Number of Links in Chain Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of links in chain = 2*(Centre Distance between Chain Pulleys/Pitch of Chain)+(Number of Teeth on Driving Sprocket+Number of Teeth on Driven Sprocket)/2+(Pitch of Chain/Centre Distance between Chain Pulleys)*((Number of Teeth on Driven Sprocket-Number of Teeth on Driving Sprocket)/2*pi)^2
Ln = 2*(C/P)+(z1+z2)/2+(P/C)*((z2-z1)/2*pi)^2
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Number of links in chain - Number of links in chain is the total (each part of the chain) links in a chain.
Centre Distance between Chain Pulleys - (Measured in Meter) - Centre Distance between Chain Pulleys is the distance between the centers of the big pulley and the small pulley of a chain drive.
Pitch of Chain - (Measured in Meter) - Pitch of Chain is usually defined as the distance between links, as measured from the center of the roller pin on one link to the center of the roller pin on the next link.
Number of Teeth on Driving Sprocket - Number of Teeth on Driving Sprocket is the number of teeth that are present on the driving sprocket.
Number of Teeth on Driven Sprocket - Number of Teeth on Driven Sprocket is the number of teeth that are present on the Driven sprocket.
STEP 1: Convert Input(s) to Base Unit
Centre Distance between Chain Pulleys: 800 Millimeter --> 0.8 Meter (Check conversion here)
Pitch of Chain: 22 Millimeter --> 0.022 Meter (Check conversion here)
Number of Teeth on Driving Sprocket: 17 --> No Conversion Required
Number of Teeth on Driven Sprocket: 34 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ln = 2*(C/P)+(z1+z2)/2+(P/C)*((z2-z1)/2*pi)^2 --> 2*(0.8/0.022)+(17+34)/2+(0.022/0.8)*((34-17)/2*pi)^2
Evaluating ... ...
Ln = 117.836942971687
STEP 3: Convert Result to Output's Unit
117.836942971687 --> No Conversion Required
FINAL ANSWER
117.836942971687 โ‰ˆ 117.8369 <-- Number of links in chain
(Calculation completed in 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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23 Geometric Relationships for Chain Calculators

Number of Links in Chain
Go Number of links in chain = 2*(Centre Distance between Chain Pulleys/Pitch of Chain)+(Number of Teeth on Driving Sprocket+Number of Teeth on Driven Sprocket)/2+(Pitch of Chain/Centre Distance between Chain Pulleys)*((Number of Teeth on Driven Sprocket-Number of Teeth on Driving Sprocket)/2*pi)^2
Roller Radius given Top Diameter of Sprocket Wheel
Go Roller Radius of Chain = (Pitch Circle Diameter of Sprocket+(Pitch of Chain*(1-(1.6/Number of teeth on sprocket)))-Top Diameter of Sprocket Wheel)/2
Roller Radius given Maximum Tooth Height above Pitch Polygon
Go Roller Radius of Chain = 0.625*Pitch of Chain-Maximum Sprocket Tooth Height+0.8*Pitch of Chain/Number of teeth on sprocket
Number of Teeth on Driving and Driven Sprockets given Average Chain Velocity
Go Number of teeth on sprocket = Average Chain Velocity*60/(Pitch of Chain*Speed of chain drive shaft in rpm)
Pitch of chain given Average Chain Velocity
Go Pitch of Chain = Average Chain Velocity*60/(Number of teeth on sprocket*Speed of chain drive shaft in rpm)
Average Chain Velocity given Number of Teeth on Sprocket
Go Average Chain Velocity = Number of teeth on sprocket*Pitch of Chain*Speed of chain drive shaft in rpm/60
Speed of Rotations of Driving and Driven Shafts given Average Chain Velocity
Go Speed of chain drive shaft in rpm = Average Chain Velocity*60/(pi*Pitch Circle Diameter of Sprocket)
Average Velocity of Chain
Go Average Chain Velocity = pi*Pitch Circle Diameter of Sprocket*Speed of chain drive shaft in rpm/60
Pitch of chain given Pitch Circle Diameter
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
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
Go Angular speed of chain driving shaft = Velocity Ratio of Chain Drive*Angular speed of chain driven shaft
Speed of Rotation of Driven Shaft given Velocity Ratio of Chain Drives
Go Angular speed of chain driven shaft = Angular speed of chain driving shaft/Velocity Ratio of Chain Drive
Velocity Ratio of Chain Drives
Go Velocity Ratio of Chain Drive = Angular speed of chain driving shaft/Angular speed of chain driven shaft
Number of Teeth on Driving Sprocket given Velocity of Chain Drives
Go Number of Teeth on Driving Sprocket = Number of Teeth on Driven Sprocket/Velocity Ratio of Chain Drive
Number of Teeth on Driven Sprocket given Velocity of Chain Drives
Go Number of Teeth on Driven Sprocket = Number of Teeth on Driving Sprocket*Velocity Ratio of Chain Drive
Roller Radius given Tooth Flank Radius
Go Roller Radius of Chain = Sprocket Tooth Flank Radius/(0.016*((Number of teeth on sprocket)^2+180))
Roller Radius given Minimum Tooth Flank Radius
Go Roller Radius of Chain = Minimum Tooth Flank Radius/((Number of teeth on sprocket+2)*0.24)
Chain Pitch given Minimum Tooth Height above Pitch Polygon
Go Pitch of Chain = (Minimum Tooth Height+Roller Radius of Chain)/0.5
Roller Radius given Minimum Tooth Height above Pitch Polygon
Go Roller Radius of Chain = 0.5*Pitch of Chain-Minimum Tooth Height
Number of Links in Chain given Length of Chain
Go Number of links in chain = Length of Chain/Pitch of Chain
Pitch of chain given Length of Chain
Go Pitch of Chain = Length of Chain/Number of links in chain
Length of Chain
Go Length of Chain = Number of links in chain*Pitch of Chain
Roller Radius given Minimum Roller Seating Radius
Go Roller Radius of Chain = Minimum Roller Seating Radius/(2*0.505)

