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(RA^2-Rwheel^2*(cos(Φgear))^2)-Rwheel*sin(Φgear)
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) - The 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: 22 Millimeter --> 0.022 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(RA^2-Rwheel^2*(cos(Φgear))^2)-Rwheel*sin(Φgear) --> sqrt(0.022^2-0.0124^2*(cos(0.55850536063808))^2)-0.0124*sin(0.55850536063808)
Evaluating ... ...
P1 = 0.0127530282978548
STEP 3: Convert Result to Output's Unit
0.0127530282978548 Meter -->12.7530282978548 Millimeter (Check conversion here)
FINAL ANSWER
12.7530282978548 12.75303 Millimeter <-- Path of Approach
(Calculation completed in 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Team Softusvista
Softusvista Office (Pune), India
Team Softusvista has verified this Calculator and 1100+ more calculators!

9 Length Calculators

Length of Path of Contact
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
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
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)
Maximum Length of Arc of Contact
Go Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)
Maximum Length of Arc of Approach
Go Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)
Maximum Length of Path of Contact
Go Path of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear)
Maximum Length of Path of Approach
Go Path of Approach = Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear)
Maximum Length of Path of Recess
Go Path of Recess = Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear)
Length of Arc of Contact
Go Length of arc of contact = Path of Contact/cos(Pressure Angle of Gear)

Length of Path of Approach Formula

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(RA^2-Rwheel^2*(cos(Φgear))^2)-Rwheel*sin(Φgear)

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, The length of path of approach is the portion of the path of contact from the beginning of contact to the pitch point. 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 (RA), Radius of Pitch Circle of Wheel (Rwheel) & Pressure Angle of Gear gear) 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(0.022^2-0.0124^2*(cos(0.55850536063808))^2)-0.0124*sin(0.55850536063808).

FAQ

What is Length of Path of Approach?
The length of path of approach is the portion of the path of contact from the beginning of contact to the pitch point and is represented as P1 = sqrt(RA^2-Rwheel^2*(cos(Φgear))^2)-Rwheel*sin(Φgear) 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 & The 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?
The length of path of approach is the portion of the path of contact from the beginning of contact to the pitch point 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 (RA), Radius of Pitch Circle of Wheel (Rwheel) & Pressure Angle of Gear gear). 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)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!