基於運動退化建立之不可分割齒輪運動鏈之運動家族研究

Abstract

結構上不可分割而運動上可分割的齒輪運動鏈的圖集中，各個齒輪運動鏈經過共軸桿件之相對運動固定的運動退化機制後，轉變為其他運動鏈的圖形，即出現其他運動鏈的運動行為，該運動退化機制使不同圖形的的齒輪運動鏈產生關聯；將這些圖集中不同自由度桿件數的齒輪運動鏈經確認並以運動退化串接後，構成了複雜密集的運動退化網路。 本文說明運動退化的作用原理，根據圖形經運動單元分割後的共軸桿件位置，將共軸桿件分成屬於運動單元內部的共軸桿件，以及屬於運動單元之間的共軸桿件。接著對兩種共軸桿件分別進行運動退化，造成運動單元內部退化以及運動單元之間退化，並伴隨著自由度與桿件數下降。此外，某些無法從現有圖集中退化而得的齒輪運動鏈，可由運動退化的法則而推測出退化前的高自由度齒輪運動鏈。 接著將每一個高自由度以及其退化後的所有低自由度齒輪運動鏈分別集合，其金字塔結構類似無輸入輸出地桿之離合器順序表，內部成員具有運動相關，故視為運動家族。各個運動家族群的低自由度成員之間具有完全相同、完全不同以及部分相同的三種特性。本文呈現出完全相同特性的運動家族群，以及在高自由度成員擁有相同的旋轉圖形卻具有完全不同特性的運動家族群。

A methodology on kinematic degeneration among structurally non-fractionated but kinematic fractionated geared kinematic chains (GKCs) is presented in graph representation using the concept of kinematic fractionation. By degenerating two or more coaxial links as a rigid link in a GKC, a higher-DOF GKC can be degenerated into lower-DOF GKC(s). According to location of coaxial links in the kinematic units (KUs) fractionated from graph representation, coaxial links are classified into intra- and inter-KU coaxial links. The characteristics and rules of intra- and inter-KU degeneration between the numbers of DOF, links as well as joints are revealed according to degeneration of intra- and inter-KU coaxial links, respectively. Due to different kinematic behaviors obtained by degenerating different coaxial links, the higher-DOF GKC and its all lower-DOF GKCs are clustered in one kinematic family. The specific relations of strength on lower-DOF members between kinematic families are expressed. Kinematic families provide compact relations between different DOFs and links of GKCs