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Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Formula

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Displacement of Roller is the linear movement of the roller as it rotates and translates along the cam's surface, affecting the follower's motion. Check FAQs

d roller = L + r - r \cdot \cos (θ 1) - \sqrt{L^{2} - r^{2} \cdot {(\sin (θ 1))}^{2}}

d_roller - Displacement of Roller?L - Distance b/w Roller Centre and Nose Centre?r - Distance b/w Cam Center and Nose Center?θ₁ - Angle Turned by Cam when Roller is at Nose Top?

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Example

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Here is how the Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact equation looks like with Values.

Here is how the Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact equation looks like with Units.

Here is how the Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact equation looks like.

6.1915 = 33.89 + 15.192 - 15.192 \cdot \cos (0.785) - \sqrt{{33.89}^{2} - {15.192}^{2} \cdot {(\sin (0.785))}^{2}}

6.1915m = 33.89m + 15.192m - 15.192m \cdot \cos (0.785rad) - \sqrt{{33.89m}^{2} - {15.192m}^{2} \cdot {(\sin (0.785rad))}^{2}}

6.1915 = 33.89 + 15.192 - 15.192 \cdot \cos (0.785) - \sqrt{{33.89}^{2} - {15.192}^{2} \cdot {(\sin (0.785))}^{2}}

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Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Solution

Follow our step by step solution on how to calculate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?

FIRST Step Consider the formula

d roller = L + r - r \cdot \cos (θ 1) - \sqrt{L^{2} - r^{2} \cdot {(\sin (θ 1))}^{2}}

Next Step Substitute values of Variables

∴

d roller = 33.89m + 15.192m - 15.192m \cdot \cos (0.785rad) - \sqrt{{33.89m}^{2} - {15.192m}^{2} \cdot {(\sin (0.785rad))}^{2}}

Next Step Prepare to Evaluate

∴

d roller = 33.89 + 15.192 - 15.192 \cdot \cos (0.785) - \sqrt{{33.89}^{2} - {15.192}^{2} \cdot {(\sin (0.785))}^{2}}

Next Step Evaluate

∴

d roller = 6.19153121359904m

LAST Step Rounding Answer

∴

d roller = 6.1915m

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Formula Elements

Variables

Functions

Displacement of Roller

Displacement of Roller is the linear movement of the roller as it rotates and translates along the cam's surface, affecting the follower's motion.

Symbol: d_roller

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Displacement of Roller

Distance b/w Roller Centre and Nose Centre

Distance b/w Roller Centre and Nose Centre is the length between the centre of the roller and the nose centre in a cam and follower mechanism.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance b/w Roller Centre and Nose Centre

Distance b/w Cam Center and Nose Center

Distance b/w cam center and nose center is the length between the center of the cam and the nose center in a cam-follower mechanism.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance b/w Cam Center and Nose Center

Angle Turned by Cam when Roller is at Nose Top

Angle Turned by cam when roller is at nose top is the rotational movement of the cam when the roller is positioned at the highest point of the cam's nose.

Symbol: θ₁

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle Turned by Cam when Roller is at Nose Top

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)

cos

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

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Tangent Cam category

Go Velocity of Follower of Roller Follower Tangent Cam for Contact with Nose

v = ω \cdot r \cdot (\sin (θ 1) + \frac{r \cdot \sin (2 \cdot θ 1)}{2 \cdot \sqrt{L^{2} - r^{2} \cdot {(\sin (θ 1))}^{2}}})

Go Velocity of Follower for Roller Follower Tangent Cam if Contact is with Straight Flanks

v = ω \cdot (r 1 + r roller) \cdot \frac{\sin (θ)}{{(\cos (θ))}^{2}}

Go Distance between Roller Center and Nose Center of Tangent Cam with Roller Follower

L = r roller + r nose

Go Condition for Contact of Roller if Straight Flank Merges into Nose Tangent Cam with Roller Follower

θ 1 = α - φ

How to Evaluate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact evaluator uses Displacement of Roller = Distance b/w Roller Centre and Nose Centre+Distance b/w Cam Center and Nose Center-Distance b/w Cam Center and Nose Center*cos(Angle Turned by Cam when Roller is at Nose Top)-sqrt(Distance b/w Roller Centre and Nose Centre^2-Distance b/w Cam Center and Nose Center^2*(sin(Angle Turned by Cam when Roller is at Nose Top))^2) to evaluate the Displacement of Roller, Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact formula is defined as the linear distance moved by the roller follower in a tangent cam mechanism, considering the nose contact point, which affects the overall motion of the follower and the cam's rotational angle. Displacement of Roller is denoted by d_roller symbol.

How to evaluate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact using this online evaluator? To use this online evaluator for Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact, enter Distance b/w Roller Centre and Nose Centre (L), Distance b/w Cam Center and Nose Center (r) & Angle Turned by Cam when Roller is at Nose Top (θ₁) and hit the calculate button.

FAQs on Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact

What is the formula to find Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?

The formula of Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact is expressed as Displacement of Roller = Distance b/w Roller Centre and Nose Centre+Distance b/w Cam Center and Nose Center-Distance b/w Cam Center and Nose Center*cos(Angle Turned by Cam when Roller is at Nose Top)-sqrt(Distance b/w Roller Centre and Nose Centre^2-Distance b/w Cam Center and Nose Center^2*(sin(Angle Turned by Cam when Roller is at Nose Top))^2). Here is an example- 6.190474 = 33.89+15.192-15.192*cos(0.785)-sqrt(33.89^2-15.192^2*(sin(0.785))^2).

How to calculate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?

With Distance b/w Roller Centre and Nose Centre (L), Distance b/w Cam Center and Nose Center (r) & Angle Turned by Cam when Roller is at Nose Top (θ₁) we can find Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact using the formula - Displacement of Roller = Distance b/w Roller Centre and Nose Centre+Distance b/w Cam Center and Nose Center-Distance b/w Cam Center and Nose Center*cos(Angle Turned by Cam when Roller is at Nose Top)-sqrt(Distance b/w Roller Centre and Nose Centre^2-Distance b/w Cam Center and Nose Center^2*(sin(Angle Turned by Cam when Roller is at Nose Top))^2). This formula also uses Sine (sin)Cosine (cos), Square Root (sqrt) function(s).

Can the Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact be negative?

Yes, the Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact, measured in Length can be negative.

Which unit is used to measure Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact can be measured.

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Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Formula

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Example

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Solution

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Formula Elements

Other formulas in Tangent Cam category

How to Evaluate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?

FAQs on Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact

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