Length of Path of Contact Calculator

✖Radius of Addendum Circle of Wheel is radial distance between the pitch circle and the root circle.ⓘ Radius of Addendum Circle of Wheel [R_a]			+10% -10%
✖Radius of Pitch Circle of Wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.ⓘ Radius of Pitch Circle of Wheel [R_w]			+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%
✖Radius of Addendum Circle of Pinion is radial distance between the pitch circle and the root circle.ⓘ Radius of Addendum Circle of Pinion [r_a]			+10% -10%
✖Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.ⓘ Radius of Pitch Circle of Pinion [r]			+10% -10%

✖Path of Contact is the path traced by the contact point of a pair of tooth profiles.ⓘ Length of Path of Contact [P]

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Length of Path of Contact Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
P = sqrt(R_a^2-R_w^2*(cos(Φ_g))^2)+sqrt(r_a^2-r^2*(cos(Φ_g))^2)-(R_w+r)*sin(Φ_g)
This formula uses 3 Functions, 6 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Path of Contact - (Measured in Meter) - Path of Contact is the path traced by the contact point of a pair of tooth profiles.
Radius of Addendum Circle of Wheel - (Measured in Meter) - Radius of Addendum Circle of Wheel is radial distance between the pitch circle and the root circle.
Radius of Pitch Circle of Wheel - (Measured in Meter) - Radius of Pitch Circle of Wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.
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.
Radius of Addendum Circle of Pinion - (Measured in Meter) - Radius of Addendum Circle of Pinion is radial distance between the pitch circle and the root circle.
Radius of Pitch Circle of Pinion - (Measured in Meter) - Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.

STEP 1: Convert Input(s) to Base Unit

Radius of Addendum Circle of Wheel: 18.63 Millimeter --> 0.01863 Meter (Check conversion here)
Radius of Pitch Circle of Wheel: 12.4 Millimeter --> 0.0124 Meter (Check conversion here)
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)
Radius of Addendum Circle of Pinion: 15.954 Millimeter --> 0.015954 Meter (Check conversion here)
Radius of Pitch Circle of Pinion: 10.2 Millimeter --> 0.0102 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = sqrt(R_a^2-R_w^2*(cos(Φ_g))^2)+sqrt(r_a^2-r^2*(cos(Φ_g))^2)-(R_w+r)*sin(Φ_g) --> sqrt(0.01863^2-0.0124^2*(cos(0.55850536063808))^2)+sqrt(0.015954^2-0.0102^2*(cos(0.55850536063808))^2)-(0.0124+0.0102)*sin(0.55850536063808)

Evaluating ... ...

P = 0.0168076646441216

STEP 3: Convert Result to Output's Unit

0.0168076646441216 Meter -->16.8076646441216 Millimeter (Check conversion here)

FINAL ANSWER

16.8076646441216 ≈ 16.80766 Millimeter <-- Path of Contact

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Toothed Gearing » Mechanical » Length » Length of Path of Contact

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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 Path of Contact Formula

LaTeX Go

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. Thus CD is the path of contact. It is also called contact length. It is the tangent to both the base circles and passes through the pitch point.

What are the advantages of smaller pressure angles?

Earlier gears with pressure angle 14.5 were commonly used because the cosine is larger for a smaller angle, providing more power transmission and less pressure on the bearing; however, teeth with smaller pressure angles are weaker. To run gears together properly their pressure angles must be matched.

How to Calculate Length of Path of Contact?

Length of Path of Contact calculator uses 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) to calculate the Path of Contact, Length of Path of Contact formula is defined as the distance traveled by the point of contact between two interacting gears or wheels during a specific period, providing insight into the mechanical interaction and motion of the system. Path of Contact is denoted by P symbol.

How to calculate Length of Path of Contact using this online calculator? To use this online calculator for Length of Path of Contact, enter Radius of Addendum Circle of Wheel (R_a), Radius of Pitch Circle of Wheel (R_w), Pressure Angle of Gear (Φ_g), Radius of Addendum Circle of Pinion (r_a) & Radius of Pitch Circle of Pinion (r) and hit the calculate button. Here is how the Length of Path of Contact calculation can be explained with given input values -> 16807.66 = sqrt(0.01863^2-0.0124^2*(cos(0.55850536063808))^2)+sqrt(0.015954^2-0.0102^2*(cos(0.55850536063808))^2)-(0.0124+0.0102)*sin(0.55850536063808).

FAQ

What is Length of Path of Contact?

Length of Path of Contact formula is defined as the distance traveled by the point of contact between two interacting gears or wheels during a specific period, providing insight into the mechanical interaction and motion of the system and is represented as P = sqrt(R_a^2-R_w^2*(cos(Φ_g))^2)+sqrt(r_a^2-r^2*(cos(Φ_g))^2)-(R_w+r)*sin(Φ_g) or 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). Radius of Addendum Circle of Wheel is radial distance between the pitch circle and the root circle, Radius of Pitch Circle of Wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space, Pressure Angle of Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent, Radius of Addendum Circle of Pinion is radial distance between the pitch circle and the root circle & Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.

How to calculate Length of Path of Contact?

Length of Path of Contact formula is defined as the distance traveled by the point of contact between two interacting gears or wheels during a specific period, providing insight into the mechanical interaction and motion of the system is calculated using 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). To calculate Length of Path of Contact, you need Radius of Addendum Circle of Wheel (R_a), Radius of Pitch Circle of Wheel (R_w), Pressure Angle of Gear (Φ_g), Radius of Addendum Circle of Pinion (r_a) & Radius of Pitch Circle of Pinion (r). With our tool, you need to enter the respective value for Radius of Addendum Circle of Wheel, Radius of Pitch Circle of Wheel, Pressure Angle of Gear, Radius of Addendum Circle of Pinion & Radius of Pitch Circle of Pinion 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 Path of Contact?

In this formula, Path of Contact uses Radius of Addendum Circle of Wheel, Radius of Pitch Circle of Wheel, Pressure Angle of Gear, Radius of Addendum Circle of Pinion & Radius of Pitch Circle of Pinion. We can use 1 other way(s) to calculate the same, which is/are as follows -

Path of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear)

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