Rack-and-pinion pairing: module, material and geometry
Pairing a rack correctly with a pinion requires verifying three parameters: module, pressure angle and tooth profile. If all three match, the system works. Here you'll find the rules to check each one in a few minutes.
The rack as a limiting case of the gear
The rack is geometrically a gear with an infinite number of teeth and an infinite pitch radius: its profile is straight, what in engineering is called the reference rack (the normalized theoretical profile from which all the teeth of spur gears derive).
This means that the pairing laws of spur gears apply in full. Module, pressure angle and tooth profile of the pinion must be compatible with those of the rack. The fundamental condition is simple: pinion and rack must have the same module.
The resulting motion is different from that between two gears: the rotation of the pinion converts into linear translation of the rack (or vice versa). There's no transmission ratio in the classic sense. The advance per pinion revolution is equal to π × m × z, where m is the module and z the number of teeth.
Compatibility rules
Besides the module, verify that pinion and rack have the same pressure angle. The standard is 20°. Profiles with different angles, such as 14.5° or 25° used in some special applications, aren't interchangeable.
When you replace a steel rack with a nylon one, also check the tooth profile. The two most common forms are the normalized full-depth profile (full depth) and the short profile (stub tooth, a tooth with reduced height). If you have doubts about which the original profile is, measure the pitch, that is, the distance between the centers of two consecutive teeth: it equals π × m. Compare it with the normalized series to trace back to the module.
Nylon racks with a steel core
Racks with a nylon profile (PA6) and a steel core offer a good compromise between quietness and structural stiffness.
The nylon profile guarantees noise damping, no forced lubrication and protection of the pinion from abrasive particles. The steel core maintains the rack's straightness, the bending strength in the plane and simplifies mechanical fixing to the structure.
In case of frequent motion reversal, the tangential forces on the screws or retention systems can be high. Verify that the fixing system is sized for the forces involved before commissioning.
Modules table: pitch, compatibility and advance
| Module | Pitch (mm) | Compatible pinions (z min – z max) | Advance per pinion rev z20 (mm) |
|---|---|---|---|
| $m = 1$ | $\pi \times 1 = 3.14$ | z = 12 ... 50 | 62.8 mm/rev |
| $m = 1.5$ | $\pi \times 1.5 = 4.71$ | z = 14 ... 60 | 94.2 mm/rev |
| $m = 2$ | $\pi \times 2 = 6.28$ | z = 15 ... 80 | 125.7 mm/rev |
| $m = 3$ | $\pi \times 3 = 9.42$ | z = 16 ... 80 | 188.5 mm/rev |
| $m = 4$ | $\pi \times 4 = 12.57$ | z = 17 ... 60 | 251.3 mm/rev |
Engagement length
To guarantee continuity of motion, the pinion must have at least 1-2 teeth engaged on the rack in every position.
The contact ratio (the average number of tooth pairs in contact simultaneously) for a standard rack with a z = 20 pinion is about 1.6 - 1.7.
Below z = 15, the contact ratio drops below 1.5 and the transmission becomes noisier. If your project involves pinions with few teeth, consider a larger module to keep the contact ratio in the safe zone.
Don't confuse pitch with module
The pitch p, expressed in millimeters, equals π × m. Racks are often cataloged by pitch rather than by module. Always convert before ordering.
A rack with a 6.28 mm pitch corresponds to module 2 (6.28 / π = 2.0). The confusion between pitch and module is one of the most common causes of wrong orders and incompatibility at assembly.
If you're evaluating a steel-to-nylon replacement or need to configure a pairing outside the standard series, write to our technical office: we verify module, profile and operating conditions together.