A two-position step-pulley drive places two selectable driver/driven pitch-diameter pairs on the same shaft centers. Moving the belt changes the ideal no-slip output/input speed ratio from one diameter quotient to the other.
Two-speed Transmission via Four Pulleys Interactive Calculator
Enter four pitch diameters for the two selectable belt positions. The tool reports each ideal no-slip output/input speed ratio, the mean paired-diameter sum and their signed sum difference; it does not calculate belt length or drive capacity.
Equation Used
- All four entries are pitch diameters, not outside diameters.
- Speed ratios assume an open belt with no slip or creep.
- Both belt positions use the same shaft centers, but center distance is not entered.
- Diameter-sum difference is only a first-order comparison, not belt-length error.
- Belt section, groove geometry, exact length, wrap angle, tension, power, torque, forces, losses, alignment, wear and suitability are omitted.
Two Selectable Pitch-Diameter Pairs
The schematic places a large and small driver step opposite a small and large driven step. The belt is shown on one pair at a time. Under the ideal no-slip condition, equal belt linear speed makes output/input shaft speed equal driver pitch diameter divided by driven pitch diameter.
What This Calculator Represents
The tool evaluates two ideal diameter quotients and compares the sums of the diameters in the two entered positions. It does not identify a belt section, determine shaft spacing or prove that one physical belt fits both positions.
Ideal Speed Ratios and Diameter-sum Comparison
position B speed ratio = DS/OL
paired sums SA = DL+OS and SB = DS+OL
mean sum = (SA+SB)/2
signed sum difference = SA-SB
Gates' Heavy Duty V-Belt Drive Design Manual gives the common open-belt length approximation L=2C+1.57(D+d)+(D-d)²/(4C). Equal sums address only the 1.57(D+d) term. Because C is not entered and the squared-difference terms may differ, this calculator does not report belt length or a belt-length error. Continental's belt manual identifies pitch diameter as the diameter used to determine transmission ratio.
Worked Ideal Example
With DL=70 mm, DS=35 mm, OL=70 mm and OS=35 mm, position A has ideal output/input speed ratio 2.00 and position B 0.50. Both paired sums are 105 mm, so the signed sum difference is 0 mm. This symmetric swap also has equal absolute diameter differences, but the calculator still does not select a belt or center distance.
Model Boundary
- Calculated: two ideal no-slip speed ratios, two pitch-diameter sums, their mean and signed difference.
- Illustrated: one belt alternating between two step pairs on parallel shafts.
- Not calculated: exact belt length, center distance, wrap angle, belt section, installation/takeup allowance, tension, power, torque, shaft load, groove geometry, slip, creep, alignment, stress, temperature, wear, life, guarding or suitability.
Frequently Asked Questions
Does zero sum difference guarantee equal belt length?
No; exact or approximate belt length also depends on center distance and diameter difference.
Are outside pulley diameters appropriate inputs?
No; use pitch diameters for the ideal speed relation.
Does the ratio include belt slip?
No.
Is the mean diameter sum a standard belt size?
No.
Are wrap angle and capacity calculated?
No.
Can this select a belt drive?
No; use a manufacturer design procedure.
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