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Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive 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 = 2 \cdot C \cdot \sin (\frac{α a - 3.14}{2}) - D

d - Diameter of Small Pulley?C - Centre Distance between Pulleys?α_a - Wrap Angle for Cross Belt Drive?D - Diameter of Big Pulley?

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

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Here is how the Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive equation looks like with Values.

Here is how the Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive equation looks like with Units.

Here is how the Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive equation looks like.

269.7203 = 2 \cdot 1575 \cdot \sin (\frac{220 - 3.14}{2}) - 810

269.7203mm = 2 \cdot 1575mm \cdot \sin (\frac{220° - 3.14}{2}) - 810mm

269.7203 = 2 \cdot 1575 \cdot \sin (\frac{220 - 3.14}{2}) - 810

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

Follow our step by step solution on how to calculate Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d = 2 \cdot 1575mm \cdot \sin (\frac{220° - 3.14}{2}) - 810mm

Next Step Convert Units

∴

d = 2 \cdot 1.575m \cdot \sin (\frac{3.8397rad - 3.14}{2}) - 0.81m

Next Step Prepare to Evaluate

∴

d = 2 \cdot 1.575 \cdot \sin (\frac{3.8397 - 3.14}{2}) - 0.81

Next Step Evaluate

∴

d = 0.269720262228634m

Next Step Convert to Output's Unit

∴

d = 269.720262228634mm

LAST Step Rounding Answer

∴

d = 269.7203mm

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

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 for Cross Belt Drive

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.

Symbol: α_a

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Wrap Angle for Cross Belt Drive

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

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 in Crossed Belt Drives category

Go Wrap Angle for Small Pulley of Cross Belt Drive

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

Go Center Distance given Wrap Angle for Small Pulley of Cross Belt Drive

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

Go Diameter of Big Pulley given Wrap Angle for Small Pulley of Cross Belt Drive

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

Go Belt Length for Cross Belt Drive

L = 2 \cdot C + (π \cdot \frac{d + D}{2}) + (\frac{{(D - d)}^{2}}{4 \cdot C})

How to Evaluate 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 evaluator 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 evaluate the Diameter of Small Pulley, Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive formula is defined as a method to determine the size of the small pulley based on the wrap angle, ensuring efficient power transmission in crossed belt drive systems. Diameter of Small Pulley is denoted by d symbol.

How to evaluate Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive using this online evaluator? To use this online evaluator 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_a) & Diameter of Big Pulley (D) and hit the calculate button.

FAQs on Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive

What is the formula to find Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive?

The formula of Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive is expressed as Diameter of Small Pulley = 2*Centre Distance between Pulleys*sin((Wrap Angle for Cross Belt Drive-3.14)/2)-Diameter of Big Pulley. Here is an example- 269720.3 = 2*1.575*sin((3.8397243543868-3.14)/2)-0.81.

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

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

Can the Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive be negative?

No, the Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive, measured in Length cannot be negative.

Which unit is used to measure 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 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 for Small Pulley of Cross Belt Drive can be measured.

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

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

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

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

Other formulas in Crossed Belt Drives category

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

FAQs on Diameter of Small Pulley given Wrap Angle for Small Pulley of Cross Belt Drive

Variable Name