Forward to non-circular gears!

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Forward to non-circular gears!
Jeff Schöner April 10, 2002 CS285, Spring 2002
Final Project
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Why non-circular gears?

• Challenge and Curiosity
• Circular gears are well studied and understood.
• Non-circular gears are usually mentioned in gear
  and mathematics texts as possible, but not fully
  described.
• Niche market exists for industrial use of these
  gears.
• Sometimes, machinery needs to turn with un-even
  velocities.
• Fun to look at and play with.

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Some examples
Flower / Square
Peanut / Trangle
Cardioid / Teardrop
above photos, from the Ohio State University
elliptical gears, from Nanni-Ingranaggi
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The Product to be Delivered

• Using the FDM machine, I will produce three or
  more interesting pairs of gears, like the ones
  shown on the previous slide.
• To the gears, handles will be added.
• These gears will be mounted on a piece of wood,
  where humans of all ages will be able to interact
  with them.
• This will be an interactive art piece.
• System could also be used to make real gears for
  industrial use.

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One Method for Shape

• Generate some interesting shapes, with parametric
  equations.
• Sample many different radial slices, taking each
  radius and theta value to compute the
  corresponding for the complementary gear.

boundary of gear a
radius a
radius b
rotation axis of b
rotation axis of a
theta
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Limitations to Overcome, Questions to Answer

• Only gears that have a fixed line of action can
  be done this way.
• Won't work for elliptical gears.
• Where are the teeth going to go?
• How does all of this figure into standard gear
  theory?
• Tk/Tcl in SLIDE can be a pain. Perhaps write a
  custom program to generate a SLIDE file
  containing the static gears.