Utilize the generating functions to enumerate the specialized mechanisms with design constraints
Utilize the generating functions to enumerate the specialized mechanisms with design constraints
- Author(s): Chiu-Chin Wu ; Shu-Hong Lin ; Yii-Wen Hwang
- DOI: 10.1049/cp.2012.1448
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- Author(s): Chiu-Chin Wu ; Shu-Hong Lin ; Yii-Wen Hwang Source: International Conference on Automatic Control and Artificial Intelligence (ACAI 2012), 2012 p. 2251 – 2255
- Conference: International Conference on Automatic Control and Artificial Intelligence (ACAI 2012)
- DOI: 10.1049/cp.2012.1448
- ISBN: 978-1-84919-537-9
- Location: Xiamen, China
- Conference date: 3-5 March 2012
- Format: PDF
This study presents a mathematical method to calculate the generating function of the specialized mechanisms in type synthesis with design constraints. First, the link permutation group is derived from a candidate kinematic chain according to the combinatorial theory. Next, according to the types of design constraints, joint, path, and adjacent (or non-adjacent) pair groups are derived from the link group respectively. Then, the generating function of these groups can be calculated mathematically based on four well defined operators and basic groups. The generating function is a polynomial to express the results of specialized mechanisms subjected to a specific design constraint. The benefit of the method is that the results of the type synthesis can be calculated directly by mathematical manner without any inspection of isomorphism.
Inspec keywords: group theory; combinatorial mathematics
Subjects: Algebra; Combinatorial mathematics; Group theory; Algebra; Combinatorial mathematics; Combinatorial mathematics; Algebra
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