LEARN · 2026-10-07
Belt vs lead screw vs ball screw vs rack and pinion: how to choose a linear drive (accuracy, speed, backlash, steps/mm)
GT2 belts, T8 lead screws, ball screws and rack and pinion compared: travel-per-revolution formulas, accuracy, backlash, speed, travel and cost tables, worked steps/mm and thrust examples, plus lead screw efficiency, self-locking and critical speed.
How the four linear drives work: travel per revolution L
A stepper motor turns; a linear axis needs something that converts rotation into travel. Whatever you choose, the first number to fix is how far the axis moves per motor revolution — the travel per revolution L. It sets steps/mm (resolution), top speed and thrust all at once.
GT2 belt: L = z · p 20-tooth pulley: L = 20 × 2 = 40 mm
Lead screw / ball screw: L = lead = pitch × starts T8 (Tr8 × 8): L = 2 × 4 = 8 mm
Rack and pinion: L = π · m · z m1, 20 teeth: L = π × 1 × 20 = 62.83 mm
steps/mm = (360° / step angle) × microsteps × i / L
i is any reduction between the motor and the drive pulley or screw (i = 1 for direct drive). Belts and racks move tens of millimetres per turn — fast, but with lower resolution and thrust. A screw moves only a few millimetres per turn, which acts like a large built-in reduction: high thrust and resolution, limited speed.
TIPScrews are specified by lead, not pitch. T8 and Tr8 × 2 look almost identical, but T8 has 4 starts and an 8 mm lead while Tr8 × 2 is single-start with a 2 mm lead — a 4× difference in steps/mm. Mark the nut and measure one turn, or count the thread starts on the screw end.
GT2 belt vs lead screw vs ball screw vs rack: comparison tables
Both tables show typical values for ordinary machines. Real performance depends on component grade, mounting stiffness and preload; accuracy means single-axis positioning error, excluding frame deflection.
| Drive | Positioning accuracy (typical) | Backlash | Speed | Practical travel |
|---|---|---|---|---|
| GT2 belt | ±0.05–0.1 mm | ≈ 0 (but the belt stretches elastically) | High | ≤ about 1.5 m |
| T8 lead screw (brass / POM nut) | ±0.05–0.1 mm | 0.05–0.2 mm; anti-backlash nut < 0.02 mm | Low–medium | ≤ about 0.5 m (whip, critical speed) |
| Ball screw (rolled C7 / ground C5) | C7 ±0.05 mm/300 mm; C5 ±0.018 mm/300 mm | 0.01–0.05 mm; preloaded ≈ 0 | Medium–high | ≤ about 1.5–3 m |
| Rack and pinion | ±0.05–0.2 mm (by quality grade) | 0.05–0.15 mm; dual pinion / spring preload ≈ 0 | High | Unlimited (joined segments) |
| Drive | Stiffness / thrust | Self-locking | Noise | Relative cost | Typical use |
|---|---|---|---|---|---|
| GT2 belt | Low / low | No | Quiet | Low | 3D printer XY, laser engravers |
| T8 lead screw | Medium / medium | Not at large leads; Tr8 × 2 can self-lock | Quiet | Low | 3D printer Z, light CNC |
| Ball screw | High / high | No (vertical axes need a brake) | Medium | Medium–high | CNC mills, linear stages |
| Rack and pinion | High / medium–high | No | Louder (helical racks are quieter) | Medium | Long gantries, sliding doors, large laser and plasma tables |
C5 and C7 are ball screw lead-accuracy grades from JIS B 1192 / ISO 3408 — smaller is more precise; the table gives the permitted variation over any 300 mm of travel.
Which one should you choose?
- Short travel, high speed, light load (printer XY, laser): GT2 belt — cheap, quiet, no lubrication.
- Vertical axis that needs thrust or must not drop when unpowered (printer Z): lead screw; smaller leads self-lock better.
- Stiffness and low backlash for cutting metal (CNC): ball screw with a preloaded nut and fixed-end bearing block.
- Travel beyond 1.5–2 m or high speed (gantries, sliding doors): rack and pinion, extended in segments without limit.
