Problem Diagram
(s = sun gear, p = planet gear,
a = arm, planet gear connector)

Cooks at Let Us Dine-R are not happy with the current salad spinning machine. It is slow and always breaks.

One suggestion is to design a high-tech salad spinner using an epicyclical gear mechanism.

What is known:

• The outside ring gear radius, r_r, is set at 2.5 in and does not rotate (fixed).
• The handle spin rate, w_a, is 1 rev/s.
• The sun gear is rigidly attached to the inside salad bowl container but is not fixed to the handle.
• The possible gear choices for the sun and planet gears are 0.5 in, 0.75 in, 1.0 in, and 1.5 in.

Using an epicyclical gear mechanism, what gear radii (r_s and r_p) are best to produce a high spin rate of the container bowl (i.e. sun gear, ω_s) with a moderate spin rate of the handle (ω_a)?

• Use the equation for motion around a fixed point.
• The tangent velocities of two touching gears are equal.
• The handle angular velocity will be directly related to the planet gear, which will in turn be related to the sun gear.