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Number of Teeth on Sprocket given Pitch Circle Diameter Formula

GoNumber of Teeth on Driving and Driven Sprockets given Average Chain Velocity Formula

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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. Check FAQs

z = 180 \cdot a \sin (\frac{P}{D})

z - Number of Teeth on Sprocket?P - Pitch of Chain?D - Pitch Circle Diameter of Sprocket?

Number of Teeth on Sprocket given Pitch Circle Diameter Example

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Here is how the Number of Teeth on Sprocket given Pitch Circle Diameter equation looks like with Values.

Here is how the Number of Teeth on Sprocket given Pitch Circle Diameter equation looks like with Units.

Here is how the Number of Teeth on Sprocket given Pitch Circle Diameter equation looks like.

23.7388 = 180 \cdot a \sin (\frac{22}{167.3})

23.7388 = 180 \cdot a \sin (\frac{22mm}{167.3mm})

23.7388 = 180 \cdot a \sin (\frac{22}{167.3})

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Number of Teeth on Sprocket given Pitch Circle Diameter Solution

Follow our step by step solution on how to calculate Number of Teeth on Sprocket given Pitch Circle Diameter?

FIRST Step Consider the formula

z = 180 \cdot a \sin (\frac{P}{D})

Next Step Substitute values of Variables

∴

z = 180 \cdot a \sin (\frac{22mm}{167.3mm})

Next Step Convert Units

∴

z = 180 \cdot a \sin (\frac{0.022m}{0.1673m})

Next Step Prepare to Evaluate

∴

z = 180 \cdot a \sin (\frac{0.022}{0.1673})

Next Step Evaluate

∴

z = 23.7388085607741

LAST Step Rounding Answer

∴

z = 23.7388

Number of Teeth on Sprocket given Pitch Circle Diameter Formula Elements

Variables

Functions

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.

Symbol: z

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on Sprocket

Pitch of Chain

Pitch of Chain is the distance between two consecutive identical links measured along the direction of the chain's length.

Symbol: P

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Pitch of Chain

Pitch Circle Diameter of Sprocket

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.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Pitch Circle Diameter of Sprocket

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.

Syntax: 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.

Syntax: asin(Number)

Other Formulas to find Number of Teeth on Sprocket

Go Number of Teeth on Driving and Driven Sprockets given Average Chain Velocity

z = v \cdot \frac{60}{P \cdot N}

Other formulas in Geometric Relationships for Chain category

Go Pitch of chain given Pitch Circle Diameter

P = D \cdot \sin (\frac{3.035}{z})

Go Velocity Ratio of Chain Drives

i = \frac{N 1}{N 2}

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

N 1 = i \cdot N 2

Go Speed of Rotation of Driven Shaft given Velocity Ratio of Chain Drives

N 2 = \frac{N 1}{i}

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

Number of Teeth on Sprocket given Pitch Circle Diameter evaluator uses Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket) to evaluate 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 evaluate Number of Teeth on Sprocket given Pitch Circle Diameter using this online evaluator? To use this online evaluator 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.

FAQs on Number of Teeth on Sprocket given Pitch Circle Diameter

What is the formula to find Number of Teeth on Sprocket given Pitch Circle Diameter?

The formula of Number of Teeth on Sprocket given Pitch Circle Diameter is expressed as Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket). Here is an example- 24.66348 = 180*asin(0.022/0.1673).

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

With Pitch of Chain (P) & Pitch Circle Diameter of Sprocket (D) we can find Number of Teeth on Sprocket given Pitch Circle Diameter using the formula - Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket). This formula also uses Sine (sin), Inverse Sine (asin) function(s).

What are the other ways to Calculate Number of Teeth on Sprocket?

Here are the different ways to Calculate Number of Teeth on Sprocket-

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

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Number of Teeth on Sprocket given Pitch Circle Diameter Formula

​GoNumber of Teeth on Driving and Driven Sprockets given Average Chain Velocity Formula

Number of Teeth on Sprocket given Pitch Circle Diameter Example

Number of Teeth on Sprocket given Pitch Circle Diameter Solution

Number of Teeth on Sprocket given Pitch Circle Diameter Formula Elements

Other Formulas to find Number of Teeth on Sprocket

Other formulas in Geometric Relationships for Chain category

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

FAQs on Number of Teeth on Sprocket given Pitch Circle Diameter

Variable Name

GoNumber of Teeth on Driving and Driven Sprockets given Average Chain Velocity Formula