Friction in Pivots and Wheels; the Perfect Round on a Plane
How a pivot's diameter reduces the weight a wheel imposes on its mover
A dense mechanical study of cylinders and wheels turning on pivots ('poli') loaded with counterweights, examining how much of a wheel's weight bears on its axle and its mover. Leonardo argues that the smaller the pivot's diameter relative to the wheel's, the less of the wheel's natural weight is felt by the mover, and that a perfectly round body set on a perfect plane can be shifted by the smallest weight. A lettered section (t, m, o, n, r, f, b, a) analyses how a 400-pound load divides across the contact n f m. A column of figures and multiplications fills the lower left, and further faded notes on the sheet were not transcribed.
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How a 400-pound load divides across the pivot contact n f m
If the weights a b are 400 pounds, they discharge onto the contact n f m, with 200 pounds resting in n f and 200 in f m. This contact greatly hinders the mover, while the pivot o r t becomes easier for the mover the smaller it is than n f.
The perfect sphere on a perfect plane
A spheric body of perfect roundness set upon a perfect plane can be moved from its place by the smallest weight. It gives of itself an equal part and weight upon the point where it rests.
Cylinder on trestle supports with hanging counterweights
A cylinder rests on supports and carries counterweights, the loads noted as 10 and 10. Leonardo begins 'in this instrument it is as if …', but the note breaks off.
Column of figures and a multiplication
A worked block of numbers fills the lower-left corner, including the multiplication of 68754 by 31 to give 2131374, with the partial products 206262 and 68754.
When the mover's circle equals the wheel's
If the circle of the mover equals that of the wheel, then by as much as the pivot's diameter enters the wheel's diameter, by so much less than its natural weight does the wheel impose upon its mover. The truest test comes when the mover touches the greatest circle of the wheel.