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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=(r+Rw)⋅tan(α)
L - Length of Arc of Contact?r - Radius of Pitch Circle of Pinion?Rw - Radius of Pitch Circle of Wheel?α - Pressure Angle Of 2 Gears?

Maximum Length of Arc of Contact Example

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

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

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

14.122Edit=(10.2Edit+12.4Edit)⋅tan(32Edit)
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HomeIcon Home » Category Physics » Category Mechanical » Category Theory of Machine » fx Maximum Length of Arc of Contact

Maximum Length of Arc of Contact Solution

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

FIRST Step Consider the formula
L=(r+Rw)⋅tan(α)
Next Step Substitute values of Variables
∴ L=(10.2mm+12.4mm)⋅tan(32°)
Next Step Convert Units
∴ L=(0.0102m+0.0124m)⋅tan(0.5585rad)
Next Step Prepare to Evaluate
∴ L=(0.0102+0.0124)⋅tan(0.5585)
Next Step Evaluate
∴L=0.0141220473531475m
Next Step Convert to Output's Unit
∴L=14.1220473531475mm
LAST Step Rounding Answer
∴L=14.122mm

Maximum 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 ContactOpen Variable
Radius of Pitch Circle of Pinion
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.
Symbol: r
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
Formulas to find Radius of Pitch Circle of PinionOpen Variable
Radius of Pitch Circle of Wheel
Radius of Pitch Circle of Wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.
Symbol: Rw
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
Formulas to find Radius of Pitch Circle of WheelOpen Variable
Pressure Angle Of 2 Gears
Pressure Angle Of 2 Gears is defined as is the angle between the tooth face and the gear wheel tangent.
Symbol: α
Measurement: AngleUnit: °
Note: Value should be between 0 to 90.
Formulas to find Pressure Angle Of 2 GearsOpen Variable
tan
The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.
Syntax: tan(Angle)

Other Formulas to find Length of Arc of Contact

​Go Length of Arc of Contact
L=Pcos(Φg)
​Go Maximum Length of Arc of Approach
L=(Rw+r)⋅tan(Φg)

Other formulas in Length category

​Go Length of Path of Approach
P1=Ra2-Rw2⋅(cos(Φg))2-Rw⋅sin(Φg)
​Go Length of Path of Contact
P=Ra2-Rw2⋅(cos(Φg))2+ra2-r2⋅(cos(Φg))2-(Rw+r)⋅sin(Φg)
​Go Length of Path of Recess
P2=ra2-r2⋅(cos(Φg))2-r⋅sin(Φg)
​Go Maximum Length of Path of Approach
P1=r⋅sin(Φg)

How to Evaluate Maximum Length of Arc of Contact?

Maximum Length of Arc of Contact evaluator uses Length of Arc of Contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears) to evaluate the Length of Arc of Contact, Maximum Length of Arc of Contact formula is defined as the distance along the circumference of a circle that an object travels while in contact with another object, typically a wheel, and is influenced by the radius of the wheel and the angle of contact. Length of Arc of Contact is denoted by L symbol.

How to evaluate Maximum Length of Arc of Contact using this online evaluator? To use this online evaluator for Maximum Length of Arc of Contact, enter Radius of Pitch Circle of Pinion (r), Radius of Pitch Circle of Wheel (Rw) & Pressure Angle Of 2 Gears (α) and hit the calculate button.

FAQs on Maximum Length of Arc of Contact

What is the formula to find Maximum Length of Arc of Contact?
The formula of Maximum Length of Arc of Contact is expressed as Length of Arc of Contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears). Here is an example- 14122.05 = (0.0102+0.0124)*tan(0.55850536063808).
How to calculate Maximum Length of Arc of Contact?
With Radius of Pitch Circle of Pinion (r), Radius of Pitch Circle of Wheel (Rw) & Pressure Angle Of 2 Gears (α) we can find Maximum Length of Arc of Contact using the formula - Length of Arc of Contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears). This formula also uses Tangent (tan) 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=Path of Contact/cos(Pressure Angle of Gear)OpenImg
  • Length of Arc of Contact=(Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)OpenImg
Can the Maximum Length of Arc of Contact be negative?
Yes, the Maximum Length of Arc of Contact, measured in Length can be negative.
Which unit is used to measure Maximum Length of Arc of Contact?
Maximum 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 Maximum Length of Arc of Contact can be measured.
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