Generating Functions Subject to Adjacency Constraints for Specialization of Mechanisms

應用生成函數產生鄰接限制之特殊化機構

10.29979/JCSME.201110.0004

林書弘(Shu-Hong Lin)；吳秋錦(Chiu-Chin Wu)；黃以文(Yii-Wen Hwang)

Type synthesis ； Generating function

中國機械工程學刊

32卷5期（2011 / 10 / 01）

401 - 408

英文

本篇文章以創新數學方法產生受鄰接限制的特殊化機構，且以生成函數來表示特殊化機構。此方法先從運動鏈的排列群求得生成函數，再將生成函數中的每一項乘上鄰接係數求得受鄰接限制的生成函數，鄰接係數的求法是從鄰接矩陣的子矩陣求得，因此他的作用相當於是在過濾鄰接限制條件，讓得到的特殊化機構符合鄰接限制條件。最後以兩個例子證明本研究提出之方法是有效率且具系統化的。

This paper proposes an innovative mathematical method for deriving the specialized mechanism expressed by generating function subject to adjacency constraints. First, generating function is driven from permutation group, and then every term in generating function multiply by an adjacency coefficient to obtain a generating function subject to adjacency constraint. The adjacency coefficient is calculated and derived from a submatrix of adjacency matrix. It acts as a filter to sieve out the specialized mechanisms that are subject to adjacency constraints. Two examples demonstrate the efficiency and systematicity of this proposed method.

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