Toothed wheel and lantern pinion: turning and rubbing
How a pinion set off the wheel's diameter wears teeth and spindles
Two circular wheels rimmed with pins are drawn at the right, each on a shaft with its pinion — the upper one topped by a lantern-like cage. The accompanying text explains that when a pinion is set outside the wheel's diameter, every engagement produces two motions at once, a turning motion and a rubbing (friction) motion. It traces how a wheel-tooth first touches a spindle high up and slides off low down, wearing both the spindles and the teeth, following a single tooth (a) from where it enters above the pinion's centre to where it exits below, at point b.
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Two toothed-wheel and lantern-pinion arrangements
The right margin holds two pinned wheels on their shafts, engaged by pinions; the upper pinion is drawn as a lantern cage. The diagrams set out the gear pairing whose contact geometry the notes dissect.
A pinion off the diameter makes both turning and rubbing
If the pinion is set outside the wheel's diameter, it produces both the turning motion and the rubbing (friction) motion. The paired points a and b mark where a tooth engages and releases.
Wear of spindles and teeth, from tooth a to point b
Because the wheel-tooth first touches the spindle toward its top and departs toward its bottom, each engagement combines a turning and a rubbing motion that heavily wears both spindles and teeth. The tooth a enters above the middle of the pinion and exits below that middle, at the point b.