Maximum Acceleration of Follower during Outstroke for Cycloidal Motion 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 Out Stroke is the angle covered by the follower during forwarding stroke.ⓘ Angular Displacement of Cam During Out Stroke [θ_o]			+10% -10%

✖Maximum Acceleration is the rate of change of the velocity of an object with respect to time.ⓘ Maximum Acceleration of Follower during Outstroke for Cycloidal Motion [a_max]

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Maximum Acceleration of Follower during Outstroke for Cycloidal Motion

Formula

a max = \frac{2 \cdot π \cdot ω^{2} \cdot S}{{θ o}^{2}}

Example

189.2745 m/s² = \frac{2 \cdot π \cdot {27 rad/s}^{2} \cdot 20 m}{{22 rad}^{2}}

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Maximum Acceleration of Follower during Outstroke 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 Out Stroke^2)
a_max = (2*pi*ω^2*S)/(θ_o^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 Out Stroke - (Measured in Radian) - The Angular Displacement of Cam during Out Stroke is the angle covered by the follower during forwarding 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 Out Stroke: 22 Radian --> 22 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_max = (2*pi*ω^2*S)/(θ_o^2) --> (2*pi*27^2*20)/(22^2)

Evaluating ... ...

a_max = 189.274466484873

STEP 3: Convert Result to Output's Unit

189.274466484873 Meter per Square Second --> No Conversion Required

FINAL ANSWER

189.274466484873 ≈ 189.2745 Meter per Square Second <-- Maximum Acceleration

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Cams » Mechanical » Acceleration Of The Follower » Maximum Acceleration of Follower during Outstroke for Cycloidal Motion

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National Institute Of Technology (NIT), Hamirpur

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< Acceleration Of The Follower Calculators

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

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

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

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

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 during Outstroke for Cycloidal Motion Formula

Maximum Acceleration = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2)
a_max = (2*pi*ω^2*S)/(θ_o^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 Outstroke for Cycloidal Motion?

Maximum Acceleration of Follower during Outstroke for Cycloidal Motion calculator uses Maximum Acceleration = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2) to calculate the Maximum Acceleration, Maximum Acceleration of Follower during Outstroke for Cycloidal Motion formula is defined as the maximum acceleration experienced by the follower during the outstroke phase of cycloidal motion, which is a fundamental concept in mechanical systems and machine design, where the follower moves in a circular path. Maximum Acceleration is denoted by a_max symbol.

How to calculate Maximum Acceleration of Follower during Outstroke for Cycloidal Motion using this online calculator? To use this online calculator for Maximum Acceleration of Follower during Outstroke for Cycloidal Motion, enter Angular Velocity of Cam (ω), Stroke of Follower (S) & Angular Displacement of Cam During Out Stroke (θ_o) and hit the calculate button. Here is how the Maximum Acceleration of Follower during Outstroke for Cycloidal Motion calculation can be explained with given input values -> 15.45098 = (2*pi*27^2*20)/(22^2).

FAQ

What is Maximum Acceleration of Follower during Outstroke for Cycloidal Motion?

Maximum Acceleration of Follower during Outstroke for Cycloidal Motion formula is defined as the maximum acceleration experienced by the follower during the outstroke phase of cycloidal motion, which is a fundamental concept in mechanical systems and machine design, where the follower moves in a circular path and is represented as a_max = (2*pi*ω^2*S)/(θ_o^2) or Maximum Acceleration = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out 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 Out Stroke is the angle covered by the follower during forwarding stroke.

How to calculate Maximum Acceleration of Follower during Outstroke for Cycloidal Motion?

Maximum Acceleration of Follower during Outstroke for Cycloidal Motion formula is defined as the maximum acceleration experienced by the follower during the outstroke phase of cycloidal motion, which is a fundamental concept in mechanical systems and machine design, where the follower moves in a circular path is calculated using Maximum Acceleration = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2). To calculate Maximum Acceleration of Follower during Outstroke for Cycloidal Motion, you need Angular Velocity of Cam (ω), Stroke of Follower (S) & Angular Displacement of Cam During Out Stroke (θ_o). With our tool, you need to enter the respective value for Angular Velocity of Cam, Stroke of Follower & Angular Displacement of Cam During Out 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 Out 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 = (pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Return Stroke^2)
Maximum Acceleration = (4*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Return Stroke^2)

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