The Gerotor: Two Rotors, One Tooth Apart

The patent defines the rotors by construction, not by formula: "Let two circles be located upon a plane, one within the other and tangent to it. Let their diameters be in proportion to the numbers of tooth divisions selected for the two rotors which should differ by one." A master curve for one rotor's tooth is rolled round with its circle and "traced in each successive position"; the curve along the crests of the traces is the other rotor's contour. "This inner circle may rotate nine times while the outer circle rotates eight times", in inverse proportion to the numbers of teeth. Hill also describes making them this way: a master tool revolved round one pitch circle cuts a blank turning at the proportional speed about the other, generating the rotor exactly as the notebook does in numbers.

Add a line to the notebook that prints the inner profile's coordinates, and save them as a CSV. Import them into your CAD program as a spline and extrude 10 mm: that is the inner rotor, bored for an 8 mm steel shaft. Draw the outer rotor as a ring with nine 4 mm half-round teeth on a 20 mm radius, 10 mm thick, turning in a round pocket in a printed housing whose centre is 2 mm off the shaft's. Cut a kidney-shaped inlet port on the side where the chambers grow and an outlet where they shrink, in a clear acrylic cover plate with an O-ring round the pocket. Print the rotors in PETG at fine layer height and sand the faces flat on glass. Drive the shaft with a cordless drill, inlet in a jug of water, outlet into a graduated cylinder. Count revolutions with a tachometer and compare the water delivered per revolution with the notebook. The printed set leaks at its faces, so expect less; the difference is its volumetric efficiency.

**Myron F. Hill** of New York filed his first gerotor applications in 1921; **US 1,682,563**, *Internal Rotor*, divided from the application of 5 November 1921, was filed 14 January 1928 and granted 28 August 1928. He published *Kinematics of Gerotors* in 1927. With toolmaker **William H. Nichols** he built machines to make the rotor sets; the first commercial use was in oil-burner pumps in the 1930s. Gerotors, many of them pressed from powdered metal, now pump oil in engines and automatic transmissions. **Honest limits.** The notebook's area is counted on a grid and each chamber is split at the pin centre-lines, so its displacement is good to a few per cent, not exact. Printed rotors leak far more than ground metal ones. And gerotors suit moderate pressures; high pressure circuits use piston pumps.