Pitch Circle Diameter given Top Diameter of Sprocket Wheel Calculator

✖Top Diameter of Sprocket Wheel is the maximum diameter of the sprocket wheel, which is the distance across the wheel passing through its center.ⓘ Top Diameter of Sprocket Wheel [d_a]			+10% -10%
✖Pitch of Chain is the distance between the centers of two consecutive teeth of a sprocket wheel, used to determine the size of the chain.ⓘ Pitch of Chain [P]			+10% -10%
✖Number of teeth on sprocket is the total count of teeth present on the circumference of the sprocket wheel, which affects the gear ratio and overall mechanism.ⓘ Number of Teeth on Sprocket [z]			+10% -10%
✖Roller Radius of Chain Sprocket Wheel is the radius of the roller of the chain sprocket wheel, which is a critical component in a bicycle's gear system.ⓘ Roller Radius of Chain [R]			+10% -10%

✖Sproket Diameter of Pitch Circle is the diameter of the circle that passes through the pitch point of the sprocket wheel's teeth.ⓘ Pitch Circle Diameter given Top Diameter of Sprocket Wheel [D_s]

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Formula

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Pitch Circle Diameter given Top Diameter of Sprocket Wheel

Formula

D s = d a - P \cdot (1 - (\frac{1.6}{z})) + 2 \cdot R

Example

131 mm = 139.1224 mm - 22 mm \cdot (1 - (\frac{1.6}{18})) + 2 \cdot 5.961 mm

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Pitch Circle Diameter given Top Diameter of Sprocket Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
D_s = d_a-P*(1-(1.6/z))+2*R
This formula uses 5 Variables

Variables Used

Sproket Diameter of Pitch Circle - (Measured in Meter) - Sproket Diameter of Pitch Circle is the diameter of the circle that passes through the pitch point of the sprocket wheel's teeth.
Top Diameter of Sprocket Wheel - (Measured in Meter) - Top Diameter of Sprocket Wheel is the maximum diameter of the sprocket wheel, which is the distance across the wheel passing through its center.
Pitch of Chain - (Measured in Meter) - Pitch of Chain is the distance between the centers of two consecutive teeth of a sprocket wheel, used to determine the size of the chain.
Number of Teeth on Sprocket - Number of teeth on sprocket is the total count of teeth present on the circumference of the sprocket wheel, which affects the gear ratio and overall mechanism.
Roller Radius of Chain - (Measured in Meter) - Roller Radius of Chain Sprocket Wheel is the radius of the roller of the chain sprocket wheel, which is a critical component in a bicycle's gear system.

STEP 1: Convert Input(s) to Base Unit

Top Diameter of Sprocket Wheel: 139.1224 Millimeter --> 0.1391224 Meter (Check conversion here)
Pitch of Chain: 22 Millimeter --> 0.022 Meter (Check conversion here)
Number of Teeth on Sprocket: 18 --> No Conversion Required
Roller Radius of Chain: 5.961 Millimeter --> 0.005961 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_s = d_a-P*(1-(1.6/z))+2*R --> 0.1391224-0.022*(1-(1.6/18))+2*0.005961

Evaluating ... ...

D_s = 0.130999955555556

STEP 3: Convert Result to Output's Unit

0.130999955555556 Meter -->130.999955555556 Millimeter (Check conversion here)

FINAL ANSWER

130.999955555556 ≈ 131 Millimeter <-- Sproket Diameter of Pitch Circle

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Chain Drives » Mechanical » Proportions of the Sprocket Wheel » Pitch Circle Diameter given Top Diameter of Sprocket Wheel

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Osmania University (OU), Hyderabad

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< Proportions of the Sprocket Wheel Calculators

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

Pitch Circle Diameter given Pitch

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

Number of Teeth on Sprocket given Pitch Angle of Sprocket

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

Pitch Angle of Sprocket

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

Pitch Circle Diameter given Top Diameter of Sprocket Wheel Formula

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
D_s = d_a-P*(1-(1.6/z))+2*R

What is a Roller Chain?

