A timing pulley's pitch differential is the radial distance between the pitch circle (where the belt's neutral axis actually runs) and the machined outside diameter, and it has a standard value for each belt section, for example 0.010 in (0.3 mm) on XL, 0.027 in (0.7 mm) on H, and 0.055 in (1.4 mm) on XH inch-pitch belts [S4].
Because the pitch circle is the circle on which belt linear velocity is calculated, any deviation in that radial gap changes the effective rolling radius and therefore the metered travel per tooth, the centre-distance algebra, and the tooth-meshing clearance, three quantities a process engineer cannot decouple from each other once a synchronous drive is in service [S4][S8].
Defining pitch line, pitch diameter, and the differential that ties them
The belt pitch line is the neutral bending axis of the belt and coincides with the centre line of the tensile cords; the pulley pitch diameter d is the diameter on which that line rides, computed as d = zp/π, where p is nominal pitch and zp is the tooth count [S4]. The radial offset between that pitch diameter and the pulley outside diameter d₀ is u, the pitch differential, and it is a published constant per belt section, not a free parameter the machinist can choose [S4].
Two families behave differently: inch-pitch (XL, L, H, XH) and metric T-series (T5, T10, T20) belts ride on the top lands of the pulley teeth, so the tolerance of d₀ directly sets the effective pitch; HTD and STD follow the same top-land rule with their own u values; AT-series belts contact the bottom lands, so the effective pitch is governed by the root diameter tolerance instead, and the standard u in that case is the radial offset from pitch diameter to root diameter [S4]. Mixing the two rules, for example assuming an AT-pulley OD tolerance delivers the same u that an XL-pulley OD tolerance does, is one of the most common ways a synchronising drive loses repeatability on a CNC or printer axis.
Why the number controls accuracy: pitch-line velocity and travel per tooth
Linear belt speed is v = π × d × n, where n is shaft speed, so the pitch diameter (not the OD) is the metered rolling diameter. If the actual u on a finished pulley drifts from the standard value, the effective d shifts, and the same n produces a different v, which in a positioning axis shows up as a steady positional error proportional to the number of teeth that have passed [S4][S8].
Tooth count amplifies the issue. A 60-tooth HTD 8 pulley has d = 60 × 8 / π = 152.8 mm and a standard u of 0.028 in (0.7 mm), giving a rated d₀ of 151.4 mm; a 0.05 mm error in u translates to roughly 0.03% error in d, which on a 1 m linear stroke is already 0.3 mm of end-of-stroke drift if uncorrected [S4]. Pulley-to-pulley u variation across a drive compounds the error, because the velocity ratio is fixed by the tooth ratio, but the absolute metered travel at the driven end is the integral of v over time, so any u deviation on the driver is mirrored at the output.
Manufacturing route: why pitch accuracy is harder on molded pulleys
Stock Drive Products' timing-belt handbook is explicit that adequate pitch-to-pitch accuracy is generally more difficult to achieve with molded pulleys than with machined pulleys, and that machined pulleys are recommended when high positional accuracy is required [S6]. The same source treats the outside diameter and the tooth-to-tooth pitch on the pitch circle as the two surfaces that must be held, and the difficulty is that molded plastic or sintered-metal tooling shrinks unevenly across tooth cavities.
For most conveyor and general power-transmission service a moulded pulley in aluminium, S45C carbon steel, or polyamide is acceptable and the catalogue tolerances on u are loose enough to swallow the variation [S6][S1]. For positioning axes (CNC rack-and-pinion feeders, 3D-printer carriages, semiconductor handlers) the practical move is a machined steel or aluminium pulley with the OD turned to a tighter tolerance, and on high-end servo drives a zero-backlash or reduced-backlash tooth profile that is designed to close the residual tooth-gap to a few microns [S3]. A related practical reference for picking the pulley body material and finish is covered in 6061 vs 7075 aluminum for structural CNC machining, which lays out the same machinability-versus-stiffness trade-off that drives the choice between cast, moulded, and billet timing pulleys.
Backlash, tooth clearance, and how u sets the starting point
Backlash in a timing-belt drive is the free motion that occurs as a belt tooth crosses the clearance between the tooth and the pulley groove while the drive reverses; that clearance exists by design so the tooth can enter and exit the groove smoothly, with too much clearance producing positional inaccuracy and too little producing noise, vibration, and wear [S2]. The standard tooth gap is set so the belt rides correctly at the published u, so any drift in u beyond the catalogue band pushes the drive off the tooth-clearance design point [S2][S4].
BRECOflex quantifies the trade-off in three product tiers: standard pulleys with the nominal gap, reduced-backlash pulleys with tighter clearance, and zero-backlash pulleys where the micro-gap is held to a minimum for the highest precision [S3]. The pitch differential does not change between those tiers; what changes is the tooth-gap allowance, but both are functions of the same geometry, and a pulley whose u is off-nominal cannot be rescued by a tighter tooth gap, because the belt will simply ride higher or lower in the groove and re-introduce a different clearance. The standard backlash tier suits high-speed conveyors and general transport; reduced and zero backlash are specified for servo-driven linear actuators, CNC machining, and pick-and-place where a fraction of a millimetre of lost motion shows up as a misaligned cut or a missed pick [S3].
