Pulley blocks: the cord must run perpendicular to the axle
Rules for cords in converging and equidistant pulley systems, with a halving number series
Two half-sheets of notes on pulleys (carrucole) and the geometry of their cords. Leonardo lays down the rule that the cord leaving a pulley must be perpendicular to its axis, meeting it at right angles, and that if the axes of two or more pulleys converge one cord cannot stay seated in all their channels, whereas equidistant axes keep it united in the grooves. Down the right margin runs a descending series of halved numbers, from 2048 through 1024, 512 and on down to 1. Faint pulley-block sketches labelled a b and f accompany the text.
On this page
The cord leaving the pulley must be perpendicular to the axle
The line of the cord coming out of the pulley must be perpendicular to the line of its axis: that is, the cord's line intersects the axis line at right angles. At both entry and exit of the pulley this perpendicularity is necessary.
Converging pulley axes unseat the cord
If the lines of the poles of two or more pulleys converge, one and the same cord cannot stay in the channels of those pulleys during the motion of its operation.
Equidistant axes keep the cord united in its grooves
But if the lines of the poles are equidistant, the cord that moves such pulleys will always stay in their channels, united with them; and the cord at entry and exit must be perpendicular to the axis.
Descending series of halved numbers (2048 to 1)
Down the right margin runs a column of successively halved figures, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, paired with small counters, echoing the mechanical advantage of a stack of pulleys.