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Diameter of Small Pully When Wrap Angle of the Big Pulley is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2)
d = D-2*C*sin((αs-180)/2)
This formula uses 1 Functions, 3 Variables
Functions Used
sin - Trigonometric sine function, sin(Angle)
Variables Used
Diameter of Big Pulley - Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley. (Measured in Millimeter)
Center Distance - Center Distance is the distance in between the centers of the big pulley and the small pulley. (Measured in Millimeter)
Wrap Angle for Small Pulley - Wrap Angle for Small Pulley is the angle that the Belt wraps around the Small Pulley. (Measured in Degree)
STEP 1: Convert Input(s) to Base Unit
Diameter of Big Pulley: 100 Millimeter --> 0.1 Meter (Check conversion here)
Center Distance: 300 Millimeter --> 0.3 Meter (Check conversion here)
Wrap Angle for Small Pulley: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = D-2*C*sin((αs-180)/2) --> 0.1-2*0.3*sin((0.785398163397301-180)/2)
Evaluating ... ...
d = 0.698449341403886
STEP 3: Convert Result to Output's Unit
0.698449341403886 Meter -->698.449341403886 Millimeter (Check conversion here)
FINAL ANSWER
698.449341403886 Millimeter <-- Diameter of Small Pulley
(Calculation completed in 00.047 seconds)

10+ Design of Belt Drives Calculators

Belt Tension in the Tight Side
belt_tension_in_tight_side = (e^Coefficient of Friction*Angle of Wrap)*(Belt Tension in loose Side-Mass of Meter Length of Belt*Belt Velocity^2)+Mass of Meter Length of Belt*Belt Velocity^2 Go
length of the Belt
belt_length = 2*Center Distance+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+((Diameter of Big Pulley-Diameter of Small Pulley)^2/4*Center Distance) Go
Center Distance from Small Pulley to Big Pulley When Wrap Angle of Small Pulley is Given
center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((180-Wrap Angle for Small Pulley)/2)) Go
Center Distance from Small Pulley to Big Pulley When Wrap Angle of Big Pulley is Given
center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle for Small Pulley-180)/2)) Go
Wrap Angle for the Small Pulley
wrap_angle_for_small_pulley = 180-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance) Go
Diameter of Small Pully When Wrap Angle of the Big Pulley is Given
diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2) Go
Diameter of Big Pulley When Wrap Angle for the Big Pulley is Given
diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2) Go
Diameter of Small Pulley When Wrap Angle of Small Pulley is Given
diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((180-Wrap Angle for Small Pulley)/2) Go
Diameter of Big Pulley When Wrap Angle of Small Pulley is Given
diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((180-Wrap Angle for Small Pulley)/2) Go
Wrap Angle for the Big Pulley
wrap_angle_for_big_pulley = 180+2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance) Go

Diameter of Small Pully When Wrap Angle of the Big Pulley is Given Formula

diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2)
d = D-2*C*sin((αs-180)/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 Pully When Wrap Angle of the Big Pulley is Given?

Diameter of Small Pully When Wrap Angle of the Big Pulley is Given calculator uses diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2) to calculate the Diameter of Small Pulley, The Diameter of Small Pully When Wrap Angle of the Big Pulley is Given formula is defined as the distance from side to side of the flat of the pulley. Diameter of Small Pulley and is denoted by d symbol.

How to calculate Diameter of Small Pully When Wrap Angle of the Big Pulley is Given using this online calculator? To use this online calculator for Diameter of Small Pully When Wrap Angle of the Big Pulley is Given, enter Diameter of Big Pulley (D), Center Distance (C) and Wrap Angle for Small Pulley s) and hit the calculate button. Here is how the Diameter of Small Pully When Wrap Angle of the Big Pulley is Given calculation can be explained with given input values -> 698.4493 = 0.1-2*0.3*sin((0.785398163397301-180)/2).

FAQ

What is Diameter of Small Pully When Wrap Angle of the Big Pulley is Given?
The Diameter of Small Pully When Wrap Angle of the Big Pulley is Given formula is defined as the distance from side to side of the flat of the pulley and is represented as d = D-2*C*sin((αs-180)/2) or diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2). Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley, Center Distance is the distance in between the centers of the big pulley and the small pulley and Wrap Angle for Small Pulley is the angle that the Belt wraps around the Small Pulley.
How to calculate Diameter of Small Pully When Wrap Angle of the Big Pulley is Given?
The Diameter of Small Pully When Wrap Angle of the Big Pulley is Given formula is defined as the distance from side to side of the flat of the pulley is calculated using diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2). To calculate Diameter of Small Pully When Wrap Angle of the Big Pulley is Given, you need Diameter of Big Pulley (D), Center Distance (C) and Wrap Angle for Small Pulley s). With our tool, you need to enter the respective value for Diameter of Big Pulley, Center Distance and Wrap Angle for 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, Center Distance and Wrap Angle for Small Pulley. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • wrap_angle_for_small_pulley = 180-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance)
  • center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((180-Wrap Angle for Small Pulley)/2))
  • diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((180-Wrap Angle for Small Pulley)/2)
  • diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((180-Wrap Angle for Small Pulley)/2)
  • wrap_angle_for_big_pulley = 180+2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance)
  • center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle for Small Pulley-180)/2))
  • diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2)
  • diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((Wrap Angle for Small Pulley-180)/2)
  • belt_length = 2*Center Distance+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+((Diameter of Big Pulley-Diameter of Small Pulley)^2/4*Center Distance)
  • belt_tension_in_tight_side = (e^Coefficient of Friction*Angle of Wrap)*(Belt Tension in loose Side-Mass of Meter Length of Belt*Belt Velocity^2)+Mass of Meter Length of Belt*Belt Velocity^2
Where is the Diameter of Small Pully When Wrap Angle of the Big Pulley is Given calculator used?
Among many, Diameter of Small Pully When Wrap Angle of the Big Pulley is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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