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Velocity of Follower after Time t for Cycloidal Motion Formula

GoVelocity of Follower for Circular Arc Cam if Contact is on Circular Flank Formula

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Velocity is the speed at which the follower moves in a specific direction, typically measured in meters per second, in a cam and follower mechanism. Check FAQs

v = \frac{ω \cdot S}{θ o} \cdot (1 - \cos (\frac{2 \cdot π \cdot θ rotation}{θ o}))

v - Velocity?ω - Angular Velocity of Cam?S - Stroke of Follower?θ_o - Angular Displacement of Cam during Out Stroke?θ_rotation - Angle through Cam Rotates?π - Archimedes' constant?

Velocity of Follower after Time t for Cycloidal Motion Example

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Here is how the Velocity of Follower after Time t for Cycloidal Motion equation looks like with Values.

Here is how the Velocity of Follower after Time t for Cycloidal Motion equation looks like with Units.

Here is how the Velocity of Follower after Time t for Cycloidal Motion equation looks like.

386.8195 = \frac{27 \cdot 20}{1.396} \cdot (1 - \cos (\frac{2 \cdot 3.1416 \cdot 0.349}{1.396}))

386.8195m/s = \frac{27rad/s \cdot 20m}{1.396rad} \cdot (1 - \cos (\frac{2 \cdot 3.1416 \cdot 0.349rad}{1.396rad}))

386.8195 = \frac{27 \cdot 20}{1.396} \cdot (1 - \cos (\frac{2 \cdot 3.1416 \cdot 0.349}{1.396}))

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Velocity of Follower after Time t for Cycloidal Motion Solution

Follow our step by step solution on how to calculate Velocity of Follower after Time t for Cycloidal Motion?

FIRST Step Consider the formula

v = \frac{ω \cdot S}{θ o} \cdot (1 - \cos (\frac{2 \cdot π \cdot θ rotation}{θ o}))

Next Step Substitute values of Variables

∴

v = \frac{27rad/s \cdot 20m}{1.396rad} \cdot (1 - \cos (\frac{2 \cdot π \cdot 0.349rad}{1.396rad}))

Next Step Substitute values of Constants

∴

v = \frac{27rad/s \cdot 20m}{1.396rad} \cdot (1 - \cos (\frac{2 \cdot 3.1416 \cdot 0.349rad}{1.396rad}))

Next Step Prepare to Evaluate

∴

v = \frac{27 \cdot 20}{1.396} \cdot (1 - \cos (\frac{2 \cdot 3.1416 \cdot 0.349}{1.396}))

Next Step Evaluate

∴

v = 386.819484240688m/s

LAST Step Rounding Answer

∴

v = 386.8195m/s

Velocity of Follower after Time t for Cycloidal Motion Formula Elements

Variables

Constants

Functions

Velocity

Velocity is the speed at which the follower moves in a specific direction, typically measured in meters per second, in a cam and follower mechanism.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity

Angular Velocity of Cam

Angular Velocity of Cam is the rate of change of angular displacement of the cam with respect to time, describing the cam's rotational motion.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity of Cam

Stroke of Follower

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.

Symbol: S

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Stroke of Follower

Angular Displacement of Cam during Out Stroke

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.

Symbol: θ_o

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angular Displacement of Cam during Out Stroke

Angle through Cam Rotates

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.

Symbol: θ_rotation

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle through Cam Rotates

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Velocity

Go Velocity of Follower for Circular Arc Cam if Contact is on Circular Flank

v = ω \cdot (R - r 1) \cdot \sin (θ turned)

Other formulas in Follower Motion category

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

t o = \frac{θ o}{ω}

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

P s = \frac{π \cdot S}{2 \cdot t o}

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

P s = \frac{π \cdot S \cdot ω}{2 \cdot θ o}

Go Mean Velocity of Follower during Return Stroke at Uniform Acceleration

V mean = \frac{S}{t R}

How to Evaluate Velocity of Follower after Time t for Cycloidal Motion?

Velocity of Follower after Time t for Cycloidal Motion evaluator uses Velocity = (Angular Velocity of Cam*Stroke of Follower)/Angular Displacement of Cam during Out Stroke*(1-cos((2*pi*Angle through Cam Rotates)/(Angular Displacement of Cam during Out Stroke))) to evaluate the Velocity, Velocity of Follower after Time t for Cycloidal Motion formula is defined as the measure of the velocity of the follower in a cam and follower system, which undergoes cycloidal motion, describing the motion of the follower as it rotates and translates in a circular path. Velocity is denoted by v symbol.

How to evaluate Velocity of Follower after Time t for Cycloidal Motion using this online evaluator? To use this online evaluator 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 (θ_o) & Angle through Cam Rotates (θ_rotation) and hit the calculate button.

FAQs on Velocity of Follower after Time t for Cycloidal Motion

What is the formula to find Velocity of Follower after Time t for Cycloidal Motion?

The formula of Velocity of Follower after Time t for Cycloidal Motion is expressed as Velocity = (Angular Velocity of Cam*Stroke of Follower)/Angular Displacement of Cam during Out Stroke*(1-cos((2*pi*Angle through Cam Rotates)/(Angular Displacement of Cam during Out Stroke))). Here is an example- 386.8195 = (27*20)/1.396*(1-cos((2*pi*0.349)/(1.396))).

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

With Angular Velocity of Cam (ω), Stroke of Follower (S), Angular Displacement of Cam during Out Stroke (θ_o) & Angle through Cam Rotates (θ_rotation) we can find Velocity of Follower after Time t for Cycloidal Motion using the formula - Velocity = (Angular Velocity of Cam*Stroke of Follower)/Angular Displacement of Cam during Out Stroke*(1-cos((2*pi*Angle through Cam Rotates)/(Angular Displacement of Cam during Out Stroke))). This formula also uses Archimedes' constant and Cosine (cos) function(s).

What are the other ways to Calculate Velocity?

Here are the different ways to Calculate Velocity-

Velocity=Angular Velocity of Cam*(Radius of Circular Flank-Radius of the Base Circle)*sin(Angle Turned by Cam)

Can the Velocity of Follower after Time t for Cycloidal Motion be negative?

Yes, the Velocity of Follower after Time t for Cycloidal Motion, measured in Speed can be negative.

Which unit is used to measure Velocity of Follower after Time t for Cycloidal Motion?

Velocity of Follower after Time t for Cycloidal Motion is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Velocity of Follower after Time t for Cycloidal Motion can be measured.

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Velocity of Follower after Time t for Cycloidal Motion Formula

​GoVelocity of Follower for Circular Arc Cam if Contact is on Circular Flank Formula

Velocity of Follower after Time t for Cycloidal Motion Example

Velocity of Follower after Time t for Cycloidal Motion Solution

Velocity of Follower after Time t for Cycloidal Motion Formula Elements

Other Formulas to find Velocity

Other formulas in Follower Motion category

How to Evaluate Velocity of Follower after Time t for Cycloidal Motion?

FAQs on Velocity of Follower after Time t for Cycloidal Motion

Variable Name

GoVelocity of Follower for Circular Arc Cam if Contact is on Circular Flank Formula