An external gear mesh reverses rotation direction. In this driver–idler–driven train there are two meshes, so the output turns in the same direction as the input. Enter tooth counts and input rpm to compare output speed, idler speed and the effect of the middle gear.
Three-Gear External Idler Train Calculator
Enter input rpm and the tooth count of each gear. The results give ideal speeds; playback is slowed so you can follow the rotation.
Equation Used
- All three gears are external spur gears with a common module.
- Adjacent pitch circles are tangent at the ideal center distances.
- Each external mesh reverses rotation direction.
- Tooth form, interference, backlash, strength, torque, power, efficiency and service limits are excluded.
The companion view shows the same pitch-circle proportions and current tooth counts.
How the three-gear train works
The driver and idler are an external mesh and therefore rotate in opposite directions. The idler and driven gear form a second external mesh, again reversing direction. The driven gear consequently rotates in the same direction as the driver.
For gears sharing one module, pitch radius is proportional to tooth count. Adjacent pitch circles are tangent at center distances r1 + r2 and r2 + r3. The animation uses those relationships.
What this model demonstrates
Try a larger driven gear to reduce output speed, or a larger driver to increase it. Changing only the idler changes its own speed and size while leaving output rpm unchanged.
This three-gear arrangement is not itself an output reverser. A single external gear pair reverses direction; inserting one idler adds another reversal. The model does not select gears or determine load capacity.
Ideal three-gear relationships
For external meshes, ni = −ninZin/Zi and nout = −niZi/Zout = +ninZin/Zout. The positive sign means input and output rotate in the same direction.
The idler count affects center spacing and idler speed but cancels from the ideal input-to-output ratio.
Default ideal example
At 1,000 rpm with 30 teeth on all three gears, the idler rotates at −1,000 rpm and the driven gear at +1,000 rpm. The overall speed ratio magnitude is 1.00 and the direction sign is +1.
Reading the results and drawing
The reported speed-ratio magnitude is output rpm divided by input rpm. A value of 0.5 means the output turns at half the input speed; 2 means it turns twice as fast. The idler has a negative rpm sign because it turns opposite to the input.
Playback is slowed independently of the calculated rpm. Pitch-circle size follows tooth count, and adjacent pitch circles meet at their ideal center distance. The whole drawing rescales to fit the window, so it does not provide physical gear dimensions.
The teeth are simplified symbols, not manufactured tooth profiles. The tool does not assess tooth interference, backlash, strength, torque capacity, bearings, lubrication or service life. Use appropriate gear specifications and manufacturer data for those decisions.
Idler-gear questions
Does one idler make the output turn opposite to the driver?
No. This three-gear train has two external meshes. Each reverses direction, so the output turns in the same direction as the driver. A single external pair has only one reversal.
Does idler tooth count affect output speed?
No. It cancels from the ideal overall ratio. Changing it affects idler speed and the space required for that middle gear.
Which speed ratio does this calculator report?
It reports output speed divided by input speed, as a positive magnitude: driver teeth divided by driven teeth. Some references use the reciprocal, input speed divided by output speed, as the reduction ratio.
Does playback run at the calculated rpm?
No. Playback is slowed for viewing. The numeric results are the ideal rpm values; the animation shows relative directions and speed proportions.
Can this calculator select real gears?
It helps compare tooth counts and ideal speed relationships. It does not calculate tooth contact, strength or service life. Actual gears also need compatible tooth specifications and engineering data for the intended load and installation.
Technical references
- KHK Gears, Idler Gear | Gear Nomenclature — the idler count cancels from the overall speed ratio.
- KHK Gears, Direction of Rotation of Gears — each external spur-gear mesh reverses rotation direction.
- KHK, The ABC's of Gears — spur-gear direction and speed-ratio relationships.
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