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Displacement of Follower after Time t for Cycloidal Motion Formula

GoDisplacement of Follower for Circular Arc Cam, there's Contact on Circular Flank Formula

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Displacement of Follower is the linear movement of the follower in a cam-follower mechanism, which converts rotary motion into linear motion. Check FAQs

d follower = S \cdot (\frac{θ rotation}{θ o} \cdot \frac{180}{π} - \sin (\frac{2 \cdot π \cdot θ rotation}{θ o}))

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

Displacement of Follower after Time t for Cycloidal Motion Example

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

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

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

266.4789 = 20 \cdot (\frac{0.349}{1.396} \cdot \frac{180}{3.1416} - \sin (\frac{2 \cdot 3.1416 \cdot 0.349}{1.396}))

266.4789m = 20m \cdot (\frac{0.349rad}{1.396rad} \cdot \frac{180}{3.1416} - \sin (\frac{2 \cdot 3.1416 \cdot 0.349rad}{1.396rad}))

266.4789 = 20 \cdot (\frac{0.349}{1.396} \cdot \frac{180}{3.1416} - \sin (\frac{2 \cdot 3.1416 \cdot 0.349}{1.396}))

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Displacement of Follower after Time t for Cycloidal Motion Solution

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

FIRST Step Consider the formula

d follower = S \cdot (\frac{θ rotation}{θ o} \cdot \frac{180}{π} - \sin (\frac{2 \cdot π \cdot θ rotation}{θ o}))

Next Step Substitute values of Variables

∴

d follower = 20m \cdot (\frac{0.349rad}{1.396rad} \cdot \frac{180}{π} - \sin (\frac{2 \cdot π \cdot 0.349rad}{1.396rad}))

Next Step Substitute values of Constants

∴

d follower = 20m \cdot (\frac{0.349rad}{1.396rad} \cdot \frac{180}{3.1416} - \sin (\frac{2 \cdot 3.1416 \cdot 0.349rad}{1.396rad}))

Next Step Prepare to Evaluate

∴

d follower = 20 \cdot (\frac{0.349}{1.396} \cdot \frac{180}{3.1416} - \sin (\frac{2 \cdot 3.1416 \cdot 0.349}{1.396}))

Next Step Evaluate

∴

d follower = 266.478897565412m

LAST Step Rounding Answer

∴

d follower = 266.4789m

Displacement of Follower after Time t for Cycloidal Motion Formula Elements

Variables

Constants

Functions

Displacement of Follower

Displacement of Follower is the linear movement of the follower in a cam-follower mechanism, which converts rotary motion into linear motion.

Symbol: d_follower

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Displacement of Follower

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

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

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

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

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.

Syntax: sin(Angle)

Other Formulas to find Displacement of Follower

Go Displacement of Follower for Circular Arc Cam, there's Contact on Circular Flank

d follower = (r Base - r 1) \cdot (1 - \cos (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 Displacement of Follower after Time t for Cycloidal Motion?

Displacement of Follower after Time t for Cycloidal Motion evaluator 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 evaluate 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 evaluate Displacement of Follower after Time t for Cycloidal Motion using this online evaluator? To use this online evaluator 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.

FAQs on Displacement of Follower after Time t for Cycloidal Motion

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

The formula of Displacement of Follower after Time t for Cycloidal Motion is expressed as 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))). Here is an example- 266.4789 = 20*(0.349/1.396*180/pi-sin((2*pi*0.349)/(1.396))).

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

With Stroke of Follower (S), Angle through Cam Rotates (θ_rotation) & Angular Displacement of Cam during Out Stroke (θ_o) we can find Displacement of Follower after Time t for Cycloidal Motion using the formula - 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))). This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Displacement of Follower?

Here are the different ways to Calculate Displacement of Follower-

Displacement of Follower=(Base Radius of Truncated Cone-Radius of the Base Circle)*(1-cos(Angle Turned by Cam))

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

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

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

Displacement of Follower after Time t for Cycloidal Motion is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Displacement of Follower after Time t for Cycloidal Motion can be measured.

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Displacement of Follower after Time t for Cycloidal Motion Formula

​GoDisplacement of Follower for Circular Arc Cam, there's Contact on Circular Flank Formula

Displacement of Follower after Time t for Cycloidal Motion Example

Displacement of Follower after Time t for Cycloidal Motion Solution

Displacement of Follower after Time t for Cycloidal Motion Formula Elements

Other Formulas to find Displacement of Follower

Other formulas in Follower Motion category

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

FAQs on Displacement of Follower after Time t for Cycloidal Motion

Variable Name

GoDisplacement of Follower for Circular Arc Cam, there's Contact on Circular Flank Formula