Acceleration of Follower after Time t 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%
✖The angle through which cam rotates is the angle through which the cam turns while the follower remains stationary at the highest or the lowest position.ⓘ Angle through which cam rotates [θ_rotation]			+10% -10%

✖Acceleration of follower is the rate of change in velocity to the change in time.ⓘ Acceleration of Follower after Time t for Cycloidal Motion [a]

⎘ Copy

👎

Formula

✖

Acceleration of Follower after Time t for Cycloidal Motion

Formula

`"a" = (2*pi*"ω"^2*"S")/("θ"_{"o"}^2)*sin((2*pi*"θ"_{"rotation"})/("θ"_{"o"}))`

Example

`"18.83455m/s²"=(2*pi*("27rad/s")^2*"20m")/(("22rad")^2)*sin((2*pi*"0.349rad")/("22rad"))`

Calculator

LaTeX

Reset

👍

Download Theory of Machine Formula PDF

Acceleration of Follower after Time t for Cycloidal Motion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
a = (2*pi*ω^2*S)/(θ_o^2)*sin((2*pi*θ_rotation)/(θ_o))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Acceleration of follower - (Measured in Meter per Square Second) - Acceleration of follower is the rate of change in velocity to the change in 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.
Angle through which cam rotates - (Measured in Radian) - The angle through which cam rotates is the angle through which the cam turns while the follower remains stationary at the highest or the lowest position.

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
Angle through which cam rotates: 0.349 Radian --> 0.349 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = (2*pi*ω^2*S)/(θ_o^2)*sin((2*pi*θ_rotation)/(θ_o)) --> (2*pi*27^2*20)/(22^2)*sin((2*pi*0.349)/(22))

Evaluating ... ...

a = 18.8345518910704

STEP 3: Convert Result to Output's Unit

18.8345518910704 Meter per Square Second --> No Conversion Required

FINAL ANSWER

18.8345518910704 ≈ 18.83455 Meter per Square Second <-- Acceleration of follower

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Theory of Machine » Cams » Acceleration Of The Follower » Acceleration of Follower after Time t for Cycloidal Motion

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Calculator and 1900+ more calculators!

< 8 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)

Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank

Go Acceleration of follower = Angular velocity of cam^2*(Radius of circular flank-Radius of the base circle)*cos(Total angle of action of cam)

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)

Centripetal Acceleration of Point P on Circumference

Go Centripetal acceleration = (pi^2*Angular velocity of cam^2*Stroke of Follower)/(2*Angular Displacement of Cam during Out Stroke^2)

Minimum Acceleration of Follower for Tangent Cam with Roller Follower

Go Acceleration of follower = Angular velocity of cam^2*(Radius of the base circle+Radius of Roller)

Centripetal Acceleration of Point P on Circumference when Follower Moves with SHM

Go Centripetal acceleration = (2*Peripheral Speed^2)/(Stroke of Follower)

Acceleration of Follower after Time t for Cycloidal Motion Formula

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 Acceleration of Follower after Time t for Cycloidal Motion?

Acceleration of Follower after Time t for Cycloidal Motion calculator uses 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)) to calculate the Acceleration of follower, The Acceleration of follower after time t for cycloidal motion formula is defined as the rate of change of the velocity of an object with respect to time. Acceleration of follower is denoted by a symbol.

How to calculate Acceleration of Follower after Time t for Cycloidal Motion using this online calculator? To use this online calculator for Acceleration of Follower after Time t for Cycloidal Motion, enter Angular velocity of cam (ω), Stroke of Follower (S), Angular Displacement of Cam during Out Stroke (θ_o) & Angle through which cam rotates (θ_rotation) and hit the calculate button. Here is how the Acceleration of Follower after Time t for Cycloidal Motion calculation can be explained with given input values -> 18.83455 = (2*pi*27^2*20)/(22^2)*sin((2*pi*0.349)/(22)).

FAQ

What is Acceleration of Follower after Time t for Cycloidal Motion?

The Acceleration of follower after time t 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 a = (2*pi*ω^2*S)/(θ_o^2)*sin((2*pi*θ_rotation)/(θ_o)) or 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)). 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 & The angle through which cam rotates is the angle through which the cam turns while the follower remains stationary at the highest or the lowest position.

How to calculate Acceleration of Follower after Time t for Cycloidal Motion?

The Acceleration of follower after time t for cycloidal motion formula is defined as the rate of change of the velocity of an object with respect to time is calculated using 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)). To calculate Acceleration of Follower after Time t for Cycloidal Motion, you need Angular velocity of cam (ω), Stroke of Follower (S), Angular Displacement of Cam during Out Stroke (θ_o) & Angle through which cam rotates (θ_rotation). 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 & Angle through which cam rotates 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 Acceleration of follower?

In this formula, Acceleration of follower uses Angular velocity of cam, Stroke of Follower, Angular Displacement of Cam during Out Stroke & Angle through which cam rotates. We can use 5 other way(s) to calculate the same, which is/are as follows -

Acceleration of follower = Angular velocity of cam^2*(Radius of circular flank-Radius of the base circle)*cos(Angle turned by cam)
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 = 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 = Angular velocity of cam^2*(Radius of the base circle+Radius of Roller)
Acceleration of follower = Angular velocity of cam^2*(Radius of circular flank-Radius of the base circle)*cos(Total angle of action of cam)

Home

FREE PDFs

🔍 Search