Wheels, axles and levers for hauling a cart
Four iron-ringed wheels, a two-part rod on a pulley, and the mechanical advantage of the pivot
Pen studies of wheeled hauling gear fill the sheet: a group of parallel wheels labelled a, b, n and C at the top, a large wheel carrying an axle and a long lever at the right, and a two-part rod slung on a pulley. The notes size four wooden wheels ringed with iron — the great wheel e of 2 braccia down to wheel a of 1/3 braccio — and their iron pivots 2/3 of an oncia thick. Leonardo argues the mechanical advantage of turning a pivot within the radius of its wheel, likening the pivot of a cart to that of a bell, and reckons that a lever four times the wheel's semidiameter makes the pull four times easier. A short multiplication (3600 by 18) and the name 'Biagio', written with the sheet inverted, also appear.
On this page
The pivot as lever: cart, bell and wheel compared
The pivot of a cart performs upon the ground the same office as the pivot of a bell upon its rest: the more times that pivot fits within the lever of the bell, the more easily it yields to its mover. Likewise, the more times a wheel's pole can be counted within the space from it to the wheel's rim, the more easily the wheel turns. Turning the pole while the wheel stands still costs the same effort, over a lever equal to the wheel's semidiameter, as letting the pole stand fixed and turning the wheel upon it.
Axle-lever a and the four-fold gain in pulling
The effort of turning the cart's axle with lever a equals the effort of dragging the cart over a perfectly flat surface. If lever a is four times the wheel's semidiameter, the motion made with the lever is four times easier than hauling the cart; and conversely, if the wheel's semidiameter equals lever a, hauling the cart is easier than turning the lever.
Four iron-ringed wheels and their pivots
Each of the four wheels is to be of wood ringed with iron: the largest, e, of 2 braccia, wheel b of one braccio, and wheel a of 1/3 braccio. Wheel a may be omitted, but not wheel n, which eases the pull. The iron pivots are 2/3 of an oncia thick, so the great lever-wheel spans 36/3 of an oncia from pivot to ground against 1/3 of an oncia at the pivot's upper side.
Multiplication 3600 by 18
A worked multiplication set out in a column: 3600 multiplied by 18, giving 28800 with 3600, the running figures for the dimensions and loads reckoned elsewhere on the sheet.
The name 'Biagio'
The personal name 'Biagio' is jotted on the sheet with the page turned upside down, unconnected to the mechanical notes around it.