Minimum Linear Velocity of Sprocket Calculator

✖Pitch Circle Diameter of Sprocket is the diameter of the circle that passes through the centers of the sprocket's teeth.ⓘ Pitch Circle Diameter of Sprocket [D]			+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%

✖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]

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Minimum Linear Velocity of Sprocket Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
v_min = pi*D*N*cos(α/2)/60
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

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.
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.
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

Pitch Circle Diameter of Sprocket: 164.2479 Millimeter --> 0.1642479 Meter (Check conversion here)
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

v_min = pi*D*N*cos(α/2)/60 --> pi*0.1642479*500*cos(1.67551608191424/2)/60

Evaluating ... ...

v_min = 2.87726158508135

STEP 3: Convert Result to Output's Unit

2.87726158508135 Meter per Second --> No Conversion Required

FINAL ANSWER

2.87726158508135 ≈ 2.877262 Meter per Second <-- Minimum Linear Velocity of Sprocket

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Chain Drives » Mechanical » Polygonal Effect » Minimum Linear Velocity of Sprocket

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 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

Minimum Linear Velocity of Sprocket Formula

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
v_min = pi*D*N*cos(α/2)/60

What is Minimum Linear velocity?

Minimum linear velocity refers to the lowest speed at which an object must travel along a path to maintain a specific function or avoid certain issues. In contexts like chain drives, it might be the speed required to ensure smooth engagement between the chain and sprockets, preventing slippage or loss of power transmission.

How to Calculate Minimum Linear Velocity of Sprocket?

Minimum Linear Velocity of Sprocket calculator uses 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 to calculate the Minimum Linear Velocity of Sprocket, Minimum Linear Velocity of Sprocket formula is defined as the lowest velocity at which a sprocket can rotate without slipping, considering the diameter of the sprocket, the rotational speed, and the angle of engagement, providing a critical value for designing and optimizing mechanical systems. Minimum Linear Velocity of Sprocket is denoted by v_min symbol.

How to calculate Minimum Linear Velocity of Sprocket using this online calculator? To use this online calculator for Minimum Linear Velocity of Sprocket, enter Pitch Circle Diameter of Sprocket (D), Speed of Chain Drive Shaft in RPM (N) & Pitch Angle of Sprocket (α) and hit the calculate button. Here is how the Minimum Linear Velocity of Sprocket calculation can be explained with given input values -> 2.877262 = pi*0.1642479*500*cos(1.67551608191424/2)/60.

FAQ

What is Minimum Linear Velocity of Sprocket?

Minimum Linear Velocity of Sprocket formula is defined as the lowest velocity at which a sprocket can rotate without slipping, considering the diameter of the sprocket, the rotational speed, and the angle of engagement, providing a critical value for designing and optimizing mechanical systems and is represented as v_min = pi*D*N*cos(α/2)/60 or 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 is the diameter of the circle that passes through the centers of the sprocket's teeth, 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 Minimum Linear Velocity of Sprocket?

Minimum Linear Velocity of Sprocket formula is defined as the lowest velocity at which a sprocket can rotate without slipping, considering the diameter of the sprocket, the rotational speed, and the angle of engagement, providing a critical value for designing and optimizing mechanical systems is calculated using 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. To calculate Minimum Linear Velocity of Sprocket, you need Pitch Circle Diameter of Sprocket (D), Speed of Chain Drive Shaft in RPM (N) & Pitch Angle of Sprocket (α). With our tool, you need to enter the respective value for Pitch Circle Diameter 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.

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