A Spring-Driven Toothed Drum and the Unequal Force of Springs
'Here is the spring that moves' — why a coiled or fusee spring does not give equal service through its turns
The page is dominated by a carefully shaded drawing of a large toothed drum mounted in a frame, with a flat spring coiled inside driving a central toothed wheel; a note within the figure reads 'Here is the spring that moves' and labels it m f g n. Leonardo argues that springs do not do equal work in each half-turn: a toothed spring packs more teeth into its first half-turn (between m and n) than into the next, so it spends itself unevenly even though it is built of equal power throughout. He extends the point to a cord winding on a pyramidal screw (a fusee), which consumes the spring as much on its thin turn as on its thick one. A heading above declares that toward the end of its motion the weight always increases while the force always diminishes.
On this page
Of force and weight: weight grows and force wanes toward the end of motion
A short heading, 'De forza e peso' (Of force and weight): toward the end of its motion the weight always goes on increasing, and the force always diminishes.
The driving spring inside the toothed drum (m f g n)
A note set inside the large drum identifies the coiled flat spring, m f g n, as the mover: 'Here is the spring that moves.' The spring winds within the barrel and drives the central toothed wheel.
Why a spring gives unequal service across its half-turns, and the fusee
All springs fail to do equal service in each half-turn. If toothed, more teeth fall in the first half-turn (m n) than in the next (f n), so the spring spends equal parts of itself but yields unequal effect, degrading toward f g. A cord winding on a pyramidal screw behaves the same, consuming the spring as much on the screw's thin turn as on its thick turn, with less movement than other wheels.