Belt stretch, tension, and how u errors look in service
Once a drive is installed, the belt itself contributes positional error through elastic stretch under load and through poor fit on the pulley, both of which the operator can see as a phase shift between driver and driven shafts that grows with belt age [S5]. A pulley whose u is within tolerance cannot compensate for a belt that has stretched 0.5% over its service life, and conversely a fresh belt on a u-out-of-tolerance pulley will look like a stretched belt because the linear velocity is wrong by the same order [S4][S5].
Gates' timing-belt white paper fixes the relationship for centre-distance and belt-length calculations: belt length L is measured along the pitch line and must equal a whole number of belt pitches, so the centre-distance algebra, the wrap angle on the small pulley, and the tooth-in-mesh count all depend on d, and therefore on u [S4]. The wrap-angle term is sensitive at small pinions: a 14-tooth HTD 5 driver has a 5 mm pitch, a standard u of 0.7 mm, and a wrap angle that drops fast if the centre distance is wrong, and the tooth-in-mesh count falls with it, which is why a u error on a small pinion costs more accuracy per metre of travel than the same u error on a large pulley [S4].
Specifying pulleys to keep u inside the working window
The synchronising-belt specification flow published by Linear Motion Tips states that the pitch diameter is slightly larger than the outer diameter of the pulley and corresponds to the pitch line of the belt, which is the line formed by the tensile cords as they wrap the pulley [S8]. In other words, OD, pitch diameter, and root diameter are three concentric features that the supplier has to hold together, and the published u is the contract between the belt maker and the pulley maker on what the resulting centre distance will be [S4][S8].
Three rules follow for spec sheets. First, quote pitch diameter and the number of teeth, not OD, when computing ratios, because the ratio is exact at the pitch circle and only approximate at the OD. Second, name the belt section (XL, L, H, XH, T5/T10/T20, HTD 5/8/14, STD 5/8/14, AT5/AT10/AT20) so the supplier can look up the standard u from Gates' Table 1 or Table 2 instead of guessing. Third, for positioning axes, require a machined pulley and a reduced- or zero-backlash tooth profile, and for general power transmission a moulded pulley with the standard tooth profile is acceptable, matching the SDP-SI guidance that moulded pulleys are adequate for general service but machined pulleys are recommended when high accuracy is needed [S6][S3][S4]. The wider choice of timing pulleys and the timing belt families they are matched to is covered in the catalogue references, where each section's u is published alongside p, tooth height, and belt height so the designer can audit the geometry before the part hits the shop floor.
What goes wrong when u is wrong: failure modes and limits
Three failure modes trace back to u being out of band. A positive error, where the actual OD is smaller than the design OD, lowers the effective d and shortens the linear travel per revolution, so an axis programmed to move 100 mm arrives at 99.7 mm; this is the common case on over-polished or over-turned pulleys. A negative error, OD larger than design, lengthens the travel and the drive overruns the target, which on a servo loop is normally caught and corrected but on an open-loop stepper drive becomes a steady positional bias [S4][S5].
The third mode is tooth-clearance drift: as u moves, the belt rides higher or lower in the groove, backlash changes by tens of microns even on a zero-backlash profile, and on a reversing drive the result is a square-wave tooth-mesh error that shows up as a periodic position ripple at the shaft-rotation frequency, which is the same frequency that machine-tool surface finish picks up if the drive is feeding a linear axis [S2][S3]. On a conveyor or general power-transmission line this is invisible; on a printing press or a surface-grinder dressing slide it is the spec sheet. The practical ceiling on u tolerance is therefore not a single number, it is the application's tolerance for end-of-stroke drift and tooth-mesh ripple, and that ceiling is roughly 0.05 mm for general automation, 0.02 mm for precision linear axes, and 0.005 mm for the kind of zero-backlash, machined-pulley, ground-belt pairing that the catalogue positions for semiconductor and metrology service [S3][S4][S6].
The next signal to track is the AT-series root-diameter tolerance band, which is where moulded-pulley makers are still catching up to machined accuracy and where most new mould-tool releases over the next two quarters will be benchmarked against Gates' Table 2 u values of 0.047 in (1.2 mm) on AT5, 0.098 in (2.5 mm) on AT10, and 0.236 in (6.0 mm) on AT20 [S4]. A second trackable signal is the spread of zero-backlash tooth profiles in the BRECO T, AT, and ATN series, which is the practical ceiling on tooth-gap-independent accuracy once u is already held inside the standard band [S3].
Component reference pages worth checking: differential pressure transmitter.