Number of Teeth on Sprocket given Pitch Angle of Sprocket Calculator

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Design of Chain Drives

Design of Brakes

Design of Flywheel

Design of Friction Clutches

Design of Shafts

Design of Splines

Design of Springs

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Proportions of the Sprocket Wheel

Geometric Relationships for Chain

Polygonal Effect

Power Rating of Roller Chains

✖The Pitch Angle of Sprocket is generally the angle subtended by a small line called pitch. It is generally used in sprockets.ⓘ Pitch Angle of Sprocket [α]

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✖Number of teeth on sprocket is defined as the number of teeth (which mesh with another compatible toothed part to the chain or convert torque and speed).ⓘ Number of Teeth on Sprocket given Pitch Angle of Sprocket [z]

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Formula

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Number of Teeth on Sprocket given Pitch Angle of Sprocket

Formula

`"z" = 360/("α"*(180/pi))`

Example

`"20"=360/("18°"*(180/pi))`

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Number of Teeth on Sprocket given Pitch Angle of Sprocket Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of teeth on sprocket = 360/(Pitch Angle of Sprocket*(180/pi))
z = 360/(α*(180/pi))
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Number of teeth on sprocket - Number of teeth on sprocket is defined as the number of teeth (which mesh with another compatible toothed part to the chain or convert torque and speed).
Pitch Angle of Sprocket - (Measured in Radian) - The Pitch Angle of Sprocket is generally the angle subtended by a small line called pitch. It is generally used in sprockets.

STEP 1: Convert Input(s) to Base Unit

Pitch Angle of Sprocket: 18 Degree --> 0.31415926535892 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = 360/(α*(180/pi)) --> 360/(0.31415926535892*(180/pi))

Evaluating ... ...

z = 20.0000000000038

STEP 3: Convert Result to Output's Unit

20.0000000000038 --> No Conversion Required

FINAL ANSWER

20.0000000000038 ≈ 20 <-- Number of teeth on sprocket

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Chain Drives » Proportions of the Sprocket Wheel » Number of Teeth on Sprocket given Pitch Angle of Sprocket

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 22 Proportions of the Sprocket Wheel Calculators

Pitch Circle Diameter given Top Diameter of Sprocket Wheel

Go Sproket Diameter of Pitch Circle = Top Diameter of Sprocket Wheel-Pitch of Chain*(1-(1.6/Number of teeth on sprocket))+2*Roller Radius of Chain

Top Diameter of Sprocket Wheel

Go Top Diameter of Sprocket Wheel = Sproket Diameter of Pitch Circle+Pitch of Chain*(1-(1.6/Number of teeth on sprocket))-2*Roller Radius of Chain

Number of Teeth given Maximum Tooth Height above Pitch Polygon

Go Number of teeth on sprocket = 0.8*Pitch of Chain/(Maximum Sprocket Tooth Height-0.625*Pitch of Chain+Roller Radius of Chain)

Maximum Tooth Height above Pitch Polygon

Go Maximum Sprocket Tooth Height = 0.625*Pitch of Chain-Roller Radius of Chain+(0.8*Pitch of Chain/Number of teeth on sprocket)

Chain Pitch given Maximum Tooth Height above Pitch Polygon

Go Pitch of Chain = Maximum Sprocket Tooth Height/(0.625-Roller Radius of Chain+0.8/Number of teeth on sprocket)

Pitch Circle Diameter given Average Velocity of Chain

Go Sproket Diameter of Pitch Circle = Average Chain Velocity*60/(pi*Speed of chain drive shaft in rpm)

Pitch Circle Diameter given Pitch

Go Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/Number of teeth on sprocket)

Roller Seating Radius given Roller Radius

Go Roller Seating Radius = (1.010*Roller Radius of Chain)+(0.00069*((2*Roller Radius of Chain)^(1/3)))

Tooth Flank Radius

Go Sprocket Tooth Flank Radius = 0.016*Roller Radius of Chain*((Number of teeth on sprocket)^2+180)

Roller Seating Radius given Root Diameter of Sprocket Wheel

Go Roller Seating Radius = (Sproket Diameter of Pitch Circle-Root Diameter of Sprocket Wheel)/2

Pitch Circle Diameter given Root Diameter of Sprocket Wheel

Go Sproket Diameter of Pitch Circle = Root Diameter of Sprocket Wheel+2*Roller Seating Radius

