Diameter of Small Pulley given Wrap Angle of Big Pulley Calculator

✖Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.ⓘ Diameter of Big Pulley [D]			+10% -10%
✖Centre Distance between Pulleys is the distance between the centers of the big pulley and the small pulley.ⓘ Centre Distance between Pulleys [C]			+10% -10%
✖Wrap Angle on Big Pulley is the angle that the Belt wraps around the Big Pulley.ⓘ Wrap Angle on Big Pulley [α_b]			+10% -10%

✖Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.ⓘ Diameter of Small Pulley given Wrap Angle of Big Pulley [d]

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Diameter of Small Pulley given Wrap Angle of Big Pulley Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2))
d = D-(2*C*sin((α_b-3.14)/2))
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Diameter of Small Pulley - (Measured in Meter) - Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.
Diameter of Big Pulley - (Measured in Meter) - Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.
Centre Distance between Pulleys - (Measured in Meter) - Centre Distance between Pulleys is the distance between the centers of the big pulley and the small pulley.
Wrap Angle on Big Pulley - (Measured in Radian) - Wrap Angle on Big Pulley is the angle that the Belt wraps around the Big Pulley.

STEP 1: Convert Input(s) to Base Unit

Diameter of Big Pulley: 810 Millimeter --> 0.81 Meter (Check conversion here)
Centre Distance between Pulleys: 1600 Millimeter --> 1.6 Meter (Check conversion here)
Wrap Angle on Big Pulley: 200 Degree --> 3.490658503988 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = D-(2*C*sin((α_b-3.14)/2)) --> 0.81-(2*1.6*sin((3.490658503988-3.14)/2))

Evaluating ... ...

d = 0.251816475753736

STEP 3: Convert Result to Output's Unit

0.251816475753736 Meter -->251.816475753736 Millimeter (Check conversion here)

FINAL ANSWER

251.816475753736 ≈ 251.8165 Millimeter <-- Diameter of Small Pulley

(Calculation completed in 00.005 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Introduction of Belt Drives Calculators

Wrap Angle for Small Pulley

Go Wrap Angle on Small Pulley = 3.14-(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))

Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley

Go Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Small Pulley given Wrap Angle of Small Pulley

Go Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Big Pulley given Wrap Angle of Small Pulley

Go Diameter of Big Pulley = Diameter of Small Pulley+(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Small Pulley given Wrap Angle of Big Pulley Formula

Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2))
d = D-(2*C*sin((α_b-3.14)/2))

Define a Wrap Angle?

The wrap angle is defined as the angle between the run-up and run-off of the belt on the pulley. In addition, the greater curvature causes greater bending stresses in the belt, which also limits the transmittable belt force. So-called idler pulleys can be used to increase the wrap angle.

How to Calculate Diameter of Small Pulley given Wrap Angle of Big Pulley?

Diameter of Small Pulley given Wrap Angle of Big Pulley calculator uses Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2)) to calculate the Diameter of Small Pulley, The Diameter of Small Pulley given Wrap Angle of Big Pulley formula is defined as distance from side to side of flat part of smaller pulley. Diameter of Small Pulley is denoted by d symbol.

How to calculate Diameter of Small Pulley given Wrap Angle of Big Pulley using this online calculator? To use this online calculator for Diameter of Small Pulley given Wrap Angle of Big Pulley, enter Diameter of Big Pulley (D), Centre Distance between Pulleys (C) & Wrap Angle on Big Pulley (α_b) and hit the calculate button. Here is how the Diameter of Small Pulley given Wrap Angle of Big Pulley calculation can be explained with given input values -> 251816.5 = 0.81-(2*1.6*sin((3.490658503988-3.14)/2)).

FAQ

What is Diameter of Small Pulley given Wrap Angle of Big Pulley?

The Diameter of Small Pulley given Wrap Angle of Big Pulley formula is defined as distance from side to side of flat part of smaller pulley and is represented as d = D-(2*C*sin((α_b-3.14)/2)) or Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2)). Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley, Centre Distance between Pulleys is the distance between the centers of the big pulley and the small pulley & Wrap Angle on Big Pulley is the angle that the Belt wraps around the Big Pulley.

How to calculate Diameter of Small Pulley given Wrap Angle of Big Pulley?

The Diameter of Small Pulley given Wrap Angle of Big Pulley formula is defined as distance from side to side of flat part of smaller pulley is calculated using Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2)). To calculate Diameter of Small Pulley given Wrap Angle of Big Pulley, you need Diameter of Big Pulley (D), Centre Distance between Pulleys (C) & Wrap Angle on Big Pulley (α_b). With our tool, you need to enter the respective value for Diameter of Big Pulley, Centre Distance between Pulleys & Wrap Angle on Big Pulley and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Diameter of Small Pulley?

In this formula, Diameter of Small Pulley uses Diameter of Big Pulley, Centre Distance between Pulleys & Wrap Angle on Big Pulley. We can use 1 other way(s) to calculate the same, which is/are as follows -

Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

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