A two-position stepped-pulley drive can use a third idler to guide or tension the belt while two selectable driver/driven pitch-diameter pairs provide different ideal speed ratios. An ideal idler changes belt routing, not the speed ratio.
Two-speed Transmission with Three Pulleys Interactive Calculator
Enter four pitch diameters for two selectable driver/driven pairs. The tool reports ideal speed and lossless torque ratios; the third pulley is schematic and does not create another ratio or solve belt length, tension or shifting.
Equation Used
- All four entries are pitch diameters.
- Each position uses one driver step and one driven step; the third pulley is an ideal freely rotating idler.
- The belt is inextensible and has no slip or creep for the speed calculation.
- Torque ratios assume lossless steady power transfer and exclude idler losses.
- Center distances, belt length, idler diameter and travel, wrap, tension, power capacity, shaft load, shift procedure, guarding, wear and suitability are omitted.
Two Selectable Pairs and One Idler
The schematic shows a stepped driver shaft, a stepped driven shaft and a third freely rotating idler. Position A pairs the large driver pitch diameter with the small driven pitch diameter; position B pairs the small driver with the large driven diameter.
For an ideal belt with no slip, belt linear speed is common at the driver and driven pitch circles. A freely rotating idler redirects the belt but does not alter the diameter quotient.
What This Calculator Represents
The tool compares two ideal pitch-diameter quotients and their reciprocal lossless torque ratios. The third pulley is shown only as an idler in a schematic path.
It does not determine whether one belt and idler can accommodate both entered positions, and it does not represent shifting under power.
Ideal Speed and Torque Ratios
position B speed ratio = driver-small pitch diameter / driven-large pitch diameter
ideal torque ratio = 1 / speed ratio
Continental identifies pitch diameter as the diameter used to determine transmission ratio. Gates' belt-drive design procedure separately requires belt length, center distance, wrap and power checks that are outside this calculator.
Worked Ideal Example
With 150 mm and 75 mm driver steps opposite 150 mm and 75 mm driven steps, position A has an ideal output/input speed ratio of 2.00 and torque ratio of 0.50. Position B has an ideal speed ratio of 0.50 and torque ratio of 2.00.
Model Boundary
- Calculated: two ideal no-slip pitch-diameter speed ratios and reciprocal lossless torque ratios.
- Illustrated: two selectable stepped-pulley paths through a schematic idler.
- Not calculated: belt length, center distance, idler size or travel, wrap angle, tension, efficiency, power, shaft load, pulley grooves, slip, creep, shift behavior, alignment, wear, guarding or suitability.
Frequently Asked Questions
Does the third pulley change the speed ratio?
No. An ideal freely rotating idler redirects the belt without changing the driver/driven pitch-diameter quotient.
Are outside diameters valid inputs?
No; use pitch diameters for this ideal relation.
Are the torque ratios real delivered torque?
No. They are lossless reciprocal ratios.
Does the calculator determine belt length or idler travel?
No.
Does the animation recommend shifting while running?
No.
Can this select or rate a belt drive?
No; use a manufacturer design procedure.
References
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
