Fareed Mohmed · Engineering
Rack and Pinion Selector
Load · Force · Rack · Pinion · Part Number
Enter the moved mass, acceleration, speed, friction and stroke. The tool works out the force on the rack over the move, finds the pinion size, and picks racks and pinions from the KHK, YYC, Andantex, APEX, ATLANTA and MISUMI catalogues by part number, using the standard gear-strength method or each catalogue's own method. It then shows how many pieces the stroke needs and every calculation step.
Part numbers and allowable forces are catalogue values from KHK (racks KRG, KRGF, KRGCP, KKRGCPF-H, KSRGCP, KSRCP, KSROCP, KSRO, KSROS, KSURO), YYC (helical and straight racks with matching pinions) and Andantex (series A10 to A41 module racks and A50 to A70 circular-pitch racks, with plain-bore and bored-and-keyed pinions) and APEX (helical and straight racks of quality Q4 to Q10 with flange-mount pinions, and AP, MG and MGH gearboxes) and ATLANTA Drive Systems (helical and straight racks of quality 5 to 10 with a maximum feed force for each module, and 205 helical pinions: ISO 9409 flange, TR and TRS, DIN 5480 spline, keyed and plain bore). Wittenstein is not loaded yet. This sizes industrial machines only. Always confirm the final choice with the supplier.
Start Here: The Selection Process
Ten steps from the move to the part number, in the order the tool works. Read this once, then use sections 01 to 03. Steps with a button link to where you enter or read that step. Step 9 is done outside the tool.
Describe the move
Write down what the rack drives before touching the tool.
- Moved mass: the load plus the carriage and tooling
- Acceleration (also used for braking) and maximum speed
- Guide friction, and any process or pressing force
- Stroke: the travel along the rack
Choose the direction of motion
Horizontal or vertical decides how gravity loads the rack.
- Horizontal: gravity is carried by the guides, so only friction counts
- Vertical, lifting: gravity always loads the rack, and the load can drive the pinion backwards if power is lost
Work out the force on the rack
The tool finds the force at every stage: accelerating, constant speed and braking.
- Horizontal: F = mass × acceleration + friction × mass × 9.81 + external force
- Vertical: F = mass × 9.81 + mass × acceleration + external force
Set the service factor and alignment
The service factor covers shock and uneven load. Alignment and rigidity set how evenly the load spreads across the tooth width. A loose or flexible mounting needs a larger value.
Set them in section 01 →Choose the pinion
Pitch diameter d = module × teeth. Pinion speed follows from the line speed: n = 60000 × v ÷ (π × d). Torque = force × d ÷ 2000 in N·m.
Choose the calculation method
This decides how the rack is rated.
- Standard: an ISO 6336 style strength check that works for any rack
- Each catalogue’s own method: KHK forces, YYC and ATLANTA feed force, Andantex and APEX torque rating. Use this when you will order from that brand
- Peak and equivalent force: the supplier-style check on KHK data
Read the result and the part number
The tool picks the smallest rack that passes. Read the verdict, then the warnings under it. A pass with a warning still needs a decision from you.
See the result in section 03 →Compare brands, series and methods
Section 02 lists every rack from every brand that passes your duty, and says why each of the others fails. Section 04 shows a rack from each series with its part number. Section 05 shows the same rack under every method, so you can see how much the method matters.
See what passes in section 02 → Compare series in section 04 →Plan the rack length and joints
Rack length needed = stroke + one tooth pitch. The tool counts how many racks in a row the stroke needs, using the longest length the catalogue lists.
Check what the tool does not, then order
- A brake on vertical drives, plus gearbox backdriving
- Backlash, lubrication, mounting torque, and pinion bore and shaft design
- Wear life under a heavy duty cycle
- Confirm the final choice with the supplier’s catalogue before ordering
Six common mistakes
Brands that make this product
Filled gold: loaded in this tool and rated from the catalogue. Outlined gold: loaded for part numbers only, not strength-checked. Grey dashed: not loaded yet. Hover a brand for what is loaded. Six brands are loaded and rated here. For another brand, take the force and torque from section 03 and check them against that brand’s own ratings.
KHKrated
YYCrated
Andantexrated
APEXrated
ATLANTArated
MISUMIrated
Wittensteinnot yet
Güdelnot yet
Rollonnot yetTo use a brand that is not loaded, take the peak force on the rack from section 03 to that brand’s catalogue and compare it with the rated force for the rack size and pinion teeth. The “Rack to check” list in section 01 offers only the loaded brands.
