Ball Bearings

number of tangent circles

3

answer

A ball bearing consists of a central cylinder of radius

r

surrounded by

n

tangent balls of radius

ρ

. All the balls are circumscribed by a hollow cylinder with radius

R=1

, for simplicity.

In the cross section, the cylinder is shown as an orange disk, the balls are shown as purple disks, and the hollow cylinder is shown as a circle.

The radius of the central cylinder is

r=(1-sin(π/n))/(1+sin(π/n))

.

The radius of any purple ball is

ρ=(1-r)/2

.