Number of Links in Chain Formula

Number of links in chain = 2*(Centre Distance between Chain Pulleys/Pitch of Chain)+(Number of Teeth on Driving Sprocket+Number of Teeth on Driven Sprocket)/2+(Pitch of Chain/Centre Distance between Chain Pulleys)*((Number of Teeth on Driven Sprocket-Number of Teeth on Driving Sprocket)/2*pi)^2
Ln = 2*(C/P)+(z1+z2)/2+(P/C)*((z2-z1)/2*pi)^2

Define a Chain Drive?

Chain drive is a way of transmitting mechanical power from one place to another. It is often used to convey power to the wheels of a vehicle, particularly bicycles and motorcycles. It is also used in a wide variety of machines besides vehicles.

How to Calculate Number of Links in Chain?

Number of Links in Chain calculator uses Number of links in chain = 2*(Centre Distance between Chain Pulleys/Pitch of Chain)+(Number of Teeth on Driving Sprocket+Number of Teeth on Driven Sprocket)/2+(Pitch of Chain/Centre Distance between Chain Pulleys)*((Number of Teeth on Driven Sprocket-Number of Teeth on Driving Sprocket)/2*pi)^2 to calculate the Number of links in chain, The Number of links in Chain formula is defined as total number of links that are present on chain in chain drive. Number of links in chain is denoted by Ln symbol.

How to calculate Number of Links in Chain using this online calculator? To use this online calculator for Number of Links in Chain, enter Centre Distance between Chain Pulleys (C), Pitch of Chain (P), Number of Teeth on Driving Sprocket (z1) & Number of Teeth on Driven Sprocket (z2) and hit the calculate button. Here is how the Number of Links in Chain calculation can be explained with given input values -> 117.8369 = 2*(0.8/0.022)+(17+34)/2+(0.022/0.8)*((34-17)/2*pi)^2.

FAQ

What is Number of Links in Chain?
The Number of links in Chain formula is defined as total number of links that are present on chain in chain drive and is represented as Ln = 2*(C/P)+(z1+z2)/2+(P/C)*((z2-z1)/2*pi)^2 or Number of links in chain = 2*(Centre Distance between Chain Pulleys/Pitch of Chain)+(Number of Teeth on Driving Sprocket+Number of Teeth on Driven Sprocket)/2+(Pitch of Chain/Centre Distance between Chain Pulleys)*((Number of Teeth on Driven Sprocket-Number of Teeth on Driving Sprocket)/2*pi)^2. Centre Distance between Chain Pulleys is the distance between the centers of the big pulley and the small pulley of a chain drive, Pitch of Chain is usually defined as the distance between links, as measured from the center of the roller pin on one link to the center of the roller pin on the next link, Number of Teeth on Driving Sprocket is the number of teeth that are present on the driving sprocket & Number of Teeth on Driven Sprocket is the number of teeth that are present on the Driven sprocket.
How to calculate Number of Links in Chain?
The Number of links in Chain formula is defined as total number of links that are present on chain in chain drive is calculated using Number of links in chain = 2*(Centre Distance between Chain Pulleys/Pitch of Chain)+(Number of Teeth on Driving Sprocket+Number of Teeth on Driven Sprocket)/2+(Pitch of Chain/Centre Distance between Chain Pulleys)*((Number of Teeth on Driven Sprocket-Number of Teeth on Driving Sprocket)/2*pi)^2. To calculate Number of Links in Chain, you need Centre Distance between Chain Pulleys (C), Pitch of Chain (P), Number of Teeth on Driving Sprocket (z1) & Number of Teeth on Driven Sprocket (z2). With our tool, you need to enter the respective value for Centre Distance between Chain Pulleys, Pitch of Chain, Number of Teeth on Driving Sprocket & Number of Teeth on Driven 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 links in chain?
In this formula, Number of links in chain uses Centre Distance between Chain Pulleys, Pitch of Chain, Number of Teeth on Driving Sprocket & Number of Teeth on Driven Sprocket. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Number of links in chain = Length of Chain/Pitch of Chain
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