Radius of Curvature at Point on Helical Gear Calculator

✖Semi Major Axis of Helical Gear Teeth is one-half of the major axis of the elliptical cross-section of the teeth of a helical gear.ⓘ Semi Major Axis of Helical Gear Teeth [a]			+10% -10%
✖Semi Minor Axis of Helical Gear Teeth is one-half of the minor axis of the elliptical cross-section of the teeth of a helical gear.ⓘ Semi Minor Axis of Helical Gear Teeth [b]			+10% -10%

✖Radius of Curvature of Helical Gear is the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point.ⓘ Radius of Curvature at Point on Helical Gear [r']

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Radius of Curvature at Point on Helical Gear Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Curvature of Helical Gear = Semi Major Axis of Helical Gear Teeth^2/Semi Minor Axis of Helical Gear Teeth
r' = a^2/b
This formula uses 3 Variables

Variables Used

Radius of Curvature of Helical Gear - (Measured in Meter) - Radius of Curvature of Helical Gear is the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point.
Semi Major Axis of Helical Gear Teeth - (Measured in Meter) - Semi Major Axis of Helical Gear Teeth is one-half of the major axis of the elliptical cross-section of the teeth of a helical gear.
Semi Minor Axis of Helical Gear Teeth - (Measured in Meter) - Semi Minor Axis of Helical Gear Teeth is one-half of the minor axis of the elliptical cross-section of the teeth of a helical gear.

STEP 1: Convert Input(s) to Base Unit

Semi Major Axis of Helical Gear Teeth: 19.5 Millimeter --> 0.0195 Meter (Check conversion here)
Semi Minor Axis of Helical Gear Teeth: 5.5 Millimeter --> 0.0055 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r' = a^2/b --> 0.0195^2/0.0055

Evaluating ... ...

r' = 0.0691363636363636

STEP 3: Convert Result to Output's Unit

0.0691363636363636 Meter -->69.1363636363636 Millimeter (Check conversion here)

FINAL ANSWER

69.1363636363636 ≈ 69.13636 Millimeter <-- Radius of Curvature of Helical Gear

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Gears » Design of Helical Gears » Mechanical » Helix Geometry » Radius of Curvature at Point on Helical Gear

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< Helix Geometry Calculators

Helix Angle of Helical Gear given Normal Circular Pitch

LaTeX Go Helix Angle of Helical Gear = acos(Normal Circular Pitch of Helical Gear/Pitch of Helical Gear)

Pitch of Helical Gear given Normal Circular Pitch

LaTeX Go Pitch of Helical Gear = Normal Circular Pitch of Helical Gear/cos(Helix Angle of Helical Gear)

Normal Circular Pitch of Helical Gear

LaTeX Go Normal Circular Pitch of Helical Gear = Pitch of Helical Gear*cos(Helix Angle of Helical Gear)

Transverse Diametrical Pitch of Helical Gear given Transverse Module

LaTeX Go Transverse Diametrical Pitch of Helical Gear = 1/Transverse Module of Helical Gear

Radius of Curvature at Point on Helical Gear Formula

LaTeX Go

Radius of Curvature of Helical Gear = Semi Major Axis of Helical Gear Teeth^2/Semi Minor Axis of Helical Gear Teeth
r' = a^2/b

Define Helical Gears

A helical gear has a cylindrical pitch surface and teeth that follow a helix on the pitch cylinder. External helical gears have teeth that project outwards, whereas internal helical gears have teeth that project inwards.

How to Calculate Radius of Curvature at Point on Helical Gear?

Radius of Curvature at Point on Helical Gear calculator uses Radius of Curvature of Helical Gear = Semi Major Axis of Helical Gear Teeth^2/Semi Minor Axis of Helical Gear Teeth to calculate the Radius of Curvature of Helical Gear, The Radius of Curvature at Point on Helical Gear formula is defined as the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point. Radius of Curvature of Helical Gear is denoted by r' symbol.

How to calculate Radius of Curvature at Point on Helical Gear using this online calculator? To use this online calculator for Radius of Curvature at Point on Helical Gear, enter Semi Major Axis of Helical Gear Teeth (a) & Semi Minor Axis of Helical Gear Teeth (b) and hit the calculate button. Here is how the Radius of Curvature at Point on Helical Gear calculation can be explained with given input values -> 69136.36 = 0.0195^2/0.0055.

FAQ

What is Radius of Curvature at Point on Helical Gear?

The Radius of Curvature at Point on Helical Gear formula is defined as the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point and is represented as r' = a^2/b or Radius of Curvature of Helical Gear = Semi Major Axis of Helical Gear Teeth^2/Semi Minor Axis of Helical Gear Teeth. Semi Major Axis of Helical Gear Teeth is one-half of the major axis of the elliptical cross-section of the teeth of a helical gear & Semi Minor Axis of Helical Gear Teeth is one-half of the minor axis of the elliptical cross-section of the teeth of a helical gear.

How to calculate Radius of Curvature at Point on Helical Gear?

The Radius of Curvature at Point on Helical Gear formula is defined as the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point is calculated using Radius of Curvature of Helical Gear = Semi Major Axis of Helical Gear Teeth^2/Semi Minor Axis of Helical Gear Teeth. To calculate Radius of Curvature at Point on Helical Gear, you need Semi Major Axis of Helical Gear Teeth (a) & Semi Minor Axis of Helical Gear Teeth (b). With our tool, you need to enter the respective value for Semi Major Axis of Helical Gear Teeth & Semi Minor Axis of Helical Gear Teeth 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 Radius of Curvature of Helical Gear?

In this formula, Radius of Curvature of Helical Gear uses Semi Major Axis of Helical Gear Teeth & Semi Minor Axis of Helical Gear Teeth. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Curvature of Helical Gear = Diameter of Pitch Circle of Helical Gear/(2*(cos(Helix Angle of Helical Gear))^2)
Radius of Curvature of Helical Gear = Pitch Circular Diameter of Helical Virtual Gear/2

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