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Wrap Angle for Small Pulley of Cross Belt Drive Formula

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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. Check FAQs

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

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

Wrap Angle for Small Pulley of Cross Belt Drive Example

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

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

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

219.358 = 3.14 + (2 \cdot a \sin (\frac{810 + 270}{2 \cdot 1600}))

219.358° = 3.14 + (2 \cdot a \sin (\frac{810mm + 270mm}{2 \cdot 1600mm}))

219.358 = 3.14 + (2 \cdot a \sin (\frac{810 + 270}{2 \cdot 1600}))

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Wrap Angle for Small Pulley of Cross Belt Drive Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

α a = 3.14 + (2 \cdot a \sin (\frac{810mm + 270mm}{2 \cdot 1600mm}))

Next Step Convert Units

∴

α a = 3.14 + (2 \cdot a \sin (\frac{0.81m + 0.27m}{2 \cdot 1.6m}))

Next Step Prepare to Evaluate

∴

α a = 3.14 + (2 \cdot a \sin (\frac{0.81 + 0.27}{2 \cdot 1.6}))

Next Step Evaluate

∴

α a = 3.82851959869742rad

Next Step Convert to Output's Unit

∴

α a = 219.358014788523°

LAST Step Rounding Answer

∴

α a = 219.358°

Wrap Angle for Small Pulley of Cross Belt Drive Formula Elements

Variables

Functions

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

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 centres 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

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)

asin

The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: asin(Number)

Other formulas in Crossed Belt Drives category

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

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

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 Wrap Angle for Small Pulley of Cross Belt Drive?

Wrap Angle for Small Pulley of Cross Belt Drive evaluator uses Wrap Angle for Cross Belt Drive = 3.14+(2*asin((Diameter of Big Pulley+Diameter of Small Pulley)/(2*Centre Distance between Pulleys))) to evaluate the Wrap Angle for Cross Belt Drive, The Wrap Angle for Small Pulley of Cross Belt Drive formula is defined as the angle between the run-up and run-off of the belt on the pulley. Wrap Angle for Cross Belt Drive is denoted by α_a symbol.

How to evaluate Wrap Angle for Small Pulley of Cross Belt Drive using this online evaluator? To use this online evaluator for Wrap Angle for Small Pulley of Cross Belt Drive, enter Diameter of Big Pulley (D), Diameter of Small Pulley (d) & Centre Distance between Pulleys (C) and hit the calculate button.

FAQs on Wrap Angle for Small Pulley of Cross Belt Drive

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

The formula of Wrap Angle for Small Pulley of Cross Belt Drive is expressed as Wrap Angle for Cross Belt Drive = 3.14+(2*asin((Diameter of Big Pulley+Diameter of Small Pulley)/(2*Centre Distance between Pulleys))). Here is an example- 12568.29 = 3.14+(2*asin((0.81+0.27)/(2*1.6))).

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

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

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

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

Which unit is used to measure Wrap Angle for Small Pulley of Cross Belt Drive?

Wrap Angle for Small Pulley of Cross Belt Drive is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Wrap Angle for Small Pulley of Cross Belt Drive can be measured.

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Wrap Angle for Small Pulley of Cross Belt Drive Formula

Wrap Angle for Small Pulley of Cross Belt Drive Example

Wrap Angle for Small Pulley of Cross Belt Drive Solution

Wrap Angle for Small Pulley of Cross Belt Drive Formula Elements

Other formulas in Crossed Belt Drives category

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

FAQs on Wrap Angle for Small Pulley of Cross Belt Drive

Variable Name