Infinite Bar-Joint Frameworks
J.C. Owen, S.C. Power
TL;DR
This paper develops a mathematical theory for the rigidity and flexibility of infinite frameworks, providing conditions for flexibility and methods to simulate continuous paths using infinite linkages.
Contribution
It introduces new sufficient conditions for flexibility in infinite frameworks and demonstrates how to simulate continuous planar paths with infinite Kempe linkages.
Findings
Established conditions for the existence of proper flexes in infinite frameworks.
Showed how infinite Kempe linkages can simulate continuous paths in the plane.
Advanced the understanding of rigidity and flexibility in infinite structures.
Abstract
Some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained. In the first sufficient conditions, of a uniform local nature, are obtained for the existence of a proper flex of an infinite framework. In the second it is shown how continuous paths in the plane may be simulated by infinite Kempe linkages.
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Taxonomy
TopicsStructural Analysis and Optimization · Advanced Materials and Mechanics · Cellular Mechanics and Interactions