Displacement of Follower after Time t for Cycloidal Motion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Displacement = Stroke of Follower*(Angle through which cam rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through which cam rotates)/(Angular Displacement of Cam during Out Stroke)))
d = S*(θrotation/θo*180/pi-sin((2*pi*θrotation)/(θo)))
This formula uses 1 Constants, 1 Functions, 4 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
Displacement - (Measured in Meter) - Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
Stroke of Follower - (Measured in Meter) - Stroke of Follower is the greatest distance or angle through which the follower moves or rotates.
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.
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
Stroke of Follower: 20 Meter --> 20 Meter No Conversion Required
Angle through which cam rotates: 0.349 Radian --> 0.349 Radian 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
d = S*(θrotationo*180/pi-sin((2*pi*θrotation)/(θo))) --> 20*(0.349/22*180/pi-sin((2*pi*0.349)/(22)))
Evaluating ... ...
d = 16.1882041057383
STEP 3: Convert Result to Output's Unit
16.1882041057383 Meter --> No Conversion Required
FINAL ANSWER
16.1882041057383 16.1882 Meter <-- Displacement
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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13 Cam and Follower Calculators

Displacement of Follower after Time t for Cycloidal Motion
Go Displacement = Stroke of Follower*(Angle through which cam rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through which cam rotates)/(Angular Displacement of Cam during Out Stroke)))
Velocity of Follower after Time t for Cycloidal Motion
Go Velocity = (Angular velocity of cam*Stroke of Follower)/Angular Displacement of Cam during Out Stroke*(1-cos((2*pi*Angle through which cam rotates)/(Angular Displacement of Cam during Out Stroke)))
Velocity of Follower for Circular Arc Cam if Contact is on Circular Flank
Go Velocity = Angular velocity of cam*(Radius of circular flank-Radius of the base circle)*sin(Angle turned by cam)
Peripheral Speed of Projection of Point P' (Projection of Point P on Dia) for SHM of Follower
Go Peripheral Speed = (pi*Stroke of Follower*Angular velocity of cam)/(2*Angular Displacement of Cam during Out Stroke)
Displacement of Follower for Circular Arc Cam, there's Contact on Circular Flank
Go Displacement = (Radius of circular flank-Radius of the base circle)*(1-cos(Angle turned by cam))
Peripheral Speed of Projection of Point P on Diameter for SHM of Follower
Go Peripheral Speed = (pi*Stroke of Follower)/(2*Time required for the outstroke)
Time Required by Follower for Return Stroke at Uniform Acceleration
Go Time required for the return stroke = Angular displacement of cam during return stroke/Angular velocity of cam
Time Required for Out Stroke of Follower when Follower Moves with SHM
Go Time required for the outstroke = Angular Displacement of Cam during Out Stroke/Angular velocity of cam
Time Required for Follower during Outstroke for Uniform Acceleration
Go Time required for the outstroke = Angular Displacement of Cam during Out Stroke/Angular velocity of cam
Mean Velocity of Follower during Return Stroke at Uniform Acceleration
Go Mean Velocity = Stroke of Follower/Time required for the return stroke
Mean Velocity of Follower during Outstroke at Uniform Acceleration
Go Mean Velocity = Stroke of Follower/Time required for the outstroke
Condition for Maximum Acceleration of Follower Exhibiting Cycloidal Motion
Go Angle through which cam rotates = Angular Displacement of Cam during Out Stroke/4
Condition for Maximum Velocity of Follower Exhibiting Cycloidal Motion
Go Angle through which cam rotates = Angular Displacement of Cam during Out Stroke/2

Displacement of Follower after Time t for Cycloidal Motion Formula

Displacement = Stroke of Follower*(Angle through which cam rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through which cam rotates)/(Angular Displacement of Cam during Out Stroke)))
d = S*(θrotation/θo*180/pi-sin((2*pi*θrotation)/(θo)))

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 Displacement of Follower after Time t for Cycloidal Motion?

Displacement of Follower after Time t for Cycloidal Motion calculator uses Displacement = Stroke of Follower*(Angle through which cam rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through which cam rotates)/(Angular Displacement of Cam during Out Stroke))) to calculate the Displacement, The Displacement of follower after time t for Cycloidal motion formula implies that the follower has moved, or has been displaced. Displacement is denoted by d symbol.

How to calculate Displacement of Follower after Time t for Cycloidal Motion using this online calculator? To use this online calculator for Displacement of Follower after Time t for Cycloidal Motion, enter Stroke of Follower (S), Angle through which cam rotates rotation) & Angular Displacement of Cam during Out Stroke o) and hit the calculate button. Here is how the Displacement of Follower after Time t for Cycloidal Motion calculation can be explained with given input values -> 16.1882 = 20*(0.349/22*180/pi-sin((2*pi*0.349)/(22))).

FAQ

What is Displacement of Follower after Time t for Cycloidal Motion?
The Displacement of follower after time t for Cycloidal motion formula implies that the follower has moved, or has been displaced and is represented as d = S*(θrotationo*180/pi-sin((2*pi*θrotation)/(θo))) or Displacement = Stroke of Follower*(Angle through which cam rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through which cam rotates)/(Angular Displacement of Cam during Out Stroke))). Stroke of Follower is the greatest distance or angle through which the follower moves or rotates, 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 & The Angular Displacement of Cam during Out Stroke is the angle covered by the follower during forwarding stroke.
How to calculate Displacement of Follower after Time t for Cycloidal Motion?
The Displacement of follower after time t for Cycloidal motion formula implies that the follower has moved, or has been displaced is calculated using Displacement = Stroke of Follower*(Angle through which cam rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through which cam rotates)/(Angular Displacement of Cam during Out Stroke))). To calculate Displacement of Follower after Time t for Cycloidal Motion, you need Stroke of Follower (S), Angle through which cam rotates rotation) & Angular Displacement of Cam during Out Stroke o). With our tool, you need to enter the respective value for Stroke of Follower, Angle through which cam rotates & 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 Displacement?
In this formula, Displacement uses Stroke of Follower, Angle through which cam rotates & Angular Displacement of Cam during Out Stroke. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Displacement = (Radius of circular flank-Radius of the base circle)*(1-cos(Angle turned by cam))
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