See every hardware and brand →Brand names and logos are trademarks of their owners and are shown only to identify catalogues.
Application
Choose from the lists, or pick "Type a value…" to enter your own number. The sketch shows your data on the layout.
Gearbox and motor optional
Optional. Enter the gearbox ratio and ratings to run YYC's gearbox and motor checks on the rack you pick. Leave the ratio empty to skip.
Brands And Racks That Pass
Your duty is checked against every rack in every catalogue loaded. A rack is listed when at least one pinion inside your settings passes: Pinion teeth, Pinion material, Safety coefficient and Calculation method. Auto tries the smallest pinion first, so each rack shows its smallest passing pinion. Click a card to show one brand. Click Select on a row to see the full working for that rack in section 03.
Result
Gearbox For The Pinion, APEX
Rack From Each Series, With Part Number
Show every rack in the catalogue data
The Same Rack Under Each Method
Margin is the allowed force divided by the force the method requires. A value of 1.00 or more passes. The standard method needs the tooth width, so it is not run for round racks.
Calculation Steps
How each method is calculated
How It Is Calculated
Force on the rack
Horizontal move: force = mass × acceleration + friction coefficient × mass × 9.81 + external force while accelerating, the friction and external force alone at constant speed, and the braking force while stopping. Vertical move: gravity always loads the rack, so lifting force is mass × (9.81 + acceleration) + external force, and the braking phase is mass × (9.81 − acceleration) + external force. The largest of the three is the peak force. The equivalent force is the cube-mean over the moving time, the cube root of Σ(F³ × t) / Σt, which weights the high-load phases more because gear tooth fatigue depends steeply on load.
Pinion
Pitch diameter d = module × teeth. Speed n = 60000 × v / (π × d) in RPM. Torque at the shaft = force × d / 2000 in N·m. The tool picks the smallest pinion, from 17 teeth up, whose own teeth pass the strength check. Pinions under 17 teeth can undercut and are not offered.
Standard method (ISO 6336 style)
Tooth bending stress σF = Ft × KA × KV × Kβ × YFS × Yε / (b × m). Contact stress σH = ZE × ZH × Zε × √[Ft × KA × KV × Kβ / (b × d)] for a rack, where the ratio of the mating gear to the pinion is infinite. Safety against breakage is σFlim / σF and against pitting is σHlim × ZLVR / σH. A rack passes when both the rack and the pinion reach 1.4 for bending and 1.1 for pitting. The material strengths are the KHK allowable stress values. YFS comes from the Lewis form factor, YFS = 1.45 / Y, which approximates the ISO tooth form and stress correction factors. Yε = 0.25 + 0.75/εα and Zε = √((4 − εα)/3), with εα the transverse contact ratio of the pinion on the rack. ZE = 189.8 √MPa for steel on steel, ZH = 2.495 for 20° pressure angle, and ZLVR = 0.85 covers lubrication, speed and roughness. KV is the AGMA dynamic factor for the rack's precision grade.
KHK catalogue method
KHK publishes, for each rack, an allowable force for bending strength and one for surface durability. They are calculated to JGMA 401-01 and JGMA 402-01 at 100 RPM, over 10⁷ cycles, with a bending safety factor of 1.2 and a surface safety factor of 1.15, uniform load, bidirectional, 40 °C, grease. The tool requires peak force × service factor × a speed correction, the ratio of the dynamic factor at your speed to that at 100 RPM (never below 1), to stay under the smaller of the two published forces. The pinion is checked with the standard formulas at KHK's 1.2 and 1.15 safety factors.
YYC feed-force method
YYC (Taiwan) rates a rack and pinion pair by a maximum feed force Fmax, printed in its load tables for each module, rack grade (DIN 5 to DIN 10, ground, milled, hardened or quenched and tempered) and pinion tooth count from 18 to 30. The tool follows the YYC selection page. Required feed force F1 = m g \u03bc + m a (\u03bc is set to 1 for a vertical move, so F1 = m(g + a)). Design feed force Fs = F1 with the load factor KA (1 uniform, 1.25 medium, 1.75 heavy) and safety coefficient SB (1 to 4). The pair passes when Fmax \u2265 Fs. YYC then checks the drive. The pinion torque T1 = F1 \u00d7 d / 2000 becomes Ts with the same factors, the motor torque is T2 = Ts / ratio and the gearbox input speed is N2 = N1 \u00d7 ratio, where N1 is the pinion speed. The gearbox torque must reach Ts, the motor torque T2, and the gearbox and motor speeds N2. YYC prints Fs = F1 / (KA \u00b7 SB), which would lower the design force. Its example uses 1 for both, so the tool multiplies. The load tables assume 1.5 m/s and grease lubrication.
