Ball Bearings

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.

[more]

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 .

The radius of any purple ball is .

[less]

Contributed by: Abraham Gadalla (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Joining the center of the orange disk O to the centers P and Q of two successive purple disks shows that the center angle is , where is the number of purple disks. The line segment connecting O to the tangent point of two consecutive purple disks bisects this angle, so each smaller angle measures . The line segment connecting P and Q is perpendicular to the line segment between the center of the orange disk and the tangent point of the two blue balls. Therefore:

.

Simplifying, .



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send