Rules of gearing: pinions, wheels and direction of turn
Whether meshing wheels turn together or opposed, and the tooth-spacing of pinion versus wheel.
Folio 15v is filled with gear studies: a spoked wheel on an axle, a crown wheel on a cone, lantern pinions, several meshing wheel-pairs, a boxed wheel raising a weight, and a small diagram of three circles inside a ring. The notes set out rules of gearing (texts 1-6): a driving pinion needs wider tooth-spaces than its wheel, externally meshing wheels turn in opposite senses while an internal engagement turns them the same way, and same-sense drive between two wheels requires a third (the 'third degree of motion'). A figure lettered a, b, c, d demonstrates how turning one wheel fixes the sense in which all the others turn.
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Pinion and wheel: tooth-space proportion
If a pinion is to drive a wheel, the spaces between the pinion's teeth must be larger than those of the wheel; if instead the wheel drives the pinion, the reverse holds. But if both are well made, equal teeth and spaces serve well.
Meshing wheels turn in opposite senses
Two toothed wheels touching on the outside turn contrary to one another; but if one wheel's outside drives the other on its inside, they turn in one and the same direction, whichever of the two is the source of motion. Turning one joined wheel likewise reverses the other.
Same-sense drive requires a third wheel
To make the wheel of the first motion drive another wheel turning the same way as itself, that second wheel must stand in the third degree of motion, i.e. a third wheel is interposed.
Direction of turn in the train a, b, c, d
In the lettered figure, whichever way the wheel d is turned, a and b turn the same way while c turns contrary; and if c is turned, every other wheel turns contrary to it.