Andantex torque-rating method
Andantex sells Güdel and WMH Herion racks and pinions as a modular system. Its selection page works with torque. Force at the rack Fr = μ m g + m a + F (horizontal) or m g + m a + F (vertical). Application torque Tp = Fr × d / 2000, where d is the pinion pitch diameter in mm. Design torque Td = Tp × service factor SF, and the maximum pinion speed is Np = 19100 × v / d. The pair passes when the catalogue torque rating for the module, rack grade and pinion teeth is above Td. The ratings (pages 59 to 61) are for 1.5 m/s, shock-free running, good lubrication, a rigid cantilever pinion support and 20,000 hours, with a 16MnCr5 hardened and ground pinion of quality 7e25 or better. Rack grades are A10 hardened and ground, A20 quenched and tempered, A30 soft and A40 induction hardened, with A11, A21, A31 and A41 for helical teeth, and A50, A60 and A70 for circular pitch. Andantex also asks you to check the cumulative pitch error Fp of the quality level, which this tool does not do. The catalogue leaves SF to experience, between 1.0 and 4.0. This tool uses the load factor multiplied by the safety coefficient.
APEX torque-rating method and gearbox pick
APEX Dynamics (Taiwan) makes racks, pinions and planetary gearboxes. Its selection page uses the same steps as Andantex: Fr = μ m g + m a + F (horizontal) or m g + m a + F (vertical), torque T = Fr × d / 2000, design torque TNV = T × SB with SB between 1 and 4, and pinion speed Np = 19100 × v / d. The pinion is chosen so that its maximum driving torque T2B, printed for each module, tooth count and rack quality (Q4 to Q10), is above TNV. The tables assume 1.5 m/s, good lubrication, tooth root safety of at least 1.4, surface safety of at least 1 and 20,000 hours, so the permitted torque falls at higher speed. The tool then picks the gearbox: its maximum acceleration torque T2B (1.5 × nominal torque T2N) must be above the design torque, T2N above the continuous equivalent torque, and the input speed (pinion RPM × ratio) within the motor speed you choose and the gearbox maximum input speed. It takes the smallest frame, then the ratio that uses the motor speed best.
ATLANTA feed-force method
ATLANTA Drive Systems (Germany) publishes one maximum feed force per pinion contact for each rack class, quality and module. The classes are UHPR (quality 5), HPR (quality 6 and 7), PR (quality 8) and BR (quality 10). The tool takes the tangential force Fu = m g \u03bc + m a (peak) and multiplies it by the load factor and safety coefficient. The rack passes when the catalogue maximum feed force is at least that design force. The table values are for rack lengths of 1,000 mm and for the ATLANTA special steel, and a 500 mm rack joined by screws is limited to 50 % of the value (the catalogue marks these). ATLANTA\u2019s own worked example (page C-28) also chooses a pinion: it needs torque T2 = Fu \u00d7 d / 2000, and divides the pinion table torque by KA \u00d7 S \u00d7 bB (load factor 1.25, safety 1.3, operating-time factor 1.2) before choosing a gearbox. The torque table is on pages C-44 to C-55, which were not supplied, so the pinion is not rated here. Only the splined pinions list a feed force (Fu Tab.), which is limited by the spline.
Peak and equivalent force method
Many supplier catalogues rate a rack or pinion drive with two limits, a maximum force for the peak of the cycle and a nominal force for the continuous equivalent load. This tool applies that approach to the KHK data by checking peak force × service factor against the bending-strength force, and equivalent force × service factor × the speed correction against the surface-durability force. It is not any one supplier's formula. Wittenstein and Misumi calculation pages could not be loaded here, so their exact limits and life factors are not included. Send those catalogue pages and they can be added as separate methods.
