Difference between the maximum and the minimum height of a oloid

Description

Oloid is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the other circle. The distance between the circle centers equals the radius of the circles. One third of each circle’s’ perimeter lies inside the convex hull, so the same shape may be also formed as the convex hull of the two remaining circular arcs each spanning an angle of 4π/3. While rolling the oloid it develops its entire surface: every point of the oloid touches the plane on which it is rolling, at some point during the rolling movement. The distance between the oloid’s center of mass and the rolling surface has two minima and two maxima. The difference between the maximum and the minimum height can be calculated by the radius.

Related formulas

Variables

ΔhThe difference between the maximum and the minimum height (m)
rRadius of the circle (or the distance between the circle centers) (m)