TL;DR
This paper investigates the minimal size of a circle that can hold a convex body without intersecting its interior, establishing bounds related to the body's width.
Contribution
It introduces bounds on the diameter of a holding circle, showing it can be smaller than the body's width but always exceeds two-thirds of it.
Findings
Diameter of a holding circle can be less than the body's width.
Diameter of a holding circle is always greater than two-thirds of the body's width.
Abstract
A circle C holds a convex body K if C does not meet the interior of K and if there does not exist any euclidean displacement which moves C as far as desired from K, avoiding the interior of K. The purpose of this note is to explore how small can be a holding circle. In particular it is shown that the diameter of such a holding circle can be less than the width w of the body but is always greater than 2w/3.
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Taxonomy
TopicsStructural Analysis and Optimization · Robotic Mechanisms and Dynamics · Elasticity and Material Modeling