Toothed wheels, proportional circles and gear contact
Notes on how geared wheels mesh and on double, triple and quintuple proportion
The sheet mixes mechanics with mathematics: sketches of two partially toothed wheels accompany a note that meshing wheels engage tooth against tooth along a straight line of contact running to the poles of each wheel. Pairs of proportional circles illustrate a rule about how removing equal parts from two surfaces alters their ratio, worked through the example of double, triple and quintuple proportion. Faint further drawings and jottings remain on the sheet beyond the transcribed passages, including a small radiating sun-like figure.
On this page
How toothed wheels engage
Two partially toothed wheels are labelled a b and c d. The note explains that wheels turning by their teeth always take up and release one another through those teeth, and that for the engaging teeth the line of their contacts must run straight to the poles of each wheel, which happens when the teeth taper as pyramids toward the wheels' centres.
Double, triple and quintuple proportion
Pairs of circles are marked triple proportion and double proportion. Removing equal parts from two surfaces in a given ratio changes that ratio: from 8 and 4 (double), removing 2 from each leaves 6 and 2 (triple), while removing 3 from each leaves 5 and 1 (quintuple).
Circle diagram with points a and b
In the upper-left corner two tangent circles are drawn with converging lines and the letters a and b, part of a study connected to the angles of incidence explored on the sheet.
Radiating figure
A small radiating, sun-like figure is drawn in the upper-centre of the sheet among further untranscribed sketches; it lies outside the transcribed passages.