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STATICS - CASE STUDY

    Introduction


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, rr, is set at 2.5 in and does not rotate (fixed).
  • The handle spin rate, wa, 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.
     


  Question
 

Using an epicyclical gear mechanism, what gear radii (rs and rp) are best to produce a high spin rate of the container bowl (i.e. sun gear, ωs) with a moderate spin rate of the handle (ωa)?

   
  Approach

 
  • 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.
     

Planetary Gear System in the Volt Electric Car