具有全旋轉對之平面單自由度平行運動機構之設計

Abstract

本文呈現了一個用於合成單自由度、全旋轉對平行運動機構（PMG）的方法，在機構中有兩非鄰接桿件被指定為平行桿件，平行桿件是指一對桿件在該機構的任何構型中永遠固定一相對角度差。 而平行桿件之間的固定角度差關係對於機構來說是設計者給的外部運動限制。 普遍的來說，當一個外部限制被引入到機構中，對於平面多自由度機構來說會減少一個自由度數，但對單自由度機構來說，它會轉變成一個過度拘束機構（over-constrained mechanism），並可由Grubler–Kutzbach equation證明得知。 藉由改變該過度拘束機構的獨立桿件數以及獨立迴路數，使它的運動行為與單自由度機構相同，就可得到用以合成平行運動機構的特殊桿件長度條件。 首先以四桿平行機構詳述本方法的觀念，接著列出多迴路機構與單迴路機構的不同之處，並以一個六桿平行機構的例子，敘述多迴路平行機構的作法。 最後，為了證明本方法的廣泛應用性，除了四桿、六桿平行機構之外，八桿平行機構一樣可以本方法得到，將所有可行的八桿平行機構分類，並從每一類中取出一個例子實行之。

A design methodology for the one degree of freedom (DOF), all-revolute, planar, parallel motion generators (PMGs) is proposed, where two non-adjacent links of the linkage are designated as parallel links, for which the relative orientation between the two links is kept constant at all configurations of the linkage. The relation that holds the paired links to have invariant relative angle is an additional motion constraint given to the system by the designer. In general, while any auxiliary constraint is imposed, a multiple-DOF planar linkage may lose one of its DOF’s and a one-DOF linkage may turn into an over-constrained linkage which can proof by Grubler–Kutzbach equation. By adjusting the number of independent links and independent loops, the over-constrained linkage will have the same behavior as the one-DOF linkage, and the special geometric conditions for PMG could be obtained. Elaborate the overall concept of the method with four-bar linkage firstly, and add the difference between multiple-loops and single-loop linkage with the aid of the example of six-bar linkage, finally, for the purpose of generalized of the method, examples of eight-bar linkage are demonstrated. Classify all admissible assignments of parallel links in eight-bar linkage into several types, and take one example of each type of admissible assignments.