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 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: 1575 Millimeter --> 1.575 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*1.575*sin(3.490658503988-3.14)/2)
Evaluating ... ...
d = 0.268961805854119
STEP 3: Convert Result to Output's Unit
0.268961805854119 Meter -->268.961805854119 Millimeter (Check conversion ​here)
FINAL ANSWER
268.961805854119 268.9618 Millimeter <-- Diameter of Small Pulley
(Calculation completed in 00.004 seconds)

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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 Big Pulley Formula

​LaTeX ​Go
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, Diameter of Small Pulley given Wrap Angle of Big Pulley formula is defined as a method to determine the size of a small pulley based on the wrap angle of a larger pulley, ensuring efficient belt drive design in mechanical systems. 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 -> 268961.8 = 0.81-(2*1.575*sin(3.490658503988-3.14)/2).

FAQ

What is Diameter of Small Pulley given Wrap Angle of Big Pulley?
Diameter of Small Pulley given Wrap Angle of Big Pulley formula is defined as a method to determine the size of a small pulley based on the wrap angle of a larger pulley, ensuring efficient belt drive design in mechanical systems 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 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?
Diameter of Small Pulley given Wrap Angle of Big Pulley formula is defined as a method to determine the size of a small pulley based on the wrap angle of a larger pulley, ensuring efficient belt drive design in mechanical systems 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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