Length of Arc of Contact Calculator

✖Path of Contact is the path traced by the contact point of a pair of tooth profiles.ⓘ Path of Contact [P]			+10% -10%
✖Pressure Angle of Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.ⓘ Pressure Angle of Gear [Φ_g]			+10% -10%

✖Length of Arc of Contact is the ratio of length of path of contact and the cosine of the pressure angle.ⓘ Length of Arc of Contact [L]

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Length of Arc of Contact Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear)
L = P/cos(Φ_g)
This formula uses 1 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Length of Arc of Contact - (Measured in Meter) - Length of Arc of Contact is the ratio of length of path of contact and the cosine of the pressure angle.
Path of Contact - (Measured in Meter) - Path of Contact is the path traced by the contact point of a pair of tooth profiles.
Pressure Angle of Gear - (Measured in Radian) - Pressure Angle of Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

STEP 1: Convert Input(s) to Base Unit

Path of Contact: 11.97618 Millimeter --> 0.01197618 Meter (Check conversion here)
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = P/cos(Φ_g) --> 0.01197618/cos(0.55850536063808)

Evaluating ... ...

L = 0.0141220528107761

STEP 3: Convert Result to Output's Unit

0.0141220528107761 Meter -->14.1220528107761 Millimeter (Check conversion here)

FINAL ANSWER

14.1220528107761 ≈ 14.12205 Millimeter <-- Length of Arc of Contact

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Length Calculators

Length of Path of Contact

LaTeX Go Path of Contact = sqrt(Radius of Addendum Circle of Wheel^2-Radius of Pitch Circle of Wheel^2*(cos(Pressure Angle of Gear))^2)+sqrt(Radius of Addendum Circle of Pinion^2-Radius of Pitch Circle of Pinion^2*(cos(Pressure Angle of Gear))^2)-(Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear)

Length of Path of Recess

LaTeX Go Path of Recess = sqrt(Radius of Addendum Circle of Pinion^2-Radius of Pitch Circle of Pinion^2*(cos(Pressure Angle of Gear))^2)-Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear)

Length of Path of Approach

LaTeX Go Path of Approach = sqrt(Radius of Addendum Circle of Wheel^2-Radius of Pitch Circle of Wheel^2*(cos(Pressure Angle of Gear))^2)-Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear)

Length of Arc of Contact

LaTeX Go Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear)

Length of Arc of Contact Formula

LaTeX Go

Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear)
L = P/cos(Φ_g)

What is length of path of contact?

Path of contact is the locus of the point of contact on two mating teeth from the beginning of engagement to the end of it. It is also called contact length. It is the tangent to both the base circles and passes through the pitch point.

How to Calculate Length of Arc of Contact?

Length of Arc of Contact calculator uses Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear) to calculate 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 calculate Length of Arc of Contact using this online calculator? To use this online calculator for Length of Arc of Contact, enter Path of Contact (P) & Pressure Angle of Gear (Φ_g) and hit the calculate button. Here is how the Length of Arc of Contact calculation can be explained with given input values -> 14122.05 = 0.01197618/cos(0.55850536063808).

FAQ

What is 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 and is represented as L = P/cos(Φ_g) or Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear). Path of Contact is the path traced by the contact point of a pair of tooth profiles & Pressure Angle of Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

How to calculate 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 is calculated using Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear). To calculate Length of Arc of Contact, you need Path of Contact (P) & Pressure Angle of Gear (Φ_g). With our tool, you need to enter the respective value for Path of Contact & Pressure Angle of Gear and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Length of Arc of Contact?

In this formula, Length of Arc of Contact uses Path of Contact & Pressure Angle of Gear. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)

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