Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM Calculator

✖Angular velocity of cam refers to how fast an object rotates or revolves relative to another point.ⓘ Angular Velocity of Cam [ω]			+10% -10%
✖Stroke of Follower is the greatest distance or angle through which the follower moves or rotates.ⓘ Stroke of Follower [S]			+10% -10%
✖The angular displacement of cam during return stroke is the angle covered by the follower during the return stroke.ⓘ Angular Displacement of Cam During Return Stroke [θ_R]			+10% -10%

✖Maximum Acceleration is the rate of change of the velocity of an object with respect to time.ⓘ Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM [a_max]

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Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Acceleration = (pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Return Stroke^2)
a_max = (pi^2*ω^2*S)/(2*θ_R^2)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Maximum Acceleration - (Measured in Meter per Square Second) - Maximum Acceleration is the rate of change of the velocity of an object with respect to time.
Angular Velocity of Cam - (Measured in Radian per Second) - Angular velocity of cam refers to how fast an object rotates or revolves relative to another point.
Stroke of Follower - (Measured in Meter) - Stroke of Follower is the greatest distance or angle through which the follower moves or rotates.
Angular Displacement of Cam During Return Stroke - (Measured in Radian) - The angular displacement of cam during return stroke is the angle covered by the follower during the return stroke.

STEP 1: Convert Input(s) to Base Unit

Angular Velocity of Cam: 27 Radian per Second --> 27 Radian per Second No Conversion Required
Stroke of Follower: 20 Meter --> 20 Meter No Conversion Required
Angular Displacement of Cam During Return Stroke: 77.5 Radian --> 77.5 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_max = (pi^2*ω^2*S)/(2*θ_R^2) --> (pi^2*27^2*20)/(2*77.5^2)

Evaluating ... ...

a_max = 11.9790911273992

STEP 3: Convert Result to Output's Unit

11.9790911273992 Meter per Square Second --> No Conversion Required

FINAL ANSWER

11.9790911273992 ≈ 11.97909 Meter per Square Second <-- Maximum Acceleration

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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Acceleration of Follower of Roller Follower Tangent Cam, there's Contact with Nose

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*Distance b/w Cam Center and Nose Center*(cos(Angle Turned by Cam When Roller is at Nose Top)+(Distance b/w Roller Centre and Nose Centre^2*Distance b/w Cam Center and Nose Center*cos(2*Angle Turned by Cam When Roller is at Nose Top)+Distance b/w Cam Center and Nose Center^3*(sin(Angle Turned by Cam When Roller is at Nose Top))^4)/sqrt(Distance b/w Roller Centre and Nose Centre^2-Distance b/w Cam Center and Nose Center^2*(sin(Angle Turned by Cam When Roller is at Nose Top))^2))

Acceleration of Follower after Time t for Cycloidal Motion

LaTeX Go Acceleration of Follower = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2)*sin((2*pi*Angle Through Which Cam Rotates)/(Angular Displacement of Cam During Out Stroke))

Acceleration of Follower for Roller Follower Tangent Cam, there's Contact with Straight Flanks

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*(Radius of the Base Circle+Radius of Roller)*(2-cos(Angle Turned by Cam from Beginning of Roller))^2/((cos(Angle Turned by Cam from Beginning of Roller))^3)

Acceleration of Follower for Circular Arc Cam if there's Contact on Circular Flank

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Angle Turned by Cam)

Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM Formula

LaTeX Go

Maximum Acceleration = (pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Return Stroke^2)
a_max = (pi^2*ω^2*S)/(2*θ_R^2)

What is a cam and follower used for?

The cam and follower mechanism is widely used for operating the inlet and exhaust valves of internal combustion engines. They are used in wall clocks and the feed mechanism of automatic lathe machines. They are also used in paper cutting machines and weaving textile machinery.

What are the different types of motion with which a follower can move?

The follower may move as a slider, reciprocating in a linear direction, or as a rocker, oscillating around a fixed pivot. There can be overlapping functionality between cams and linkages (such as crank-rockers).

How to Calculate Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM?

Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM calculator uses Maximum Acceleration = (pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Return Stroke^2) to calculate the Maximum Acceleration, Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM formula is defined as the maximum acceleration of the follower during its return stroke when it moves with simple harmonic motion, which is a critical parameter in understanding the dynamics of mechanical systems. Maximum Acceleration is denoted by a_max symbol.

How to calculate Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM using this online calculator? To use this online calculator for Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM, enter Angular Velocity of Cam (ω), Stroke of Follower (S) & Angular Displacement of Cam During Return Stroke (θ_R) and hit the calculate button. Here is how the Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM calculation can be explained with given input values -> 70.2631 = (pi^2*27^2*20)/(2*77.5^2).

FAQ

What is Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM?

Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM formula is defined as the maximum acceleration of the follower during its return stroke when it moves with simple harmonic motion, which is a critical parameter in understanding the dynamics of mechanical systems and is represented as a_max = (pi^2*ω^2*S)/(2*θ_R^2) or Maximum Acceleration = (pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Return Stroke^2). Angular velocity of cam refers to how fast an object rotates or revolves relative to another point, Stroke of Follower is the greatest distance or angle through which the follower moves or rotates & The angular displacement of cam during return stroke is the angle covered by the follower during the return stroke.

How to calculate Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM?

Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM formula is defined as the maximum acceleration of the follower during its return stroke when it moves with simple harmonic motion, which is a critical parameter in understanding the dynamics of mechanical systems is calculated using Maximum Acceleration = (pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Return Stroke^2). To calculate Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM, you need Angular Velocity of Cam (ω), Stroke of Follower (S) & Angular Displacement of Cam During Return Stroke (θ_R). With our tool, you need to enter the respective value for Angular Velocity of Cam, Stroke of Follower & Angular Displacement of Cam During Return Stroke 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 Maximum Acceleration?

In this formula, Maximum Acceleration uses Angular Velocity of Cam, Stroke of Follower & Angular Displacement of Cam During Return Stroke. We can use 3 other way(s) to calculate the same, which is/are as follows -

Maximum Acceleration = (pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Out Stroke^2)
Maximum Acceleration = (4*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Return Stroke^2)
Maximum Acceleration = (4*Angular Velocity of Cam*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke*Time Required for the Outstroke)

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