THE CHARACTERISTIC POLYNOMIALS OF KINEMATIC CHAINS
Abstract
The application of graph theory to the structural analysis and synthesis of kinematic chains has been the subject of a number of studies in recent years. Since the structure of a kinematic chain is completely determined by its links and joints, a graph with points and lines can be related to a kinematic chain. Furthermore, since a graph is characterized by either its adjacencies or incidences, matrices can be defined to represent the graph. Therefore, it is possible to define a kinematic chain by its adjacency matrix, or one step further, by its characteristic polynomial. The purpose of this work is to study the properties of the characteristic polynomials of kinematic chains. An inspecting rule for obtaining the characteristic coefficients is presented, the physical meaning of the characteristic coefficients is explained, some assembly theorems for this polynomial are derived, and finally the uniqueness of this polynomial is investigated. It is hoped that this work can contribute to the identification of unknown kinematic chains and to the automated recognition of linkage structure in generalized computer-aided-design programs.
Degree
Ph.D.
Subject Area
Mechanical engineering
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