Sizing a Güdel rack and pinion drive comes down to four numbers: the mass to move, the acceleration you want, the pinion pitch diameter and the number of load cycles. Work out the peak feed force, convert it to pinion torque, check the rack’s published permissible feed force, then pick the module. Everything else follows.
The sequence below follows Güdel’s own selection flow — determine the maximum application force first, then evaluate load capacity against the published load case table, repeating the comparison until a rack fits.
The four numbers that decide the size
A rack and pinion drive is not sized by looking up a part number. Four inputs feed one comparison.
- Mass. Not only the payload. On a gantry axis you also accelerate the carriage, tooling, part of the beam and the cable chain. Undersize it and every number after it is wrong.
- Acceleration. This sets the force. Güdel’s own documentation puts it directly — the feed force requirement follows from the desired dynamics or acceleration and the mass to be moved. A slow indexing axis and a high-speed placement head of the same mass are different drives.
- Pinion pitch diameter. Set by module and tooth count. For a straight-tooth pinion it is module times tooth count, so a module 4 pinion with 20 teeth runs on an 80 mm pitch circle. Helical pinions reach the same diameter with a smaller module because the tooth is angled.
- Load cycles. Load tables are quoted at a stated number of cycles. A drive running 20 cycles an hour for ten years is not the same duty as one running continuously.
The sizing sequence
1. Find the maximum application force. Güdel’s published selection flow starts here, and the first branch is horizontal or vertical.
For a horizontal axis, with mass m, acceleration a and friction coefficient µ:
F = m × a + µ × m × g
The friction term covers guide friction, seals and cable chain. Profile rail guides sit between 0.005 and 0.01; a conservative 0.01 costs little and covers a worn machine.
For a vertical axis, gravity does not disappear into the guides:
F = m × a + m × g + friction
2. Convert feed force into pinion torque. Only the pitch radius matters.
T = F × (D₀ / 2), where D₀ = mn × z for straight teeth
For a helical rack, divide by the cosine of the helix angle, so the same pitch diameter needs a smaller module.
3. Turn linear speed into pinion and motor speed.
n = v / (π × D₀)
Multiply the pinion speed by the gearbox ratio for the motor speed, and divide the pinion torque by the ratio and gearbox efficiency for the motor torque. This is where a matched gearbox earns its place — it decides how much motor torque reaches the rack.
4. Check the rack’s permissible feed force. In the flow diagram this is the second half. Evaluate load capacity, select a rack and its permissible feed force from the load case table, and compare it against the force you calculated. The selection flow notes that the comparison may have to be repeated until a suitable rack has been found.
5. Work out rack length.
L = stroke + carriage footprint + 2 × end margin
Racks come in fixed lengths and are joined end to end, so the practical answer is a section count. If the sum is 8,700 mm, that is six 1,500 mm sections. On a long axis those joints decide whether the axis holds accuracy, which is why rack mounting aids are a separate line item rather than an afterthought.
6. Choose the accuracy class, not only the size. Two drives can run the same module and differ in how much clearance they hold over a long travel.
Worked example: a 1,200 kg gantry axis
| Input | Value |
|---|---|
| Moving mass | 1,200 kg |
| Peak acceleration | 3 m/s² |
| Guide friction coefficient | 0.01 |
| Maximum speed | 1.5 m/s |
| Stroke | 8,000 mm |
| Pinion | module 4, 20 teeth, straight |
| Gearbox ratio | 10 |
| Step | Calculation | Result |
|---|---|---|
| Friction force | 1,200 × 9.81 × 0.01 | 118 N |
| Peak feed force | 1,200 × 3 + 118 | 3,718 N (3.7 kN) |
| Pitch diameter | 4 × 20 | 80 mm |
| Peak pinion torque | 3,718 × 0.040 | 149 N·m |
| Torque at 1.5 service factor | 149 × 1.5 | 223 N·m |
| Pinion speed at 1.5 m/s | 1.5 / (π × 0.080) | 5.97 rev/s = 358 rpm |
| Motor speed | 358 × 10 | 3,580 rpm |
| Motor torque, peak | 149 / (10 × 0.94) | 15.8 N·m |
| Rack length | 8,000 + 500 + 2 × 100 | 8,700 mm |
Three things fall out of that table. The number you carry to the load table is the peak force, not the average. The motor torque, about 16 N·m, sits inside what a mid-size servo offers, so the limit here is the rack and pinion rather than the motor. And rack length drives the section count and the number of joints — an accuracy question before a price question.
