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Length of Arc of Contact Formula

GoMaximum Length of Arc of Contact Formula

GoMaximum Length of Arc of Approach Formula

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Length of Arc of Contact is the ratio of length of path of contact and the cosine of the pressure angle. Check FAQs

L = \frac{P}{\cos (Φ g)}

L - Length of Arc of Contact?P - Path of Contact?Φ_g - Pressure Angle of Gear?

Length of Arc of Contact Example

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Here is how the Length of Arc of Contact equation looks like with Values.

Here is how the Length of Arc of Contact equation looks like with Units.

Here is how the Length of Arc of Contact equation looks like.

14.1221 = \frac{11.9762}{\cos (32)}

14.1221mm = \frac{11.9762mm}{\cos (32°)}

14.1221 = \frac{11.9762}{\cos (32)}

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Length of Arc of Contact Solution

Follow our step by step solution on how to calculate Length of Arc of Contact?

FIRST Step Consider the formula

L = \frac{P}{\cos (Φ g)}

Next Step Substitute values of Variables

∴

L = \frac{11.9762mm}{\cos (32°)}

Next Step Convert Units

∴

L = \frac{0.012m}{\cos (0.5585rad)}

Next Step Prepare to Evaluate

∴

L = \frac{0.012}{\cos (0.5585)}

Next Step Evaluate

∴

L = 0.0141220528107761m

Next Step Convert to Output's Unit

∴

L = 14.1220528107761mm

LAST Step Rounding Answer

∴

L = 14.1221mm

Length of Arc of Contact Formula Elements

Variables

Functions

Length of Arc of Contact

Length of Arc of Contact is the ratio of length of path of contact and the cosine of the pressure angle.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Arc of Contact

Path of Contact

Path of Contact is the path traced by the contact point of a pair of tooth profiles.

Symbol: P

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Path of Contact

Pressure Angle of Gear

Pressure Angle of Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

Symbol: Φ_g

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle of Gear

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Length of Arc of Contact

Go Maximum Length of Arc of Contact

L = (r + R w) \cdot \tan (α)

Go Maximum Length of Arc of Approach

L = (R w + r) \cdot \tan (Φ g)

Other formulas in Length category

Go Length of Path of Approach

P 1 = \sqrt{{R a}^{2} - {R w}^{2} \cdot {(\cos (Φ g))}^{2}} - R w \cdot \sin (Φ g)

Go Length of Path of Contact

P = \sqrt{{R a}^{2} - {R w}^{2} \cdot {(\cos (Φ g))}^{2}} + \sqrt{{r a}^{2} - r^{2} \cdot {(\cos (Φ g))}^{2}} - (R w + r) \cdot \sin (Φ g)

Go Length of Path of Recess

P 2 = \sqrt{{r a}^{2} - r^{2} \cdot {(\cos (Φ g))}^{2}} - r \cdot \sin (Φ g)

Go Maximum Length of Path of Approach

P 1 = r \cdot \sin (Φ g)

How to Evaluate Length of Arc of Contact?

Length of Arc of Contact evaluator uses Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear) to evaluate the Length of Arc of Contact, Length of Arc of Contact formula is defined as a measure of the distance along the circumference of a gear that is in contact with another gear during rotation, providing insight into the gear's rotational motion and interaction with other gears in a mechanical system. Length of Arc of Contact is denoted by L symbol.

How to evaluate Length of Arc of Contact using this online evaluator? To use this online evaluator for Length of Arc of Contact, enter Path of Contact (P) & Pressure Angle of Gear (Φ_g) and hit the calculate button.

FAQs on Length of Arc of Contact

What is the formula to find Length of Arc of Contact?

The formula of Length of Arc of Contact is expressed as Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear). Here is an example- 14122.05 = 0.01197618/cos(0.55850536063808).

How to calculate Length of Arc of Contact?

With Path of Contact (P) & Pressure Angle of Gear (Φ_g) we can find Length of Arc of Contact using the formula - Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Length of Arc of Contact?

Here are the different ways to Calculate Length of Arc of Contact-

Length of Arc of Contact=(Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)
Length of Arc of Contact=(Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)

Can the Length of Arc of Contact be negative?

Yes, the Length of Arc of Contact, measured in Length can be negative.

Which unit is used to measure Length of Arc of Contact?

Length of Arc of Contact is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Arc of Contact can be measured.

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Length of Arc of Contact Formula

​GoMaximum Length of Arc of Contact Formula

​GoMaximum Length of Arc of Approach Formula

Length of Arc of Contact Example

Length of Arc of Contact Solution

Length of Arc of Contact Formula Elements

Other Formulas to find Length of Arc of Contact

Other formulas in Length category

How to Evaluate Length of Arc of Contact?

FAQs on Length of Arc of Contact

Variable Name

GoMaximum Length of Arc of Contact Formula

GoMaximum Length of Arc of Approach Formula