齒輪機構之運動特徵分析與合成

Abstract

本論文主要利用運動分解的概念進行齒輪機構運動的特徵分析與合成，以及經由運動特徵進行齒輪機構的分類。齒輪機構可被分解為數個單自由度的運動單元，每個運動單元則被視為齒輪機構內的運動傳輸模組。運動單元間的拓樸構造連接可分為雙鏈結型與同軸三角型，內文將分析內含四個運動單元，單自由度至六桿，以及兩個自由度至七桿的齒輪機構，並且說明及表列其對應的拓樸構造；藉由選擇輸入與輸出端的位置，可得到齒輪機構內所有可能的運動傳輸路徑並將路徑以控制區塊圖表示。利用控制區塊的增益計算公式，將輸入端與輸出端的運動關係公式化為增益矩陣。 接著進一步討論運動單元內部條件對整體運動增益的影響；運動單元內輸出入桿件的不同及運動單元間的共同連接部分的接頭條件會共同影響整體增益的表現形式，利用增益表現形式的差異可將內含四個運動單元，單自由度至六桿，以及兩個自由度至七桿的齒輪機構做完整分類，根據增益型式分類及運動特徵可得到功能導向之齒輪設計方法。

A methodology based on the concept of kinematic fractionation for the revelation of kinematic characteristics and classification of geared mechanisms is presented. It is shown that structurally non-fractionated geared mechanisms can be considered as the combination of kinematic units (KUs). Each KU is considered as the basic motion transmission module inside a geared mechanism. Admissible connections of KUs are identified according to the structural characteristics of one- and two-DOF geared mechanisms of up to four KUs. Such configurations are then used to construct possible propagation paths of motion via the assignments of input and output links. Since the propagation paths can be modeled by the control block diagram problems, the kinematic relations between input and output links are formulated to gain matrices. According to the types of entities in a gain matrix, various kinematic behaviors are disclosed. The complete kinematic behavior of single KU is revealed and three gain forms of KU is basic of global gain since the geared mechanism is combination of KUs. The global gain of the mechanism is determined by three factors: the configuration decides the transmission flow at KU level, the common linkage between KUs of the mechanism limit the thin edge type of local input and output in the connection of KUs, the assignment of input, ground and output decides the thin edge type of global input and output. From the factor of global gain, there are three gain type are identified and characteristics of geared mechanism are more clear. It is believed that such kinematic characteristics can be readily transformed into the functional requirements and synthesis of geared mechanisms of up to four KUs can be accomplished much easier.