Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive Solution

STEP 0: Pre-Calculation Summary
Formula Used
Diameter of Small Pulley = (2*Centre Distance between Pulleys*sin((Wrap Angle for Cross Belt Drive-3.14)/2))-Diameter of Big Pulley
d = (2*C*sin((α-3.14)/2))-D
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.
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.
Wrap Angle for Cross Belt Drive - (Measured in Radian) - Wrap Angle for Cross Belt Drive is the angle that the Belt wraps around the Small Pulley and is the same as around the Big 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.
STEP 1: Convert Input(s) to Base Unit
Centre Distance between Pulleys: 1600 Millimeter --> 1.6 Meter (Check conversion here)
Wrap Angle for Cross Belt Drive: 220 Degree --> 3.8397243543868 Radian (Check conversion here)
Diameter of Big Pulley: 810 Millimeter --> 0.81 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = (2*C*sin((α-3.14)/2))-D --> (2*1.6*sin((3.8397243543868-3.14)/2))-0.81
Evaluating ... ...
d = 0.286858679089406
STEP 3: Convert Result to Output's Unit
0.286858679089406 Meter -->286.858679089406 Millimeter (Check conversion here)
FINAL ANSWER
286.858679089406 286.8587 Millimeter <-- Diameter of Small Pulley
(Calculation completed in 00.004 seconds)

Credits

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Osmania University (OU), Hyderabad
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5 Crossed Belt Drives Calculators

Belt Length for Cross Belt Drive
Go Belt Length = 2*Centre Distance between Pulleys+(pi*(Diameter of Small Pulley+Diameter of Big Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys))
Wrap Angle for Small Pulley of Cross Belt Drive
Go Wrap Angle for Cross Belt Drive = 3.14+(2*asin((Diameter of Big Pulley+Diameter of Small Pulley)/(2*Centre Distance between Pulleys)))
Center Distance given Wrap Angle for Small Pulley of Cross Belt Drive
Go Centre Distance between Pulleys = (Diameter of Big Pulley+Diameter of Small Pulley)/(2*sin((Wrap Angle for Cross Belt Drive-3.14)/2))
Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive
Go Diameter of Small Pulley = (2*Centre Distance between Pulleys*sin((Wrap Angle for Cross Belt Drive-3.14)/2))-Diameter of Big Pulley
Diameter of Big Pulley given Wrap Angle for Small Pulley of Cross Belt Drive
Go Diameter of Big Pulley = (2*sin((Wrap Angle for Cross Belt Drive-3.14)/2)*Centre Distance between Pulleys)-Diameter of Small Pulley

Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive Formula

Diameter of Small Pulley = (2*Centre Distance between Pulleys*sin((Wrap Angle for Cross Belt Drive-3.14)/2))-Diameter of Big Pulley
d = (2*C*sin((α-3.14)/2))-D

Applications of Belt Drives?

A belt drive is used to transfer power.
The belt drive is used in the Mill industry.
The belt drive is used in Conveyor.

How to Calculate Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive?

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

How to calculate Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive using this online calculator? To use this online calculator for Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive, enter Centre Distance between Pulleys (C), Wrap Angle for Cross Belt Drive (α) & Diameter of Big Pulley (D) and hit the calculate button. Here is how the Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive calculation can be explained with given input values -> 286858.7 = (2*1.6*sin((3.8397243543868-3.14)/2))-0.81.

FAQ

What is Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive?
The Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive formula is defined as the distance from side to side of the flat of the pulley and is represented as d = (2*C*sin((α-3.14)/2))-D or Diameter of Small Pulley = (2*Centre Distance between Pulleys*sin((Wrap Angle for Cross Belt Drive-3.14)/2))-Diameter of Big Pulley. Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley, Wrap Angle for Cross Belt Drive is the angle that the Belt wraps around the Small Pulley and is the same as around the Big Pulley & Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.
How to calculate Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive?
The Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive formula is defined as the distance from side to side of the flat of the pulley is calculated using Diameter of Small Pulley = (2*Centre Distance between Pulleys*sin((Wrap Angle for Cross Belt Drive-3.14)/2))-Diameter of Big Pulley. To calculate Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive, you need Centre Distance between Pulleys (C), Wrap Angle for Cross Belt Drive (α) & Diameter of Big Pulley (D). With our tool, you need to enter the respective value for Centre Distance between Pulleys, Wrap Angle for Cross Belt Drive & Diameter of Big Pulley and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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