Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Acceleration = (2*pi*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2)
amax = (2*pi*ω^2*S)/(θR^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: 32 Radian --> 32 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
amax = (2*pi*ω^2*S)/(θR^2) --> (2*pi*27^2*20)/(32^2)
Evaluating ... ...
amax = 89.4617595494906
STEP 3: Convert Result to Output's Unit
89.4617595494906 Meter per Square Second --> No Conversion Required
FINAL ANSWER
89.4617595494906 89.46176 Meter per Square Second <-- Maximum Acceleration
(Calculation completed in 00.004 seconds)

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Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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12 Maximum Accelaration Calculators

Maximum Acceleration of Follower for Tangent Cam with Roller Follower
Go Maximum Acceleration = Angular velocity of cam^2*(Radius of the base circle+Radius of Roller)*((2-(cos(Angle turned by the cam for contact of roller))^2)/((cos(Angle turned by the cam for contact of roller))^3))
Max Acceleration of Follower during Return Stroke if Follower Stroke is Known Uniform Acceleration
Go Maximum Acceleration = (4*Angular velocity of cam*Stroke of Follower)/(Angular displacement of cam during return stroke*Time required for the return stroke)
Max Acceleration of Follower during Outstroke if Stroke of Follower is known Uniform Acceleration
Go Maximum Acceleration = (4*Angular velocity of cam*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke*Time required for the outstroke)
Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion
Go Maximum Acceleration = (2*pi*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2)
Maximum Acceleration of Follower during Outstroke for Cycloidal Motion
Go Maximum Acceleration = (2*pi *Angular velocity of cam^2*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke^2)
Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM
Go Maximum Acceleration = (pi^2*Angular velocity of cam^2*Stroke of Follower)/(2*Angular displacement of cam during return stroke^2)
Maximum Acceleration of Follower on Outstroke when Follower Moves with SHM
Go Maximum Acceleration = (pi^2*Angular velocity of cam^2*Stroke of Follower)/(2*Angular Displacement of Cam during Out Stroke^2)
Maximum Uniform Acceleration of Follower during Return Stroke
Go Maximum Acceleration = (4*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2)
Maximum Uniform Acceleration of Follower during Outstroke
Go Maximum Acceleration = (4*Angular velocity of cam^2*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke^2)
Maximum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank
Go Maximum Acceleration = Angular velocity of cam^2*(Radius of circular flank-Radius of the base circle)
Max Acceleration of Follower during Return Stroke if Follower Speed is known Uniform Acceleration
Go Maximum Acceleration = (2*Maximum velocity of follower)/Time required for the return stroke
Max Acceleration of Follower during Outstroke if Outstroke Velocity is known Uniform Acceleration
Go Maximum Acceleration = (2*Maximum velocity of follower)/Time required for the outstroke

Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion Formula

Maximum Acceleration = (2*pi*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2)
amax = (2*pi*ω^2*S)/(θR^2)

What is cycloidal motion?

In geometry, a cycloid is a curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve.

How to Calculate Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion?

Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion calculator uses Maximum Acceleration = (2*pi*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2) to calculate the Maximum Acceleration, The Maximum acceleration of follower during return stroke for Cycloidal motion formula is defined as the rate of change of the velocity of an object with respect to time. Maximum Acceleration is denoted by amax symbol.

How to calculate Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion using this online calculator? To use this online calculator for Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion, enter Angular velocity of cam (ω), Stroke of Follower (S) & Angular displacement of cam during return stroke R) and hit the calculate button. Here is how the Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion calculation can be explained with given input values -> 89.46176 = (2*pi*27^2*20)/(32^2).

FAQ

What is Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion?
The Maximum acceleration of follower during return stroke for Cycloidal motion formula is defined as the rate of change of the velocity of an object with respect to time and is represented as amax = (2*pi*ω^2*S)/(θR^2) or Maximum Acceleration = (2*pi*Angular velocity of cam^2*Stroke of Follower)/(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 during Return Stroke for Cycloidal Motion?
The Maximum acceleration of follower during return stroke for Cycloidal motion formula is defined as the rate of change of the velocity of an object with respect to time is calculated using Maximum Acceleration = (2*pi*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2). To calculate Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion, you need Angular velocity of cam (ω), Stroke of Follower (S) & Angular displacement of cam during return stroke 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 11 other way(s) to calculate the same, which is/are as follows -
  • 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^2*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke^2)
  • Maximum Acceleration = (pi^2*Angular velocity of cam^2*Stroke of Follower)/(2*Angular displacement of cam during return stroke^2)
  • Maximum Acceleration = (pi^2*Angular velocity of cam^2*Stroke of Follower)/(2*Angular Displacement of Cam during Out Stroke^2)
  • Maximum Acceleration = Angular velocity of cam^2*(Radius of the base circle+Radius of Roller)*((2-(cos(Angle turned by the cam for contact of roller))^2)/((cos(Angle turned by the cam for contact of roller))^3))
  • Maximum Acceleration = Angular velocity of cam^2*(Radius of circular flank-Radius of the base circle)
  • Maximum Acceleration = (2*pi *Angular velocity of cam^2*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke^2)
  • Maximum Acceleration = (4*Angular velocity of cam*Stroke of Follower)/(Angular displacement of cam during return stroke*Time required for the return stroke)
  • Maximum Acceleration = (2*Maximum velocity of follower)/Time required for the return stroke
  • Maximum Acceleration = (4*Angular velocity of cam*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke*Time required for the outstroke)
  • Maximum Acceleration = (2*Maximum velocity of follower)/Time required for the outstroke
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