Length of Path of Approach 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%

✖Path of Approach is the portion of the path of contact from the beginning of contact to the pitch point.ⓘ Length of Path of Approach [P₁]

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Length of Path of Approach Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
P₁ = sqrt(R_a^2-R_w^2*(cos(Φ_g))^2)-R_w*sin(Φ_g)
This formula uses 3 Functions, 4 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 Approach - (Measured in Meter) - Path of Approach is the portion of the path of contact from the beginning of contact to the pitch point.
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.

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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P₁ = sqrt(R_a^2-R_w^2*(cos(Φ_g))^2)-R_w*sin(Φ_g) --> sqrt(0.01863^2-0.0124^2*(cos(0.55850536063808))^2)-0.0124*sin(0.55850536063808)

Evaluating ... ...

P₁ = 0.00880739265951993

STEP 3: Convert Result to Output's Unit

0.00880739265951993 Meter -->8.80739265951993 Millimeter (Check conversion here)

FINAL ANSWER

8.80739265951993 ≈ 8.807393 Millimeter <-- Path of Approach

(Calculation completed in 00.004 seconds)

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

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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 Approach Formula

LaTeX Go

What is meant by arc of approach in gears?

We have already defined that the arc of contact is the path traced by a point on the pitch circle from the beginning to the end of the engagement of a given pair of teeth.

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 Approach?

Length of Path of Approach calculator uses 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) to calculate the Path of Approach, Length of Path of Approach formula is defined as the distance a wheel travels while making contact with the road surface, taking into account the radius of the wheel and the angle of the gear, providing a crucial parameter in vehicle dynamics and suspension system design. Path of Approach is denoted by P₁ symbol.

How to calculate Length of Path of Approach using this online calculator? To use this online calculator for Length of Path of Approach, enter Radius of Addendum Circle of Wheel (R_a), Radius of Pitch Circle of Wheel (R_w) & Pressure Angle of Gear (Φ_g) and hit the calculate button. Here is how the Length of Path of Approach calculation can be explained with given input values -> 12753.03 = sqrt(0.01863^2-0.0124^2*(cos(0.55850536063808))^2)-0.0124*sin(0.55850536063808).

FAQ

What is Length of Path of Approach?

Length of Path of Approach formula is defined as the distance a wheel travels while making contact with the road surface, taking into account the radius of the wheel and the angle of the gear, providing a crucial parameter in vehicle dynamics and suspension system design and is represented as P₁ = sqrt(R_a^2-R_w^2*(cos(Φ_g))^2)-R_w*sin(Φ_g) or 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). 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.

How to calculate Length of Path of Approach?

Length of Path of Approach formula is defined as the distance a wheel travels while making contact with the road surface, taking into account the radius of the wheel and the angle of the gear, providing a crucial parameter in vehicle dynamics and suspension system design is calculated using 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). To calculate Length of Path of Approach, you need Radius of Addendum Circle of Wheel (R_a), Radius of Pitch Circle of Wheel (R_w) & Pressure Angle of Gear (Φ_g). 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 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 Approach?

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

Path of Approach = Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear)

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