Department of Mathematics
University College Dublin

UCD Openday 2004
Mathematics Problem

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GEAR-BOX
a problem about
converting rotation into oscillation
A ``black box'' has a handle on top. When the handle is wound, a rod emerging from the box oscillates. the rod slides to and fro along its own length.

Except for the the box, rod and handle the only permitted components are wheels. Components can be fixed together or two may be rotationally linked by an axle pin passing through a circular hole in each, see sketch. Sliding contact is not permitted.

  1. Design the mechanism.
  2. Give a geometric diagram or a formula which describes the principle of your machine.
  3. Using your diagram or formula prove that your machine performs as specified in (i)


Origin of the problem
A simplified view of a one cylinder engine is that a piston moves up and down being connected by a rod to a rotating fly wheel. However the rod does not quite move along its own length and piston motion is not quite a pure oscillation, usually called simple harmonic motion.
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Revised 10 Mar 2004.