Emerging topics on differential geometry and graph theory (Nova Science Publishers, 2010)
Includes bibliographical references and index
""EMERGING TOPICS ON DIFFERENTIALGEOMETRY AND GRAPH THEORY""; ""CONTENTS""; ""PREFACE""; ""APPLICATIONS OF GRAPH THEORY IN MECHANISMANALYSIS""; ""Abstract""; ""1. Introduction""; ""2 Graph Representation of Mechanisms""; ""2.1. Topological Graph Representation of Kcs with Simple Joints""; ""2.2. Bicolored Graph Representation of Kcs with Multiple Joints""; ""2.3. Tricolored Graph Representation of Glms""; ""2.4. Combinatorial Graph Representation of Glkcs""; ""3. Detection of Isomorphism Among Kcs and Glkcs""; ""3.1. Detection of Isomorphism Among Kcs""
""(1) Theory to Detect Isomorphism among Kcs""""(2) Method to Detect Isomorphism among Kcs""; ""(3) Illustrations""; ""Example 1. Determination of Isomorphism of Kcs.""; ""Example 2: Determination of Isomorphism of Graphs""; ""3.2. Detection of Isomorphism among Glkcs""; ""(1) Theory to Detect Isomorphism Among Glkcs""; ""(2) Method to Detect Isomorphism Among Kcs""; ""(3) Illustrations""; ""Example 1: Determination of Isomorphism of the Glkcs, as Shown in Fig. 10(A) and (B)""; ""Example 2: Determination of isomorphism of the GLKCs, as shown in Fig. 11(a) and (b).""
""4. Topology-Loop Characteristics of Kcs""""4.1. The Number of Topological Loops of Bicolored Graph""; ""4.2. The Number of Topological Loops of Tricolored Graph""; ""5. Structural Decomposition of Mechanisms""; ""5.1. Principle of Structural Decomposition""; ""5.2. Calculation of Transformation Number""; ""5.3. Types of Kinematic Units""; ""5.4. Criteria of Choosing the Sequential Circuits""; ""5.5. Examples of Structural Decomposition""; ""Example 1: Fig. 15(A) Shows A PLM with one DOF, and Fig. 15(B) the Weighted Graphand Fig. 15(C) the Decomposing Procedure.""
""Example 2: Fig. 16(A) Shows a Hydraulic Mechanism with one DOF, and Fig. 16(B) theWeighted Bicolored Graph and Fig. 16(C) the Decomposing Procedure.""""Example 3: Fig. 17(A) Shows a GLM with one DOF, and Fig. 17(B) the WeightedTricolored Graph and Fig. 17(C) the Decomposing Procedure.""; ""Example 4: Fig. 18 Shows a Complex GLM, its Tricolored Graph, and the DecomposingProcedure.""; ""6. Conclusion""; ""References""; ""A CATEGORICAL PERSPECTIVE ON CONNECTIONSWITH APPLICATION IN THE FORMULATION OFFUNCTORIAL PHYSICAL DYNAMICS""; ""Abstract""; ""1. Introduction""