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

✖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.ⓘ Distance b/w Roller Centre and Nose Centre [L]			+10% -10%
✖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.ⓘ Distance b/w Cam Center and Nose Center [r]			+10% -10%
✖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.ⓘ Angle Turned by Cam when Roller is at Nose Top [θ₁]			+10% -10%

✖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.ⓘ Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact [d_roller]

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Formula

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

Formula

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

Example

6.191531 m = 33.89 m + 15.192 m - 15.192 m \cdot \cos (0.785 rad) - \sqrt{{33.89 m}^{2} - {15.192 m}^{2} \cdot {(\sin (0.785 rad))}^{2}}

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
d_roller = L+r-r*cos(θ₁)-sqrt(L^2-r^2*(sin(θ₁))^2)
This formula uses 3 Functions, 4 Variables

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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., sqrt(Number)

Variables Used

Displacement of Roller - (Measured in Meter) - 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.
Distance b/w Roller Centre and Nose Centre - (Measured in Meter) - 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.
Distance b/w Cam Center and Nose Center - (Measured in Meter) - 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.
Angle Turned by Cam when Roller is at Nose Top - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Distance b/w Roller Centre and Nose Centre: 33.89 Meter --> 33.89 Meter No Conversion Required
Distance b/w Cam Center and Nose Center: 15.192 Meter --> 15.192 Meter No Conversion Required
Angle Turned by Cam when Roller is at Nose Top: 0.785 Radian --> 0.785 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_roller = L+r-r*cos(θ₁)-sqrt(L^2-r^2*(sin(θ₁))^2) --> 33.89+15.192-15.192*cos(0.785)-sqrt(33.89^2-15.192^2*(sin(0.785))^2)

Evaluating ... ...

d_roller = 6.19153121359904

STEP 3: Convert Result to Output's Unit

6.19153121359904 Meter --> No Conversion Required

FINAL ANSWER

6.19153121359904 ≈ 6.191531 Meter <-- Displacement of Roller

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Cams » Cam and Follower » Mechanical » Tangent Cam » Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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< Tangent Cam Calculators

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

Go Velocity = Angular Velocity of Cam*Distance b/w Cam Center and Nose Center*(sin(Angle Turned by Cam when Roller is at Nose Top)+(Distance b/w Cam Center and Nose Center*sin(2*Angle Turned by Cam when Roller is at Nose Top))/(2*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)))

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

Go 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)

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

Go Velocity = Angular Velocity of Cam*(Radius of the Base Circle+Radius of Roller)*sin(Angle Turned by Cam from Beginning of Roller)/((cos(Angle Turned by Cam from Beginning of Roller))^2)

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

Go Distance b/w Roller Centre and Nose Centre = Radius of Roller+Radius of Nose

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

What is Tangent Cam with Reciprocating Roller Follower?

Tangent cam with reciprocating followers is an example of cams with specified contours. Tangent cams are symmetric about the centerline of the camshaft and hence they fall into a category of cams with specified contours. Tangent cams are symmetrical about the centerline of the camshaft.

How to Calculate 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 calculator 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 calculate 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 calculate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact using this online calculator? To use this online calculator 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. Here is how the Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact calculation can be explained with given input values -> 6.190474 = 33.89+15.192-15.192*cos(0.785)-sqrt(33.89^2-15.192^2*(sin(0.785))^2).

FAQ

What is 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 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 and is represented as d_roller = L+r-r*cos(θ₁)-sqrt(L^2-r^2*(sin(θ₁))^2) or 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). 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, 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 & 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.

How to calculate 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 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 is calculated using 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 calculate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact, you need 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). With our tool, you need to enter the respective value for Distance b/w Roller Centre and Nose Centre, Distance b/w Cam Center and Nose Center & Angle Turned by Cam when Roller is at Nose Top and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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