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Belt Length for Cross Belt Drive Formula

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Belt Length is the length of the transmission belt that is used to transmit power from one pulley to the other. Check FAQs

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

L - Belt Length?C - Centre Distance between Pulleys?d - Diameter of Small Pulley?D - Diameter of Big Pulley?π - Archimedes' constant?

Belt Length for Cross Belt Drive Example

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Here is how the Belt Length for Cross Belt Drive equation looks like with Values.

Here is how the Belt Length for Cross Belt Drive equation looks like with Units.

Here is how the Belt Length for Cross Belt Drive equation looks like.

4892.7457 = 2 \cdot 1575 + (3.1416 \cdot \frac{270 + 810}{2}) + (\frac{{(810 - 270)}^{2}}{4 \cdot 1575})

4892.7457mm = 2 \cdot 1575mm + (3.1416 \cdot \frac{270mm + 810mm}{2}) + (\frac{{(810mm - 270mm)}^{2}}{4 \cdot 1575mm})

4892.7457 = 2 \cdot 1575 + (3.1416 \cdot \frac{270 + 810}{2}) + (\frac{{(810 - 270)}^{2}}{4 \cdot 1575})

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Belt Length for Cross Belt Drive Solution

Follow our step by step solution on how to calculate Belt Length for Cross Belt Drive?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = 2 \cdot 1575mm + (π \cdot \frac{270mm + 810mm}{2}) + (\frac{{(810mm - 270mm)}^{2}}{4 \cdot 1575mm})

Next Step Substitute values of Constants

∴

L = 2 \cdot 1575mm + (3.1416 \cdot \frac{270mm + 810mm}{2}) + (\frac{{(810mm - 270mm)}^{2}}{4 \cdot 1575mm})

Next Step Convert Units

∴

L = 2 \cdot 1.575m + (3.1416 \cdot \frac{0.27m + 0.81m}{2}) + (\frac{{(0.81m - 0.27m)}^{2}}{4 \cdot 1.575m})

Next Step Prepare to Evaluate

∴

L = 2 \cdot 1.575 + (3.1416 \cdot \frac{0.27 + 0.81}{2}) + (\frac{{(0.81 - 0.27)}^{2}}{4 \cdot 1.575})

Next Step Evaluate

∴

L = 4.8927457472242m

Next Step Convert to Output's Unit

∴

L = 4892.7457472242mm

LAST Step Rounding Answer

∴

L = 4892.7457mm

Belt Length for Cross Belt Drive Formula Elements

Variables

Constants

Belt Length

Belt Length is the length of the transmission belt that is used to transmit power from one pulley to the other.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Belt Length

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

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 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

How to Evaluate Belt Length for Cross Belt Drive?

Belt Length for Cross Belt Drive evaluator uses Belt Length = 2*Centre Distance between Pulleys+(pi*(Diameter of Small Pulley+Diameter of Big Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys)) to evaluate the Belt Length, Belt Length for Cross Belt Drive formula is defined as a method to calculate the total length of a belt required for a crossed belt drive system, considering the center distance and the diameters of the pulleys involved. Belt Length is denoted by L symbol.

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

FAQs on Belt Length for Cross Belt Drive

What is the formula to find Belt Length for Cross Belt Drive?

The formula of Belt Length for Cross Belt Drive is expressed as Belt Length = 2*Centre Distance between Pulleys+(pi*(Diameter of Small Pulley+Diameter of Big Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys)). Here is an example- 4.9E+6 = 2*1.575+(pi*(0.27+0.81)/2)+(((0.81-0.27)^2)/(4*1.575)).

How to calculate Belt Length for Cross Belt Drive?

With Centre Distance between Pulleys (C), Diameter of Small Pulley (d) & Diameter of Big Pulley (D) we can find Belt Length for Cross Belt Drive using the formula - Belt Length = 2*Centre Distance between Pulleys+(pi*(Diameter of Small Pulley+Diameter of Big Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys)). This formula also uses Archimedes' constant .

Can the Belt Length for Cross Belt Drive be negative?

No, the Belt Length for Cross Belt Drive, measured in Length cannot be negative.

Which unit is used to measure Belt Length for Cross Belt Drive?

Belt Length for 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 Belt Length for Cross Belt Drive can be measured.

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Belt Length for Cross Belt Drive Formula

Belt Length for Cross Belt Drive Example

Belt Length for Cross Belt Drive Solution

Belt Length for Cross Belt Drive Formula Elements

Other formulas in Crossed Belt Drives category

How to Evaluate Belt Length for Cross Belt Drive?

FAQs on Belt Length for Cross Belt Drive

Variable Name