Worked example: steps/mm, speed and thrust
Take a 1.8° stepper (200 full steps per turn), 16 microsteps and 0.4 N·m of low-speed torque, and compare steps/mm, travel per microstep, theoretical speed and thrust for common drives. The steps/mm calculator lets you check your own numbers.
Thrust: screw F = 2π · T · η / L belt / rack F = T · η / r (r = pitch radius, η = 0.95)
| Drive | L (mm/rev) | steps/mm | Per microstep (µm) | 600 rpm (mm/s) | 1000 rpm (mm/s) | Thrust @0.4 N·m (N) |
|---|---|---|---|---|---|---|
| GT2 16T | 32 | 100 | 10 | 320 | 533 | ≈ 75 |
| GT2 20T | 40 | 80 | 12.5 | 400 | 667 | ≈ 60 |
| T8 lead 8 (Tr8 × 8) | 8 | 400 | 2.5 | 80 | 133 | ≈ 210 (η ≈ 0.66) |
| Tr8 × 2 | 2 | 1600 | 0.63 | 20 | 33 | ≈ 460 (η ≈ 0.36) |
| SFU1204 ball screw | 4 | 800 | 1.25 | 40 | 67 | ≈ 565 (η ≈ 0.9) |
| SFU1605 ball screw | 5 | 640 | 1.56 | 50 | 83 | ≈ 450 (η ≈ 0.9) |
| Rack m1 · z20 | 62.83 | 50.93 | 19.6 | 628 | 1047 | ≈ 38 |
| Rack m1.5 · z20 | 94.25 | 33.95 | 29.5 | 942 | 1571 | ≈ 25 |
The speed columns are pure kinematics, L × rpm / 60. Stepper torque drops markedly with speed (how much depends on driver voltage and motor inductance), so a lead screw's real top speed is usually limited by the motor long before the screw. Belts and racks are the opposite: speed is easy, but the same motor pushes only a fraction of the force a screw delivers.
Resolution is not accuracy. The 12.5 µm per microstep of a GT2 20T pulley is only the smallest move the firmware can command. At 16 microsteps each microstep adds only about 9.8% of holding torque, so a little friction makes the motor bunch several microsteps together; add belt stretch and pulley run-out and real accuracy is tens of microns.
Add a reduction: steps/mm = 200 × 16 × 3 / 40 = 240 (20T → 60T, i = 3, driving a GT2 20T pulley)
TIPFor a belt reduction, find a standard closed-loop length and centre distance with the GT2 centre distance calculator, then make the 20T and 60T pulleys in the GT2 pulley generator and the matching belt in the GT2 timing belt generator. A 3:1 reduction triples resolution and thrust (minus losses) and cuts top speed to a third.
Lead screw efficiency and self-locking: why a T8 Z axis drops
A trapezoidal (Tr, 30° thread angle) nut transmits force through sliding friction, so efficiency depends on the lead angle λ and the friction angle ρ'. A ball screw rolls on steel balls and exceeds 90%.
λ = atan(L / (π · d₂)) ρ' = atan(μ / cos 15°) η = tan λ / tan(λ + ρ')
Self-locking: λ < ρ' (the load cannot back-drive the screw)
For Tr8 the pitch diameter is d₂ = d − 0.5P = 7 mm. With a lubricated brass or POM nut, μ ≈ 0.15 and ρ' ≈ 8.8°:
| Screw | Lead L (mm) | Lead angle λ | Efficiency η (μ = 0.15) | Self-locking |
|---|---|---|---|---|
| T8 (Tr8 × 8, 4 starts) | 8 | 20.0° | ≈ 0.66 | No |
| Tr8 × 4 (2 starts) | 4 | 10.3° | ≈ 0.52 | No |
| Tr8 × 2 (single start) | 2 | 5.2° | ≈ 0.36 | Yes |
| Ball screw SFU1605 | 5 | — | ≈ 0.90–0.95 | No |
With an 8 mm lead the T8's lead angle is about 20° — far above the friction angle — so the bed's own weight back-drives the screw and the Z axis creeps down when the motors are off. Tr8 × 2 at λ ≈ 5.2° is below ρ' and self-locks, but runs at only about 36% efficiency and a quarter of the speed. Ball screws never self-lock: on vertical axes rely on motor holding current, a counterweight or an electromagnetic brake.