Roller chain or bush roller chain is the type of chain drive most commonly used for transmission of mechanical power on many kinds of domestic, industrial and agricultural machinery, including conveyors, wire- and tube-drawing machines, printing presses, cars, motorcycles, and bicycles.Roller chain or bush roller chain is the type of chain drive most commonly used for transmission of mechanical power on many kinds of domestic, industrial and agricultural machinery, including conveyors, wire- and tube-drawing machines, printing presses, cars, motorcycles, and bicycles.

How to Calculate Pitch Circle Diameter given Top Diameter of Sprocket Wheel?

Pitch Circle Diameter given Top Diameter of Sprocket Wheel calculator uses 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 to calculate the Sproket Diameter of Pitch Circle, Pitch Circle Diameter given Top Diameter of Sprocket Wheel formula is defined as a measure of the diameter of the circle passing through the centers of the chain wheel teeth, which is essential in designing and manufacturing sprockets and chain drives, ensuring proper meshing and smooth operation of the machinery. Sproket Diameter of Pitch Circle is denoted by D_s symbol.

How to calculate Pitch Circle Diameter given Top Diameter of Sprocket Wheel using this online calculator? To use this online calculator for Pitch Circle Diameter given Top Diameter of Sprocket Wheel, enter Top Diameter of Sprocket Wheel (d_a), Pitch of Chain (P), Number of Teeth on Sprocket (z) & Roller Radius of Chain (R) and hit the calculate button. Here is how the Pitch Circle Diameter given Top Diameter of Sprocket Wheel calculation can be explained with given input values -> 131078 = 0.1391224-0.022*(1-(1.6/18))+2*0.005961.

FAQ

What is Pitch Circle Diameter given Top Diameter of Sprocket Wheel?

Pitch Circle Diameter given Top Diameter of Sprocket Wheel formula is defined as a measure of the diameter of the circle passing through the centers of the chain wheel teeth, which is essential in designing and manufacturing sprockets and chain drives, ensuring proper meshing and smooth operation of the machinery and is represented as D_s = d_a-P*(1-(1.6/z))+2*R or 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 is the maximum diameter of the sprocket wheel, which is the distance across the wheel passing through its center, Pitch of Chain is the distance between the centers of two consecutive teeth of a sprocket wheel, used to determine the size of the chain, Number of teeth on sprocket is the total count of teeth present on the circumference of the sprocket wheel, which affects the gear ratio and overall mechanism & Roller Radius of Chain Sprocket Wheel is the radius of the roller of the chain sprocket wheel, which is a critical component in a bicycle's gear system.

How to calculate Pitch Circle Diameter given Top Diameter of Sprocket Wheel?

Pitch Circle Diameter given Top Diameter of Sprocket Wheel formula is defined as a measure of the diameter of the circle passing through the centers of the chain wheel teeth, which is essential in designing and manufacturing sprockets and chain drives, ensuring proper meshing and smooth operation of the machinery is calculated using 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. To calculate Pitch Circle Diameter given Top Diameter of Sprocket Wheel, you need Top Diameter of Sprocket Wheel (d_a), Pitch of Chain (P), Number of Teeth on Sprocket (z) & Roller Radius of Chain (R). With our tool, you need to enter the respective value for Top Diameter of Sprocket Wheel, Pitch of Chain, Number of Teeth on Sprocket & Roller Radius of Chain 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 Sproket Diameter of Pitch Circle?

In this formula, Sproket Diameter of Pitch Circle uses Top Diameter of Sprocket Wheel, Pitch of Chain, Number of Teeth on Sprocket & Roller Radius of Chain. We can use 3 other way(s) to calculate the same, which is/are as follows -

Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/Number of Teeth on Sprocket)
Sproket Diameter of Pitch Circle = Root Diameter of Sprocket Wheel+2*Roller Seating Radius
Sproket Diameter of Pitch Circle = Average Chain Velocity*60/(pi*Speed of Chain Drive Shaft in RPM)

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