Number of Teeth on Sprocket given Pitch Circle Diameter Calculator

✖Pitch of Chain is the distance between two consecutive identical links measured along the direction of the chain's length.ⓘ Pitch of Chain [P]			+10% -10%
✖Pitch Circle Diameter of Sprocket is the diameter of the circle that passes through the center of the sprocket's teeth in a chain drive system.ⓘ Pitch Circle Diameter of Sprocket [D]			+10% -10%

✖Number of Teeth on Sprocket is the total count of teeth present on a sprocket in a chain drive system, used to transmit power and motion.ⓘ Number of Teeth on Sprocket given Pitch Circle Diameter [z]

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Number of Teeth on Sprocket given Pitch Circle Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket)
z = 180*asin(P/D)
This formula uses 2 Functions, 3 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)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

Number of Teeth on Sprocket - Number of Teeth on Sprocket is the total count of teeth present on a sprocket in a chain drive system, used to transmit power and motion.
Pitch of Chain - (Measured in Meter) - Pitch of Chain is the distance between two consecutive identical links measured along the direction of the chain's length.
Pitch Circle Diameter of Sprocket - (Measured in Meter) - Pitch Circle Diameter of Sprocket is the diameter of the circle that passes through the center of the sprocket's teeth in a chain drive system.

STEP 1: Convert Input(s) to Base Unit

Pitch of Chain: 22 Millimeter --> 0.022 Meter (Check conversion here)
Pitch Circle Diameter of Sprocket: 167.3 Millimeter --> 0.1673 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = 180*asin(P/D) --> 180*asin(0.022/0.1673)

Evaluating ... ...

z = 23.7388085607741

STEP 3: Convert Result to Output's Unit

23.7388085607741 --> No Conversion Required

FINAL ANSWER

23.7388085607741 ≈ 23.73881 <-- 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 » Mechanical » Geometric Relationships for Chain » Number of Teeth on Sprocket given Pitch Circle Diameter

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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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< Geometric Relationships for Chain Calculators

Pitch of chain given Pitch Circle Diameter

LaTeX Go Pitch of Chain = Pitch Circle Diameter of Sprocket*sin(3.035/Number of Teeth on Sprocket)

Number of Teeth on Sprocket given Pitch Circle Diameter

LaTeX Go Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket)

Speed of Rotation of Driving Shaft given Velocity Ratio of Chain Drives

LaTeX Go Angular Speed of Chain Driving Shaft = Velocity Ratio of Chain Drive*Angular Speed of Chain Driven Shaft

Velocity Ratio of Chain Drives

LaTeX Go Velocity Ratio of Chain Drive = Angular Speed of Chain Driving Shaft/Angular Speed of Chain Driven Shaft

Number of Teeth on Sprocket given Pitch Circle Diameter Formula

LaTeX Go

Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket)
z = 180*asin(P/D)

What is Pitch of Sprocket?

The pitch of a sprocket is the distance between corresponding points on adjacent teeth, typically measured at the center of the teeth. It matches the pitch of the chain and is crucial for ensuring proper engagement and smooth operation in a chain drive system. The pitch determines the compatibility between the sprocket and the chain used.

How to Calculate Number of Teeth on Sprocket given Pitch Circle Diameter?

Number of Teeth on Sprocket given Pitch Circle Diameter calculator uses Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket) to calculate the Number of Teeth on Sprocket, Number of Teeth on Sprocket given Pitch Circle Diameter formula is defined as a method to determine the number of teeth on a sprocket wheel based on its pitch circle diameter, which is a critical parameter in designing and manufacturing sprockets for various mechanical systems. Number of Teeth on Sprocket is denoted by z symbol.

How to calculate Number of Teeth on Sprocket given Pitch Circle Diameter using this online calculator? To use this online calculator for Number of Teeth on Sprocket given Pitch Circle Diameter, enter Pitch of Chain (P) & Pitch Circle Diameter of Sprocket (D) and hit the calculate button. Here is how the Number of Teeth on Sprocket given Pitch Circle Diameter calculation can be explained with given input values -> 24.66348 = 180*asin(0.022/0.1673).

FAQ

What is Number of Teeth on Sprocket given Pitch Circle Diameter?

Number of Teeth on Sprocket given Pitch Circle Diameter formula is defined as a method to determine the number of teeth on a sprocket wheel based on its pitch circle diameter, which is a critical parameter in designing and manufacturing sprockets for various mechanical systems and is represented as z = 180*asin(P/D) or Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket). Pitch of Chain is the distance between two consecutive identical links measured along the direction of the chain's length & Pitch Circle Diameter of Sprocket is the diameter of the circle that passes through the center of the sprocket's teeth in a chain drive system.

How to calculate Number of Teeth on Sprocket given Pitch Circle Diameter?

Number of Teeth on Sprocket given Pitch Circle Diameter formula is defined as a method to determine the number of teeth on a sprocket wheel based on its pitch circle diameter, which is a critical parameter in designing and manufacturing sprockets for various mechanical systems is calculated using Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket). To calculate Number of Teeth on Sprocket given Pitch Circle Diameter, you need Pitch of Chain (P) & Pitch Circle Diameter of Sprocket (D). With our tool, you need to enter the respective value for Pitch of Chain & Pitch Circle Diameter 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 of Chain & Pitch Circle Diameter of Sprocket. We can use 1 other way(s) to calculate the same, which is/are as follows -

Number of Teeth on Sprocket = Average Chain Velocity*60/(Pitch of Chain*Speed of Chain Drive Shaft in RPM)

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