# Ball Bearings

Ball Bearings

A ball bearing consists of a central cylinder of radius surrounded by tangent balls of radius . All the balls are circumscribed by a hollow cylinder with radius , for simplicity.

r

n

ρ

R=1

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