Lantern-pinion and toothed wheel: tooth wear and force
Gearing note: pinion K's teeth wear double; its force to h as 9 to 5 by 'On Motion and Force'
Two red-chalk drawings of lantern-pinions engaging toothed crown-wheels, gone over in pen, illustrate a note on gearing. Leonardo says the teeth of pinion K wear twice as fast because it has two motions, transverse and oblique, and that a moved body moves more easily when it escapes along the line of its mover's motion. He gives the force of the wheel-and-pinion train as the proportion of 9 to 5, citing the twentieth proposition of his 'On Motion and Force'.
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Lantern-pinions engaging toothed crown-wheels (K, h, m, f, r)
Two pinion-and-wheel assemblies are labelled h, K, n, f, m, r. Pinion K turns along the line m f and the wheel turns along the line f r; this train has such a proportion to pinion h in its force as 9 has to 5.
Tooth wear from double motion; the line of easiest motion
The teeth of K wear twice as much because it has two motions, transverse and oblique. A moved body will move more easily when it escapes along the line of the motion of its mover, a principle referred to the twentieth proposition of 'On Motion and Force'.