constraint that the rollers must always contact with the fixed cams, the inverted cam mechanism with springs has better performance than the one without springs. It is believed that the results of this study have aids on both academy and industrial applications.

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