Number of Teeth given Minimum Tooth Flank Radius

Go Number of teeth on sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2

Root Diameter of Sprocket Wheel

Go Root Diameter of Sprocket Wheel = Sproket Diameter of Pitch Circle-2*Roller Seating Radius

Minimum Tooth Flank Radius

Go Minimum Tooth Flank Radius = 0.24*Roller Radius of Chain*(Number of teeth on sprocket+2)

Number of Teeth given Maximum Roller Seating Angle

Go Number of teeth on sprocket = 90/(120-(Maximum Roller Seating Angle*180/pi))

Number of Teeth given Minimum Roller Seating Angle

Go Number of teeth on sprocket = 90/(140-(Minimum Roller Seating Angle*180/pi))

Maximum Roller Seating Angle

Go Maximum Roller Seating Angle = (120-(90/Number of teeth on sprocket))*pi/180

Minimum Roller Seating Angle

Go Minimum Roller Seating Angle = (140-(90/Number of teeth on sprocket))*pi/180

Number of Teeth on Sprocket given Pitch Angle of Sprocket

Go Number of teeth on sprocket = 360/(Pitch Angle of Sprocket*(180/pi))

Minimum Tooth Height above Pitch Polygon

Go Minimum Tooth Height = 0.5*Pitch of Chain-Roller Radius of Chain

Pitch Angle of Sprocket

Go Pitch Angle of Sprocket = (360/Number of teeth on sprocket)/57.24

Minimum Roller Seating Radius

Go Minimum Roller Seating Radius = 2*0.505*Roller Radius of Chain

Number of Teeth on Sprocket given Pitch Angle of Sprocket Formula

Number of teeth on sprocket = 360/(Pitch Angle of Sprocket*(180/pi))
z = 360/(α*(180/pi))

Define Sprocket?

A sprocket, sprocket-wheel or chainwheel is a profiled wheel with teeth, or cogs, that mesh with a chain, track or other perforated or indented material. The name 'sprocket' applies generally to any wheel upon which radial projections engage a chain passing over it.

How to Calculate Number of Teeth on Sprocket given Pitch Angle of Sprocket?

Number of Teeth on Sprocket given Pitch Angle of Sprocket calculator uses Number of teeth on sprocket = 360/(Pitch Angle of Sprocket*(180/pi)) to calculate the Number of teeth on sprocket, The Number of Teeth on Sprocket given Pitch Angle of Sprocket formula is defined as the number of indentations present on the sprocket wheel. Number of teeth on sprocket is denoted by z symbol.

How to calculate Number of Teeth on Sprocket given Pitch Angle of Sprocket using this online calculator? To use this online calculator for Number of Teeth on Sprocket given Pitch Angle of Sprocket, enter Pitch Angle of Sprocket (α) and hit the calculate button. Here is how the Number of Teeth on Sprocket given Pitch Angle of Sprocket calculation can be explained with given input values -> 20 = 360/(0.31415926535892*(180/pi)).

FAQ

What is Number of Teeth on Sprocket given Pitch Angle of Sprocket?

The Number of Teeth on Sprocket given Pitch Angle of Sprocket formula is defined as the number of indentations present on the sprocket wheel and is represented as z = 360/(α*(180/pi)) or Number of teeth on sprocket = 360/(Pitch Angle of Sprocket*(180/pi)). The Pitch Angle of Sprocket is generally the angle subtended by a small line called pitch. It is generally used in sprockets.

How to calculate Number of Teeth on Sprocket given Pitch Angle of Sprocket?

The Number of Teeth on Sprocket given Pitch Angle of Sprocket formula is defined as the number of indentations present on the sprocket wheel is calculated using Number of teeth on sprocket = 360/(Pitch Angle of Sprocket*(180/pi)). To calculate Number of Teeth on Sprocket given Pitch Angle of Sprocket, you need Pitch Angle of Sprocket (α). With our tool, you need to enter the respective value for Pitch Angle of Sprocket 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 Number of teeth on sprocket?

In this formula, Number of teeth on sprocket uses Pitch Angle of Sprocket. We can use 4 other way(s) to calculate the same, which is/are as follows -

Number of teeth on sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2
Number of teeth on sprocket = 90/(120-(Maximum Roller Seating Angle*180/pi))
Number of teeth on sprocket = 90/(140-(Minimum Roller Seating Angle*180/pi))
Number of teeth on sprocket = 0.8*Pitch of Chain/(Maximum Sprocket Tooth Height-0.625*Pitch of Chain+Roller Radius of Chain)

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