Pitch Circular Diameter of Gear given Radius of Curvature Calculator

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Design of Gears

Basics Of Machine Design

Design of Coupling

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Design of Helical Gears

Design of Bevel Gears

Design of Spur Gears

Design of Worm Gears

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Helix Geometry

Core Design Parameters

✖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 of Helical Gear [r']

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✖Pitch Circular Diameter of Helical Virtual Gear is the diameter of the circle which passes through the center of all the virtual gears.ⓘ Pitch Circular Diameter of Gear given Radius of Curvature [d']

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Formula

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Pitch Circular Diameter of Gear given Radius of Curvature

Formula

`"d'" = 2*"r'"`

Example

`"144mm"=2*"72mm"`

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Pitch Circular Diameter of Gear given Radius of Curvature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pitch Circular Diameter of Helical Virtual Gear = 2*Radius of Curvature of Helical Gear
d' = 2*r'
This formula uses 2 Variables

Variables Used

Pitch Circular Diameter of Helical Virtual Gear - (Measured in Meter) - Pitch Circular Diameter of Helical Virtual Gear is the diameter of the circle which passes through the center of all the virtual gears.
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.

STEP 1: Convert Input(s) to Base Unit

Radius of Curvature of Helical Gear: 72 Millimeter --> 0.072 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d' = 2*r' --> 2*0.072

Evaluating ... ...

d' = 0.144

STEP 3: Convert Result to Output's Unit

0.144 Meter -->144 Millimeter (Check conversion here)

FINAL ANSWER

144 Millimeter <-- Pitch Circular Diameter of Helical Virtual Gear

(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad

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< 25 Helix Geometry Calculators

Helix Angle of Helical Gear given Center to Center Distance between Two Gears

Go Helix Angle of Helical Gear = acos(Normal Module of Helical Gear*(Number of Teeth on 1st Helical Gear+Number of Teeth on 2nd Helical Gear)/(2*Center to Center Distance of Helical Gears))

Helix Angle of Helical Gear given Virtual Number of Teeth

Go Helix Angle of Helical Gear = acos((Diameter of Pitch Circle of Helical Gear/(Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear))^(1/2))

Transverse Pressure Angle of Helical Gear given Helix Angle

Go Transverse Pressure Angle of Helical Gear = atan(tan(Normal Pressure Angle of Helical Gear)/cos(Helix Angle of Helical Gear))

Normal Pressure Angle of Helical Gear given Helix Angle

Go Normal Pressure Angle of Helical Gear = atan(tan(Transverse Pressure Angle of Helical Gear)*cos(Helix Angle of Helical Gear))

Helix Angle of Helical Gear given Pressure Angle

Go Helix Angle of Helical Gear = acos(tan(Normal Pressure Angle of Helical Gear)/tan(Transverse Pressure Angle of Helical Gear))

Pitch Circular Diameter of Gear given Virtual Number of Teeth

Go Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2)

Helix Angle of Helical Gear given Pitch Circle Diameter

Go Helix Angle of Helical Gear = acos(Number of Teeth on Helical Gear*Normal Module of Helical Gear/Diameter of Pitch Circle of Helical Gear)

Helix Angle of Helical Gear given Radius of Curvature at Point

Go Helix Angle of Helical Gear = sqrt(acos(Diameter of Pitch Circle of Helical Gear/(2*Radius of Curvature of Helical Gear)))

Radius of Curvature of Virtual Gear given Virtual Number of Teeth

Go Virtual Pitch Circle Radius for Helical Gear = Virtual Number of Teeth on Helical Gear*Normal Circular Pitch of Helical Gear/(2*pi)

Normal Circular Pitch of Helical Gear given Virtual Number of Teeth

Go Normal Circular Pitch of Helical Gear = 2*pi*Virtual Pitch Circle Radius for Helical Gear/Virtual Number of Teeth on Helical Gear

Semi Major Axis of Elliptical Profile given Radius of Curvature at Point

Go Semi Major Axis of Helical Gear Teeth = sqrt(Radius of Curvature of Helical Gear*Semi Minor Axis of Helical Gear Teeth)

