# Contracted graphs of kinematic chains with multiple joints

Hong-Sen Yan, C. H. Hsu

Research output: Contribution to journalArticle

32 Citations (Scopus)

### Abstract

This paper presents an approach for the structural synthesis of kinematic chains with multiple joints based on the concept of contracted graphs. A graph representation of multiple joints is introduced and the modified Euler formula is derived. Then, contracted graphs of kinematic chains with m multiple joints and Lind independent loops are synthesized from the catalogs of contracted graphs of kinematic chains with simple joints and Lind + m independent loops. Finally, basic kinematic chains with multiple joints are obtained from their corresponding contracted graphs. As a result, the number of kinematic chains with one and two multiple joints up to ten links are listed.

Original language English 681-695 15 Mathematical and Computer Modelling 10 9 https://doi.org/10.1016/0895-7177(88)90158-6 Published - 1988 Jan 1

### Fingerprint

Kinematics
Graph in graph theory
Euler's formula
Graph Representation
Synthesis

### All Science Journal Classification (ASJC) codes

• Modelling and Simulation
• Computer Science Applications

### Cite this

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title = "Contracted graphs of kinematic chains with multiple joints",
abstract = "This paper presents an approach for the structural synthesis of kinematic chains with multiple joints based on the concept of contracted graphs. A graph representation of multiple joints is introduced and the modified Euler formula is derived. Then, contracted graphs of kinematic chains with m multiple joints and Lind independent loops are synthesized from the catalogs of contracted graphs of kinematic chains with simple joints and Lind + m independent loops. Finally, basic kinematic chains with multiple joints are obtained from their corresponding contracted graphs. As a result, the number of kinematic chains with one and two multiple joints up to ten links are listed.",
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In: Mathematical and Computer Modelling, Vol. 10, No. 9, 01.01.1988, p. 681-695.

Research output: Contribution to journalArticle

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T1 - Contracted graphs of kinematic chains with multiple joints

AU - Yan, Hong-Sen

AU - Hsu, C. H.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - This paper presents an approach for the structural synthesis of kinematic chains with multiple joints based on the concept of contracted graphs. A graph representation of multiple joints is introduced and the modified Euler formula is derived. Then, contracted graphs of kinematic chains with m multiple joints and Lind independent loops are synthesized from the catalogs of contracted graphs of kinematic chains with simple joints and Lind + m independent loops. Finally, basic kinematic chains with multiple joints are obtained from their corresponding contracted graphs. As a result, the number of kinematic chains with one and two multiple joints up to ten links are listed.

AB - This paper presents an approach for the structural synthesis of kinematic chains with multiple joints based on the concept of contracted graphs. A graph representation of multiple joints is introduced and the modified Euler formula is derived. Then, contracted graphs of kinematic chains with m multiple joints and Lind independent loops are synthesized from the catalogs of contracted graphs of kinematic chains with simple joints and Lind + m independent loops. Finally, basic kinematic chains with multiple joints are obtained from their corresponding contracted graphs. As a result, the number of kinematic chains with one and two multiple joints up to ten links are listed.

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