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Diameter of Small Pulley given Wrap Angle of Big Pulley Formula

GoDiameter of Small Pulley given Wrap Angle of Small Pulley Formula

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Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley. Check FAQs

d = D - (2 \cdot C \cdot \frac{\sin (α b - 3.14)}{2})

d - Diameter of Small Pulley?D - Diameter of Big Pulley?C - Centre Distance between Pulleys?α_b - Wrap Angle on Big Pulley?

Diameter of Small Pulley given Wrap Angle of Big Pulley Example

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Here is how the Diameter of Small Pulley given Wrap Angle of Big Pulley equation looks like with Values.

Here is how the Diameter of Small Pulley given Wrap Angle of Big Pulley equation looks like with Units.

Here is how the Diameter of Small Pulley given Wrap Angle of Big Pulley equation looks like.

268.9618 = 810 - (2 \cdot 1575 \cdot \frac{\sin (200 - 3.14)}{2})

268.9618mm = 810mm - (2 \cdot 1575mm \cdot \frac{\sin (200° - 3.14)}{2})

268.9618 = 810 - (2 \cdot 1575 \cdot \frac{\sin (200 - 3.14)}{2})

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Diameter of Small Pulley given Wrap Angle of Big Pulley Solution

Follow our step by step solution on how to calculate Diameter of Small Pulley given Wrap Angle of Big Pulley?

FIRST Step Consider the formula

d = D - (2 \cdot C \cdot \frac{\sin (α b - 3.14)}{2})

Next Step Substitute values of Variables

∴

d = 810mm - (2 \cdot 1575mm \cdot \frac{\sin (200° - 3.14)}{2})

Next Step Convert Units

∴

d = 0.81m - (2 \cdot 1.575m \cdot \frac{\sin (3.4907rad - 3.14)}{2})

Next Step Prepare to Evaluate

∴

d = 0.81 - (2 \cdot 1.575 \cdot \frac{\sin (3.4907 - 3.14)}{2})

Next Step Evaluate

∴

d = 0.268961805854119m

Next Step Convert to Output's Unit

∴

d = 268.961805854119mm

LAST Step Rounding Answer

∴

d = 268.9618mm

Diameter of Small Pulley given Wrap Angle of Big Pulley Formula Elements

Variables

Functions

Diameter of Small Pulley

Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Small Pulley

Diameter of Big Pulley

Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Big Pulley

Centre Distance between Pulleys

Centre Distance between Pulleys is the distance between the centers of the big pulley and the small pulley.

Symbol: C

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Centre Distance between Pulleys

Wrap Angle on Big Pulley

Wrap Angle on Big Pulley is the angle that the Belt wraps around the Big Pulley.

Symbol: α_b

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Wrap Angle on Big Pulley

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.

Syntax: sin(Angle)

Other Formulas to find Diameter of Small Pulley

Go Diameter of Small Pulley given Wrap Angle of Small Pulley

d = D - 2 \cdot C \cdot \sin (\frac{3.14 - α s}{2})

Other formulas in Introduction of Belt Drives category

Go Wrap Angle for Small Pulley

α s = 3.14 - 2 \cdot a \sin (\frac{D - d}{2 \cdot C})

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

C = \frac{D - d}{2 \cdot \sin (\frac{3.14 - α s}{2})}

Go Diameter of Big Pulley given Wrap Angle of Small Pulley

D = d + 2 \cdot C \cdot \sin (\frac{3.14 - α s}{2})

Go Wrap Angle for Big Pulley

α b = 3.14 + 2 \cdot a \sin (\frac{D - d}{2 \cdot C})

How to Evaluate Diameter of Small Pulley given Wrap Angle of Big Pulley?

Diameter of Small Pulley given Wrap Angle of Big Pulley evaluator uses Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin(Wrap Angle on Big Pulley-3.14)/2) to evaluate 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 evaluate Diameter of Small Pulley given Wrap Angle of Big Pulley using this online evaluator? To use this online evaluator 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 (α_b) and hit the calculate button.

FAQs on Diameter of Small Pulley given Wrap Angle of Big Pulley

What is the formula to find Diameter of Small Pulley given Wrap Angle of Big Pulley?

The formula of Diameter of Small Pulley given Wrap Angle of Big Pulley is expressed as Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin(Wrap Angle on Big Pulley-3.14)/2). Here is an example- 268961.8 = 0.81-(2*1.575*sin(3.490658503988-3.14)/2).

How to calculate Diameter of Small Pulley given Wrap Angle of Big Pulley?

With Diameter of Big Pulley (D), Centre Distance between Pulleys (C) & Wrap Angle on Big Pulley (α_b) we can find Diameter of Small Pulley given Wrap Angle of Big Pulley using the formula - Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin(Wrap Angle on Big Pulley-3.14)/2). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Diameter of Small Pulley?

Here are the different ways to Calculate Diameter of Small Pulley-

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

Can the Diameter of Small Pulley given Wrap Angle of Big Pulley be negative?

No, the Diameter of Small Pulley given Wrap Angle of Big Pulley, measured in Length cannot be negative.

Which unit is used to measure Diameter of Small Pulley given Wrap Angle of Big Pulley?

Diameter of Small Pulley given Wrap Angle of Big Pulley is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Diameter of Small Pulley given Wrap Angle of Big Pulley can be measured.

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Diameter of Small Pulley given Wrap Angle of Big Pulley Formula

​GoDiameter of Small Pulley given Wrap Angle of Small Pulley Formula

Diameter of Small Pulley given Wrap Angle of Big Pulley Example

Diameter of Small Pulley given Wrap Angle of Big Pulley Solution

Diameter of Small Pulley given Wrap Angle of Big Pulley Formula Elements

Other Formulas to find Diameter of Small Pulley

Other formulas in Introduction of Belt Drives category

How to Evaluate Diameter of Small Pulley given Wrap Angle of Big Pulley?

FAQs on Diameter of Small Pulley given Wrap Angle of Big Pulley

Variable Name

GoDiameter of Small Pulley given Wrap Angle of Small Pulley Formula