Then close the loop. If module 4 passes at 3.7 kN in your chosen product line and quality class, look at a smaller module before accepting the weight. If it does not pass, go up a module rather than oversizing the motor.
Why a vertical axis is a different problem
Run the same 1,200 kg upwards at 3 m/s² and gravity works against the drive rather than being carried by the guides. Friction stays at 118 N, and gravity adds 1,200 × 9.81 = 11,772 N to the 3,600 N of acceleration:
11,772 + 3,600 + 118 = 15,490 N ≈ 15.5 kN
That is roughly four times the horizontal figure from the same mass and acceleration. A vertical axis of this size will normally land one or more modules higher, and it needs a brake rather than relying on the drive to hold position. If a machine has both horizontal and vertical rack axes, size them separately — a common mistake is copying the horizontal selection across.
The three Güdel rack product lines
Güdel divides its racks into three lines, and the choice between them is a positioning and load decision rather than a price decision.
| Product line | Tooth and machining | Where it fits |
|---|---|---|
| High-End | Hardened tooth roots | Highest load capacity and feed force for a given installation space, for machine tools, process equipment and demanding automation. Lets you downsize a module |
| Performance | Precision-ground, hardened tooth flanks | High positioning accuracy and smooth running at medium dynamics — laser, plasma and waterjet cutting, tube bending |
| Basic | Milled, hardened or soft | Standard precision with raised feed force — automation gantries, pick-and-place and robot travel axes |
The downsizing effect is where the line choice pays. Güdel’s own comparison is that a module 2 High-End rack can replace a module 3 Performance rack, taking rack weight from 5.6 to 4 kg per metre. Over a 30 m axis that is up to 48 kg less moving mass, which in turn means less feed force, a smaller motor and a smaller brake.
Quality class does not follow from module
| Quality class | Use it for |
|---|---|
| 6 | Long axes and rack and pinion drives that have to run with low clearance |
| 8 or 9 | Lower accuracy requirements, such as pick-and-place tasks |
Quality 6 on a long travel is the normal choice when the axis has to hold position. Quality 8 or 9 is not a compromise on a placement head, where part tolerance is loose and cycle time short.
Feed force falls as load cycles rise
Güdel publishes feed force against number of load cycles. The published comparison chart is given for module 2.0 with a 20-tooth pinion in pulsating operation, and the rack and pinion catalogue states that the load table values assume 1 × 10⁶ load cycles for the rack and 1 × 10⁷ for the pinion, both pulsating.
Two consequences follow. A rack picked from the table without a duty cycle is only valid at that cycle count, and the same rack can pass on one machine and fail on another that looks identical on the drawing but runs three times the cycles per shift.
Which one to choose
- Basic — start here for automation gantries, pick-and-place heads and robot travel axes with standard precision. It carries the feed force and it costs the least.
- Performance — choose it when the axis cuts or measures. Laser, plasma and waterjet cutting and tube bending sit in the medium-dynamics range where positioning accuracy shows in the finished part.
- High-End — choose it when installation space is the binding constraint, when the feed force is high for the envelope available, or when removing weight from the moving mass repays the line change. A module 2 High-End rack stepping in for a module 3 Performance rack is the case to look for.
Two rules prevent most sizing errors. Select the module from the load table using the peak force and the real cycle count, never from the previous machine. And size the rack before the motor — the motor is the cheaper of the two to change.
Sourcing Güdel racks, pinions and gearboxes
Güdel is a Swiss manufacturer based in Langenthal. The rack and pinion range is designed as a system with the rest of the drive train, so racks, pinions and gearboxes — high-performance angle gearboxes and precision planetary gearboxes — are matched to each other. Racks come in steel, and in stainless steel or polyamide for medical and food applications, with straight or helical teeth and customer-specific designs beyond the standard range.
We supply Güdel rack and pinion components and the matched gearboxes. Send mass, acceleration, maximum speed, stroke, axis orientation and duty cycle, and we will confirm module, product line and accuracy class against the published load tables, and quote the section count and jointing.
- See the Güdel brand page or the full brand directory for the ranges we carry.
- Browse the motor and drive product range across all brands.
- Read more selection guides and technical articles.
- Or send the axis data straight to the inquiry form.
Every unit we supply is original and new, bought through the manufacturer and established channels, with procurement documentation for verification on arrival.
Note: the calculation above is a worked example showing the method. Permissible feed forces, torque ratings and load table values must be taken from the current official Güdel documentation for the specific product line, module and quality class.