Gear trains, shaft torsion and skewed tooth-meshing
Poles of paired wheels, how a shaft twists with length, and pinions engaging wheels at equal angles.
This crowded folio (16v) gathers several transmission studies: discs on vertical shafts driven by pinions and crank-handles, screw shafts, a large toothed ring, and a bevel-gear pair mounted on a rod. The notes label the 'poles' (axes) of paired wheels and state that turning a single handle m drives two wheels a and n in contrary senses (texts 2, 4, 7). Text 6 reasons that the farther a driven wheel or gathering-rod lies from its source of motion, the weaker it is, so that a long span a-b twists upon itself while a shorter span c-d is far stronger. The lower notes describe setting a pinion between two crosswise wheels and a 'manner of skewing wheels' so each tooth engages its pinion at equal angles (texts 8-9).
On this page
Poles of the two wheels a and b
The axes of a paired set of wheels are labelled: a is the pole of the first wheel, b the pole of the second.
One handle drives two wheels in opposite senses
Turning the single handle m makes the two wheels a and n turn in contrary motions to one another.
A shaft twists more the longer its span
The greater the distance from the driving pinion (or gathering-rod) to the place it moves, the weaker that rod is. If from a to b there is much distance, the rod between a and b twists upon itself; but a shorter span like c-d is much stronger and of greater resistance.
Pinion set between two crosswise wheels
Two toothed wheels are set crosswise, teeth facing, with a little pinion between them taking teeth of each; when the pinion turns continuously in one direction, the two wheels must turn contrary to one another.
Skewing wheels for equal-angle tooth engagement
A 'manner of skewing wheels' is proposed so that each tooth engages between equal angles with the teeth of their pinions.