Velocity of Follower after Time t for Cycloidal Motion Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
v = (ω*S)/θo*(1-cos((2*pi*θrotation)/(θo)))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Velocity - (Measured in Meter per Second) - Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position 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.
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
v = (ω*S)/θo*(1-cos((2*pi*θrotation)/(θo))) --> (27*20)/22*(1-cos((2*pi*0.349)/(22)))
Evaluating ... ...
v = 0.121827890728528
STEP 3: Convert Result to Output's Unit
0.121827890728528 Meter per Second --> No Conversion Required
FINAL ANSWER
0.121827890728528 0.121828 Meter per Second <-- Velocity
(Calculation completed in 00.004 seconds)

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!

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

Velocity of Follower after Time t for Cycloidal Motion Formula

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)))
v = (ω*S)/θo*(1-cos((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 Velocity of Follower after Time t for Cycloidal Motion?

Velocity of Follower after Time t for Cycloidal Motion calculator uses 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))) to calculate the Velocity, The Velocity of follower after time t for Cycloidal motion formula is defined as the rate of change of its position with respect to a frame of reference. Velocity is denoted by v symbol.

How to calculate Velocity of Follower after Time t for Cycloidal Motion using this online calculator? To use this online calculator for Velocity 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 o) & Angle through which cam rotates rotation) and hit the calculate button. Here is how the Velocity of Follower after Time t for Cycloidal Motion calculation can be explained with given input values -> 0.121828 = (27*20)/22*(1-cos((2*pi*0.349)/(22))).

FAQ

What is Velocity of Follower after Time t for Cycloidal Motion?
The Velocity of follower after time t for Cycloidal motion formula is defined as the rate of change of its position with respect to a frame of reference and is represented as v = (ω*S)/θo*(1-cos((2*pi*θrotation)/(θo))) or 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))). 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 Velocity of Follower after Time t for Cycloidal Motion?
The Velocity of follower after time t for Cycloidal motion formula is defined as the rate of change of its position with respect to a frame of reference is calculated using 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))). To calculate Velocity 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 o) & Angle through which cam rotates 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 Velocity?
In this formula, Velocity uses Angular velocity of cam, Stroke of Follower, Angular Displacement of Cam during Out Stroke & Angle through which cam rotates. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Velocity = Angular velocity of cam*(Radius of circular flank-Radius of the base circle)*sin(Angle turned by cam)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!