An open belt connects two pulleys on parallel shafts and turns them in the same direction. Explore Brown movement 1 and calculate ideal belt speed and driven-pulley speed from the pitch diameters and input speed.
Ideal Open-Belt Ratio Calculator
Enter declared pulley pitch diameters and driver speed. The worksheet applies ideal no-slip belt-speed equality only; it does not size a belt, calculate tension, transmit power or rate a drive.
Equation Used
- The shaft axes are parallel and the belt is open, continuous and uncrossed.
- D1 and D2 are declared effective pitch diameters.
- One ideal belt speed applies at both pulley pitch circles with no slip or stretch.
- The positive direction sign records Brown's same-direction statement; it is not a torque sign convention.
- Centre distance, wrap angle, belt length, thickness, tension, traction, power, efficiency, losses, dynamics, materials, strength, wear, life, guarding, manufacture and safety are excluded.
The uncrossed belt turns both pulleys in the same direction. Pitch diameters set the ideal speed ratio. Playback has a fixed illustrative rate; the speed input changes the numerical belt and pulley speeds.
An uncrossed belt makes both pulleys rotate in the same direction
Brown movement 1 shows two simple pulleys joined by one continuous open belt and states that both pulleys rotate in the same direction. The adjacent movement 2 substitutes a crossed belt and reverses the direction.
The schematic shows the open belt and same-direction pulley rotation. Its pulley sizes are adjusted for readability; the numeric results use the entered pitch diameters.
A historical power-transmission arrangement
The arrangement transmits rotation between parallel shafts while retaining the direction of rotation. The diameter ratio determines the ideal speed change; choosing a working belt drive also requires traction, tension, power and mounting data beyond this model.
Ideal no-slip speed relationships
The belt-speed output converts inches per minute to feet per minute. These identities do not calculate tension, traction, torque, power or efficiency.
Declared ideal example
For D1=4 in, D2=8 in and n1=1750 rpm, ideal belt speed is 1832.6 ft/min, driven speed is 875.0 rpm, reduction magnitude is 2.000:1 and the same-direction sign is +1.
Speed ratio and drive capacity
Equal belt speed at the two pitch circles gives the ideal pulley-speed relationship. It does not establish how much torque the belt can transmit without slipping, or determine its tension and service life. Those checks require the belt properties, wrap, mounting geometry and operating load.
Open-belt questions
Do the pulleys rotate in the same direction?
Yes, in Brown's open-belt arrangement.
Does the calculator size or rate a belt drive?
No.
Are the entered diameters and speed historical?
No. They are entered values for the ideal no-slip calculation.
Open-belt source
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, page 9, movements 1–2: primary public-domain plate and captions for open-belt same-direction rotation and the crossed-belt contrast.
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