Radius of Curvature at Point on Virtual Gear

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

Pitch Circular Diameter of Gear given Virtual Gear

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

Helix Angle of Helical Gear given Normal Module

Go Helix Angle of Helical Gear = acos(Normal Module of Helical Gear/Transverse Module of Helical Gear)

Helix Angle of Helical Gear given Normal Circular Pitch

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

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

Normal Circular Pitch of Helical Gear

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

Semi Minor Axis of Elliptical Profile given Radius of Curvature at Point

Go Semi Minor Axis of Helical Gear Teeth = Semi Major Axis of Helical Gear Teeth^2/Radius of Curvature of Helical Gear

Helix Angle of Helical Gear given Axial Pitch

Go Helix Angle of Helical Gear = atan(Pitch of Helical Gear/Axial Pitch of Helical Gear)

Radius of Curvature at Point on Helical Gear

Go Radius of Curvature of Helical Gear = Semi Major Axis of Helical Gear Teeth^2/Semi Minor Axis of Helical Gear Teeth

Axial Pitch of Helical Gear given Helix Angle

Go Axial Pitch of Helical Gear = Pitch of Helical Gear/tan(Helix Angle of Helical Gear)

Pitch of Helical Gear given Axial Pitch

Go Pitch of Helical Gear = Axial Pitch of Helical Gear*tan(Helix Angle of Helical Gear)

Radius of Curvature of Virtual Gear given Pitch Circular Diameter

Go Radius of Curvature of Helical Gear = Pitch Circular Diameter of Helical Virtual Gear/2

Pitch Circular Diameter of Gear given Radius of Curvature

Go Pitch Circular Diameter of Helical Virtual Gear = 2*Radius of Curvature of Helical Gear

Transverse Diametrical Pitch of Helical Gear given Transverse Module

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

Pitch Circular Diameter of Gear given Radius of Curvature Formula

Pitch Circular Diameter of Helical Virtual Gear = 2*Radius of Curvature of Helical Gear
d' = 2*r'

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 Pitch Circular Diameter of Gear given Radius of Curvature?

Pitch Circular Diameter of Gear given Radius of Curvature calculator uses Pitch Circular Diameter of Helical Virtual Gear = 2*Radius of Curvature of Helical Gear to calculate the Pitch Circular Diameter of Helical Virtual Gear, Pitch Circular Diameter of Gear given Radius of Curvature formula is the diameter of the imaginary circle on the gear about which it may be supposed to roll without slipping with the pitch circle of another gear. The point of contact of the two pitch circles becomes the pitch point. Pitch Circular Diameter of Helical Virtual Gear is denoted by d' symbol.

How to calculate Pitch Circular Diameter of Gear given Radius of Curvature using this online calculator? To use this online calculator for Pitch Circular Diameter of Gear given Radius of Curvature, enter Radius of Curvature of Helical Gear (r') and hit the calculate button. Here is how the Pitch Circular Diameter of Gear given Radius of Curvature calculation can be explained with given input values -> 144000 = 2*0.072.

FAQ

What is Pitch Circular Diameter of Gear given Radius of Curvature?

Pitch Circular Diameter of Gear given Radius of Curvature formula is the diameter of the imaginary circle on the gear about which it may be supposed to roll without slipping with the pitch circle of another gear. The point of contact of the two pitch circles becomes the pitch point and is represented as d' = 2*r' or Pitch Circular Diameter of Helical Virtual Gear = 2*Radius of Curvature of Helical Gear. 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.

How to calculate Pitch Circular Diameter of Gear given Radius of Curvature?

Pitch Circular Diameter of Gear given Radius of Curvature formula is the diameter of the imaginary circle on the gear about which it may be supposed to roll without slipping with the pitch circle of another gear. The point of contact of the two pitch circles becomes the pitch point is calculated using Pitch Circular Diameter of Helical Virtual Gear = 2*Radius of Curvature of Helical Gear. To calculate Pitch Circular Diameter of Gear given Radius of Curvature, you need Radius of Curvature of Helical Gear (r'). With our tool, you need to enter the respective value for Radius of Curvature of Helical Gear and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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