TIPSelf-locking is a static condition — vibration can still make a nut creep — and μ changes with lubrication: at μ = 0.1, ρ' is only 5.9°, leaving Tr8 × 2 very little margin. Don't rely on thread friction alone for a critical vertical axis.
Travel, critical speed and fixing backlash
The longer and thinner a screw, the more it whips like a skipping rope at speed; the resonant speed is the critical speed. A common simplified formula (THK catalogue) is below — run at no more than 80% of it:
n_c = λ₂ · d_r / L² × 10⁷ (rpm; d_r = root diameter in mm, L = unsupported length in mm)
| End support | λ₂ | Critical speed n_c (rpm) | Allowable 80% (rpm) |
|---|---|---|---|
| Fixed–free | 3.4 | 1169 | 935 |
| Supported–supported | 9.7 | 3334 | 2668 |
| Fixed–supported | 15.1 | 5191 | 4152 |
| Fixed–fixed | 21.9 | 7528 | 6022 |
Values are for a Tr8 with root diameter d₃ = 5.5 mm and 400 mm length. A printer Z screw is usually clamped only by the motor coupling with the top end free — close to fixed–free — so it is safe up to about 935 rpm, or about 125 mm/s with an 8 mm lead: plenty for Z. Make the same screw 1 m long on a horizontal axis and n_c falls to 1/6.25 (about 187 rpm), which is why long axes move to belts or racks.
Ways to remove backlash
- Lead screw: a spring-preloaded POM anti-backlash nut, or two nuts with a spring between them; on Z, gravity can keep the nut on one flank.
- GT2 belt: adequate tension and aligned idlers and pulleys; on long runs, 9 mm wide or glass-fibre-core belts stretch less.
- Ball screw: a preloaded nut (double nut or oversized balls) and paired angular-contact bearings at the fixed end (e.g. a BK block).
- Rack: two pinions preloaded against each other, a spring pressing the pinion into the rack, or a helical rack for more teeth in mesh.
TIPWith a T8 8 mm lead, one full step on Z is 8 / 200 = 0.04 mm; layer heights in multiples of 0.04 mm (0.12, 0.16, 0.2, 0.28 mm) avoid microstep-induced banding. Long racks can be split in the rack generator — give every segment a whole number of teeth so the pitch stays continuous across joints.
FAQ
Why does my T8 lead screw Z axis drop when the power is off?
A T8 (Tr8 × 8) has an 8 mm lead and a lead angle of about 20°, larger than the 6–9° friction angle of a trapezoidal thread, so it doesn't self-lock and the bed's weight back-drives it. Use a 2 mm lead Tr8 × 2, add a counterweight or brake, or keep motor current on when idle.
Belt or rack for a 2 m axis?
Keep a 6 mm GT2 belt within about 1.5 m; beyond that stretch and sag hurt positioning and stiffness. For 2 m and more, use an m1.5–m2 rack and pinion joined in segments. For light loads such as a laser, a wider or larger-pitch timing belt also works.
Can I 3D print a rack?
Yes. The rack generator makes any length; split it into segments with a whole number of teeth each when it exceeds the bed, and join them with dovetails or dowels. Use about 0.1 mm backlash on FDM and PETG or nylon. For high loads or long travel, SLS / MJF nylon warps less.
What are the steps/mm for a T8 lead screw?
With a 1.8° motor at 16 microsteps: T8 (8 mm lead) is 3200 / 8 = 400 steps/mm, Tr8 × 4 is 800 and Tr8 × 2 is 1600. In Klipper set rotation_distance to the lead (8, 4 or 2).
Ball screw or lead screw for a small CNC?
For cutting aluminium or steel, use ball screws (e.g. SFU1605) with preloaded nuts: stiff, low backlash, efficient and free of the stick-slip of sliding nuts. For wood, acrylic or PCB engraving, a lead screw with an anti-backlash nut is enough and cheaper. Ball screws don't self-lock, so Z needs motor holding torque or a brake.