MISUMI Economy series: racks and spur pinions
The MISUMI Malaysia Economy 2025 catalogue (pp. 08-024 to 08-033) lists square-section racks E-RGSA (structural or carbon steel, not heat treated), E-RGSAH (teeth induction hardened, 45 to 55 HRC) and E-RGSAS (stainless), in modules 1 to 3 and nominal lengths 100, 300, 500 and 1000 mm, with a 20\u00b0 pressure angle. The spur pinions E-GEAHB, E-GEAB and E-GEAKB (steel) and E-GEAHS, E-GEAS and E-GEAKS (stainless) are JIS/GB class 8, modules 1 to 2.5, 12 to 120 teeth. The catalogue prints an allowable transmission torque (bending strength) for each pinion, as a reference value for normal conditions, and refers to a separate Gear Transmission Power Calculation that was not in the supplied PDF. So with \u201ceach catalogue\u2019s own method\u201d the tool compares the design torque at the pinion (Fr \u00d7 d / 2000 \u00d7 SF) with that table, and with the standard method it runs the ISO 6336 style check on the rack and pinion. Racks and pinions share a module, so a rack is only rated where a pinion exists. Module 3 racks have no catalogue pinion and are not loaded. Torques are used exactly as printed, including odd tooth counts whose printed value is well below their neighbours (the catalogue does not say why), which is on the safe side. The stainless table has no module 2.5 values, so stainless racks of module 2.5 are not rated. The face width used is the smaller of the rack width and the pinion face width B. Configurable lengths (up to 980 mm), hole patterns and the rack hole positions are not loaded; the nominal-length parts are listed.
Pieces and part numbers
Rack length needed = stroke + one tooth pitch. Pieces = length needed / the length of one rack, rounded up, using the longest length the catalogue lists for that module (KHK racks from effective teeth × π × module, YYC and Andantex racks at their catalogue length). Rack joints need the pitch kept across the joint. KHK sells a short gauge rack for this. Several racks in a row also need to be dowelled, not only bolted.
What is not covered
KHK helical racks, flange and splined pinions, rack and pinion backlash, pinion bore and shaft design, mounting torque, lubrication life, and wear life under heavy duty cycles. The standard method is not run for YYC or Andantex helical racks. Andantex racks with cross-section variants (A12, A13, A32, A42, A44 and the stainless and alloy series A80 to A94) and the Andantex flange, preloaded, master and shaft pinions are not loaded, and the Andantex face width is taken from its torque-table module size. The KHK CP pinions and tapered and flexible racks are not loaded. For APEX, the pinion torque tables were read from text with no column positions, so the rack-quality columns were matched by module and checked against T2B = F2T × d / 2000. Only the flange pinions (curvic, welded and teeth plate, DIN 5480 and welded straight) are rated, the keyway, shaft and CP pinions are not, and APEX modules 8 to 12 have only a few ratings. APEX racks with linear-guide interfaces are not loaded. APEX gearboxes: right-angle K series, C series, 4-stage and integrated-motor types are not loaded, and MGO and MGOH are rated as MG and MGH because their tables match. ATLANTA: the pinion catalogue is helical only, so straight racks show no straight pinion part number, and the pinion torque rating table (pages C-44 to C-55) was not supplied, so ATLANTA pinions are not rated. ATLANTA rack ends, joint kits and the lubrication systems are not loaded. YYC pinions are limited to the tooth counts the catalogue lists for each module, and YYC has no load table for modules 1.5 and 10 straight, or module 2.5. KHK pinion part numbers are not loaded, so the KHK pinion is sized by calculation. Confirm the exact parts with the supplier.
Source
MISUMI Malaysia Economy series 2025 catalogue, Gears and Rack Gears section (pages 08-024 to 08-033: spur gear and rack tables, allowable transmission torque). KHK Gears catalogue pages for KRG, KRGF, KRGD ground racks, KSRO and KSROS round racks, KSURO stainless round racks, and the KRGCP10 CP rack (module, teeth, length, face width, allowable bending and surface forces). KHK rack technical data for the allowable stress values of SCM440, S45C, SCM415 and SUS304 and the strength conditions. YYC Catalogue 2025 (racks and pinions part numbers, the Selection and Load Tables, and the Selection and Calculation pages). KHK CP Racks and Pinions section (circular pitch 2.5 to 20, allowable forces). Andantex Modular Rack and Pinion catalogue (rack and pinion part numbers, torque ratings, selection and calculations). APEX Dynamics High Precision Rack and Pinion catalogue, the AP/APK, MG/MGK and MGO/MGOK gearbox catalogues and the L24 linear drive sheet for laser cutting. ATLANTA Servo Drive Systems catalogue pages C-12 to C-21 (helical racks), the matching straight-tooth rack pages, C-23 to C-42 (helical pinions, TR and TRS pinions) and the MPZ 001e operating manual. Gear strength factors follow ISO 6336 and AGMA 2001 in simplified form. Always check current figures with the manufacturer.