Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket Calculator

✖Minimum Linear Velocity of Sprocket is the slowest speed at which a point on the sprocket's circumference moves. It depends on the sprocket's smallest rotational speed and radius.ⓘ Minimum Linear Velocity of Sprocket [v_min]			+10% -10%
✖Speed of Chain Drive Shaft in RPM is the number of revolutions the shaft completes in one minute. It indicates the rotational speed at which the chain drive operates.ⓘ Speed of Chain Drive Shaft in RPM [N]			+10% -10%
✖Pitch Angle of Sprocket is the angle between the line connecting the centers of two consecutive teeth and the radial line through the center of the sprocket.ⓘ Pitch Angle of Sprocket [α]			+10% -10%

✖Pitch Circle Diameter of Sprocket is the diameter of the circle that passes through the centers of the sprocket's teeth.ⓘ Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket [D]

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Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pitch Circle Diameter of Sprocket = Minimum Linear Velocity of Sprocket*60/(pi*Speed of Chain Drive Shaft in RPM*cos(Pitch Angle of Sprocket/2))
D = v_min*60/(pi*N*cos(α/2))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Pitch Circle Diameter of Sprocket - (Measured in Meter) - Pitch Circle Diameter of Sprocket is the diameter of the circle that passes through the centers of the sprocket's teeth.
Minimum Linear Velocity of Sprocket - (Measured in Meter per Second) - Minimum Linear Velocity of Sprocket is the slowest speed at which a point on the sprocket's circumference moves. It depends on the sprocket's smallest rotational speed and radius.
Speed of Chain Drive Shaft in RPM - Speed of Chain Drive Shaft in RPM is the number of revolutions the shaft completes in one minute. It indicates the rotational speed at which the chain drive operates.
Pitch Angle of Sprocket - (Measured in Radian) - Pitch Angle of Sprocket is the angle between the line connecting the centers of two consecutive teeth and the radial line through the center of the sprocket.

STEP 1: Convert Input(s) to Base Unit

Minimum Linear Velocity of Sprocket: 2.877262 Meter per Second --> 2.877262 Meter per Second No Conversion Required
Speed of Chain Drive Shaft in RPM: 500 --> No Conversion Required
Pitch Angle of Sprocket: 96 Degree --> 1.67551608191424 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = v_min*60/(pi*N*cos(α/2)) --> 2.877262*60/(pi*500*cos(1.67551608191424/2))

Evaluating ... ...

D = 0.164247923685548

STEP 3: Convert Result to Output's Unit

0.164247923685548 Meter -->164.247923685548 Millimeter (Check conversion here)

FINAL ANSWER

164.247923685548 ≈ 164.2479 Millimeter <-- Pitch Circle Diameter of Sprocket

(Calculation completed in 00.020 seconds)

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< Polygonal Effect Calculators

Minimum Linear Velocity of Sprocket

LaTeX Go Minimum Linear Velocity of Sprocket = pi*Pitch Circle Diameter of Sprocket*Speed of Chain Drive Shaft in RPM*cos(Pitch Angle of Sprocket/2)/60

Pitch Circle Diameter of Sprocket given Linear Velocity of Sprocket

LaTeX Go Pitch Circle Diameter of Sprocket = Linear Velocity of Sprocket*60/(pi*Speed of Chain Drive Shaft in RPM)

Speed of Rotation of Shaft given Linear Velocity of Sprocket

LaTeX Go Speed of Chain Drive Shaft in RPM = Linear Velocity of Sprocket*60/(pi*Pitch Circle Diameter of Sprocket)

Linear Velocity of Sprocket

LaTeX Go Linear Velocity of Sprocket = pi*Pitch Circle Diameter of Sprocket*Speed of Chain Drive Shaft in RPM/60

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket Formula

LaTeX Go

Pitch Circle Diameter of Sprocket = Minimum Linear Velocity of Sprocket*60/(pi*Speed of Chain Drive Shaft in RPM*cos(Pitch Angle of Sprocket/2))
D = v_min*60/(pi*N*cos(α/2))

What is a Sprocket?

A sprocket is a wheel with teeth that engages with a chain to transmit rotary motion and force. It is commonly used in machinery, bicycles, and vehicles to transfer power and motion between components. The sprocket's teeth mesh with the chain links to create a positive drive mechanism.

How to Calculate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket calculator uses Pitch Circle Diameter of Sprocket = Minimum Linear Velocity of Sprocket*60/(pi*Speed of Chain Drive Shaft in RPM*cos(Pitch Angle of Sprocket/2)) to calculate the Pitch Circle Diameter of Sprocket, Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket formula is defined as a measure of the diameter of the pitch circle of a sprocket, which is a critical parameter in designing and optimizing sprocket-based mechanical systems, particularly in power transmission and conveyor systems. Pitch Circle Diameter of Sprocket is denoted by D symbol.

How to calculate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket using this online calculator? To use this online calculator for Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket, enter Minimum Linear Velocity of Sprocket (v_min), Speed of Chain Drive Shaft in RPM (N) & Pitch Angle of Sprocket (α) and hit the calculate button. Here is how the Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket calculation can be explained with given input values -> 158274.5 = 2.877262*60/(pi*500*cos(1.67551608191424/2)).

FAQ

What is Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket formula is defined as a measure of the diameter of the pitch circle of a sprocket, which is a critical parameter in designing and optimizing sprocket-based mechanical systems, particularly in power transmission and conveyor systems and is represented as D = v_min*60/(pi*N*cos(α/2)) or Pitch Circle Diameter of Sprocket = Minimum Linear Velocity of Sprocket*60/(pi*Speed of Chain Drive Shaft in RPM*cos(Pitch Angle of Sprocket/2)). Minimum Linear Velocity of Sprocket is the slowest speed at which a point on the sprocket's circumference moves. It depends on the sprocket's smallest rotational speed and radius, Speed of Chain Drive Shaft in RPM is the number of revolutions the shaft completes in one minute. It indicates the rotational speed at which the chain drive operates & Pitch Angle of Sprocket is the angle between the line connecting the centers of two consecutive teeth and the radial line through the center of the sprocket.

How to calculate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket formula is defined as a measure of the diameter of the pitch circle of a sprocket, which is a critical parameter in designing and optimizing sprocket-based mechanical systems, particularly in power transmission and conveyor systems is calculated using Pitch Circle Diameter of Sprocket = Minimum Linear Velocity of Sprocket*60/(pi*Speed of Chain Drive Shaft in RPM*cos(Pitch Angle of Sprocket/2)). To calculate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket, you need Minimum Linear Velocity of Sprocket (v_min), Speed of Chain Drive Shaft in RPM (N) & Pitch Angle of Sprocket (α). With our tool, you need to enter the respective value for Minimum Linear Velocity of Sprocket, Speed of Chain Drive Shaft in RPM & 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 Pitch Circle Diameter of Sprocket?

In this formula, Pitch Circle Diameter of Sprocket uses Minimum Linear Velocity of Sprocket, Speed of Chain Drive Shaft in RPM & Pitch Angle of Sprocket. We can use 1 other way(s) to calculate the same, which is/are as follows -

Pitch Circle Diameter of Sprocket = Linear Velocity of Sprocket*60/(pi*Speed of Chain Drive Shaft in RPM)

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