Center Distance from Small Pulley to Big 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%
✖Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.ⓘ Diameter of Small Pulley [d]			+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%

✖Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley.ⓘ Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley [C]

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Formula

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

Formula

`"C" = ("D"-"d")/(2*sin((3.14-"α"_{"s"})/2)) `

Example

`"3126.36mm"=("810mm"-"270mm")/(2*sin((3.14-"170°")/2)) `

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Centre Distance between Pulleys - (Measured in Meter) - Centre Distance between Pulleys is the distance between the centres of the big pulley and 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.
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.
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)
Diameter of Small Pulley: 270 Millimeter --> 0.27 Meter (Check conversion here)
Wrap Angle on Small Pulley: 170 Degree --> 2.9670597283898 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = (D-d)/(2*sin((3.14-α_s)/2)) --> (0.81-0.27)/(2*sin((3.14-2.9670597283898)/2))

Evaluating ... ...

C = 3.12635987005893

STEP 3: Convert Result to Output's Unit

3.12635987005893 Meter -->3126.35987005893 Millimeter (Check conversion here)

FINAL ANSWER

3126.35987005893 ≈ 3126.36 Millimeter <-- Centre Distance between Pulleys

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Belt Drives » Introduction of Belt Drives » Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley

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Osmania University (OU), Hyderabad

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< 15 Introduction of Belt Drives Calculators

Velocity of belt given tension of belt in tight side

Go Belt Velocity = sqrt((((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side)-Belt Tension on Tight Side)/(Mass of Meter Length of Belt*((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))-1)))

Angle of Wrap given Belt Tension in Tight Side

Go Wrap Angle on Pulley = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))/Coefficient of Friction for Belt Drive

Mass per unit length of belt

Go Mass of Meter Length of Belt = (Belt Tension on Tight Side-((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side))/((Belt Velocity^2)*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))))

Coefficient of Friction in between Surfaces given Belt Tension in Tight Side

Go Coefficient of Friction for Belt Drive = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of Belt*Belt Velocity^2))/Wrap Angle on Pulley

Belt Tension in Loose Side of Belt given Tension in Tight Side

Go Belt Tension on Loose Side = ((Belt Tension on Tight Side-(Mass of Meter Length of Belt*Belt Velocity^2))/(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley)))+(Mass of Meter Length of Belt*Belt Velocity^2)

Belt tension in tight side

Go Belt Tension on Tight Side = ((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))+(Mass of Meter Length of Belt*Belt Velocity^2)

Length of Belt

Go Belt Length = (2*Centre Distance between Pulleys)+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys))

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))

Wrap Angle for Big Pulley

Go Wrap Angle on Big 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 Big Pulley

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

Go 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 given Wrap Angle for Big Pulley

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

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

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

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

Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley calculator uses Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle on Small Pulley)/2)) to calculate the Centre Distance between Pulleys, The Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley formula is defined as the distance in between the centers of the small pulley and the big pulley. Centre Distance between Pulleys is denoted by C symbol.

How to calculate Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley using this online calculator? To use this online calculator for Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley, enter Diameter of Big Pulley (D), Diameter of Small Pulley (d) & Wrap Angle on Small Pulley (α_s) and hit the calculate button. Here is how the Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley calculation can be explained with given input values -> 3.1E+6 = (0.81-0.27)/(2*sin((3.14-2.9670597283898)/2)) .

FAQ

What is Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley?

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

How to calculate Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley?

The Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley formula is defined as the distance in between the centers of the small pulley and the big pulley is calculated using Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle on Small Pulley)/2)). To calculate Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley, you need Diameter of Big Pulley (D), Diameter of Small Pulley (d) & Wrap Angle on Small Pulley (α_s). With our tool, you need to enter the respective value for Diameter of Big Pulley, Diameter of Small Pulley & 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 Centre Distance between Pulleys?

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

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

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