The pivots of wheels: friction, wear and lubrication
Why short pivots run better than long, how a socket wears to a pyramid, and how to oil them
Under "On the pivots of the wheels," Leonardo argues that equally loaded pivots of equal thickness move with equal ease regardless of contact length (referring back to an earlier book on the friction of heavy bodies), but that this is upset by oil that thickens with heat and dust into a viscous, retarding paste (text 2). A long pivot meets proportionally more resistance than a short one, so short pivots run better, though they wear their seats faster; the consumed socket ends up pyramidal on its two sides, and the round hole is spoiled before the pivot. He classifies kinds of pivots and their contacts (text 3) and advises oiling from the seat rather than through holes that clog with worn iron (text 4). Right-hand diagrams show a pivot in its bearing, standing cylindrical and conical pivots in blocks, and a socket "consumed by the pivot that turns within it" (text 5).
On this page
Short pivots run better; oil that thickens retards motion
Equally loaded pivots of equal thickness should move with equal ease whatever their contact length, but oil thickened by heat and dust makes a viscous paste that impedes motion. A pivot ten degrees long meets ten degrees of resistance where a one-degree pivot meets only one, so the motion varies nine times more; hence pivots are better short than long.
The socket wears to a pyramid and fails before the pivot
A short pivot wears its seat faster, in proportion to the lengths of their contacts. The consumed hole stays pyramidal on its two sides, because the pivot thins as it turns and the seat wears with it; the contact shrinks as it goes. Thus the socket, losing its roundness, is spoiled before the pivot, which keeps its own.
Kinds of pivots and their contacts
Many pivots turn upon their supports; many act as supports of their own contacts, as in cart-wheel pivots; many bear weights without turning; and many turn with weights on them, some circular like grinding-wheels, some on one side like bells.
Better to oil from the seat than through holes
To give oil under the face of pivots loaded along their length, a better way than the drilled holes shown above is to raise the pivots and put the oil in the hollow where they rest, since such holes soon fill with worn iron mixed with oil and dust.