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((αb-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 centres 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((αb-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 00.020 seconds)

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15 Introductory Formulas for 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))

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((αb-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 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((αb-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 centres 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 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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