Diameter of Small Pulley given Wrap Angle of Small 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 Small Pulley is the angle that the Belt wraps around the Small Pulley.ⓘ Wrap Angle on Small Pulley [α_s]			+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 Small Pulley [d]

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Diameter of Small Pulley given Wrap Angle of Small Pulley Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Small Pulley = Diameter of Big Pulley-2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2)
d = D-2*C*sin((3.14-α_s)/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 Small Pulley - (Measured in Radian) - Wrap Angle on Small Pulley is the angle that the Belt wraps around the Small 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: 1575 Millimeter --> 1.575 Meter (Check conversion here)
Wrap Angle on Small Pulley: 160.67 Degree --> 2.80422050917876 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = D-2*C*sin((3.14-α_s)/2) --> 0.81-2*1.575*sin((3.14-2.80422050917876)/2)

Evaluating ... ...

d = 0.283628261728119

STEP 3: Convert Result to Output's Unit

0.283628261728119 Meter -->283.628261728119 Millimeter (Check conversion here)

FINAL ANSWER

283.628261728119 ≈ 283.6283 Millimeter <-- Diameter of Small Pulley

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< Introduction of Belt Drives Calculators

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

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

Wrap Angle for Small Pulley

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

Diameter of Small Pulley given Wrap Angle of Small Pulley

LaTeX 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

LaTeX 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 Small Pulley Formula

LaTeX Go

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

Diameter of Small Pulley given Wrap Angle of Small Pulley calculator uses Diameter of Small Pulley = Diameter of Big Pulley-2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2) to calculate the Diameter of Small Pulley, Diameter of Small Pulley given Wrap Angle of Small Pulley formula is defined as a method to determine the diameter of a small pulley based on the wrap angle, which influences the efficiency and performance of belt drives in mechanical systems. Diameter of Small Pulley is denoted by d symbol.

How to calculate Diameter of Small Pulley given Wrap Angle of Small Pulley using this online calculator? To use this online calculator for Diameter of Small Pulley given Wrap Angle of Small Pulley, enter Diameter of Big Pulley (D), Centre Distance between Pulleys (C) & Wrap Angle on Small Pulley (α_s) and hit the calculate button. Here is how the Diameter of Small Pulley given Wrap Angle of Small Pulley calculation can be explained with given input values -> 283628.3 = 0.81-2*1.575*sin((3.14-2.80422050917876)/2).

FAQ

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

Diameter of Small Pulley given Wrap Angle of Small Pulley formula is defined as a method to determine the diameter of a small pulley based on the wrap angle, which influences the efficiency and performance of belt drives in mechanical systems and is represented as d = D-2*C*sin((3.14-α_s)/2) or 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 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 Small Pulley is the angle that the Belt wraps around the Small Pulley.

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

Diameter of Small Pulley given Wrap Angle of Small Pulley formula is defined as a method to determine the diameter of a small pulley based on the wrap angle, which influences the efficiency and performance of belt drives in mechanical systems is calculated using Diameter of Small Pulley = Diameter of Big Pulley-2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2). To calculate Diameter of Small Pulley given Wrap Angle of Small Pulley, you need Diameter of Big Pulley (D), Centre Distance between Pulleys (C) & Wrap Angle on Small Pulley (α_s). With our tool, you need to enter the respective value for Diameter of Big Pulley, Centre Distance between Pulleys & Wrap Angle on Small 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 Small 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(Wrap Angle on Big Pulley-3.14)/2)

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