Displacement of Follower after Time t for Cycloidal Motion Calculator

✖Stroke of Follower is the maximum distance the follower moves away from the cam's surface during the return stroke in a cam-follower mechanism.ⓘ Stroke of Follower [S]			+10% -10%
✖Angle through Cam Rotates is the angle through which the cam rotates to move the follower in a specific path, controlling the follower's motion.ⓘ Angle through Cam Rotates [θ_rotation]			+10% -10%
✖Angular Displacement of Cam during Out Stroke is the rotation of the cam during the outward movement of the cam follower in a mechanical system.ⓘ Angular Displacement of Cam during Out Stroke [θ_o]			+10% -10%

✖Displacement of Follower is the linear movement of the follower in a cam-follower mechanism, which converts rotary motion into linear motion.ⓘ Displacement of Follower after Time t for Cycloidal Motion [d_follower]

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Displacement of Follower after Time t for Cycloidal Motion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Displacement of Follower = Stroke of Follower*(Angle through Cam Rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through Cam Rotates)/(Angular Displacement of Cam during Out Stroke)))
d_follower = S*(θ_rotation/θ_o*180/pi-sin((2*pi*θ_rotation)/(θ_o)))
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 of Follower - (Measured in Meter) - Displacement of Follower is the linear movement of the follower in a cam-follower mechanism, which converts rotary motion into linear motion.
Stroke of Follower - (Measured in Meter) - Stroke of Follower is the maximum distance the follower moves away from the cam's surface during the return stroke in a cam-follower mechanism.
Angle through Cam Rotates - (Measured in Radian) - Angle through Cam Rotates is the angle through which the cam rotates to move the follower in a specific path, controlling the follower's motion.
Angular Displacement of Cam during Out Stroke - (Measured in Radian) - Angular Displacement of Cam during Out Stroke is the rotation of the cam during the outward movement of the cam follower in a mechanical system.

STEP 1: Convert Input(s) to Base Unit

Stroke of Follower: 20 Meter --> 20 Meter No Conversion Required
Angle through Cam Rotates: 0.349 Radian --> 0.349 Radian No Conversion Required
Angular Displacement of Cam during Out Stroke: 1.396 Radian --> 1.396 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_follower = S*(θ_rotation/θ_o*180/pi-sin((2*pi*θ_rotation)/(θ_o))) --> 20*(0.349/1.396*180/pi-sin((2*pi*0.349)/(1.396)))

Evaluating ... ...

d_follower = 266.478897565412

STEP 3: Convert Result to Output's Unit

266.478897565412 Meter --> No Conversion Required

FINAL ANSWER

266.478897565412 ≈ 266.4789 Meter <-- Displacement of Follower

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Cams » Cam and Follower » Mechanical » Follower Motion » Displacement of Follower after Time t for Cycloidal Motion

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National Institute Of Technology (NIT), Hamirpur

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< Follower Motion Calculators

Peripheral Speed of Projection of Point P' (Projection of Point P on Dia) for SHM of Follower

LaTeX Go Peripheral Speed = (pi*Stroke of Follower*Angular Velocity of Cam)/(2*Angular Displacement of Cam during Out Stroke)

Peripheral Speed of Projection of Point P on Diameter for SHM of Follower

LaTeX Go Peripheral Speed = (pi*Stroke of Follower)/(2*Time Required for the Outstroke)

Time Required for Out Stroke of Follower when Follower Moves with SHM

LaTeX 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

LaTeX Go Mean Velocity = Stroke of Follower/Time Required for the Return Stroke

Displacement of Follower after Time t for Cycloidal Motion Formula

LaTeX Go

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 of Follower = Stroke of Follower*(Angle through Cam Rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through Cam Rotates)/(Angular Displacement of Cam during Out Stroke))) to calculate the Displacement of Follower, Displacement of Follower after Time t for Cycloidal Motion formula is defined as the linear distance travelled by the follower in a cam-follower mechanism during a specific time period, considering the rotational motion of the cam and the follower's oscillations. Displacement of Follower is denoted by d_follower 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 Cam Rotates (θ_rotation) & Angular Displacement of Cam during Out Stroke (θ_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 -> 266.4789 = 20*(0.349/1.396*180/pi-sin((2*pi*0.349)/(1.396))).

FAQ

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

Displacement of Follower after Time t for Cycloidal Motion formula is defined as the linear distance travelled by the follower in a cam-follower mechanism during a specific time period, considering the rotational motion of the cam and the follower's oscillations and is represented as d_follower = S*(θ_rotation/θ_o*180/pi-sin((2*pi*θ_rotation)/(θ_o))) or Displacement of Follower = Stroke of Follower*(Angle through Cam Rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through Cam Rotates)/(Angular Displacement of Cam during Out Stroke))). Stroke of Follower is the maximum distance the follower moves away from the cam's surface during the return stroke in a cam-follower mechanism, Angle through Cam Rotates is the angle through which the cam rotates to move the follower in a specific path, controlling the follower's motion & Angular Displacement of Cam during Out Stroke is the rotation of the cam during the outward movement of the cam follower in a mechanical system.

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

Displacement of Follower after Time t for Cycloidal Motion formula is defined as the linear distance travelled by the follower in a cam-follower mechanism during a specific time period, considering the rotational motion of the cam and the follower's oscillations is calculated using Displacement of Follower = Stroke of Follower*(Angle through Cam Rotates/Angular Displacement of Cam during Out Stroke*180/pi-sin((2*pi*Angle through 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 Cam Rotates (θ_rotation) & Angular Displacement of Cam during Out Stroke (θ_o). With our tool, you need to enter the respective value for Stroke of Follower, Angle through 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 of Follower?

In this formula, Displacement of Follower uses Stroke of Follower, Angle through 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 of Follower = (Base Radius of Truncated Cone-Radius of the Base Circle)*(1-cos(Angle Turned by Cam))

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