Displacement of Needle for Tangent Cam with Needle-Bearing Follower Calculator

✖Radius of the Base Circle is the radius of the circular base of the cam follower, which is a crucial component in mechanical systems.ⓘ Radius of the Base Circle [r₁]			+10% -10%
✖Radius of Roller is the distance from the center of the roller to its periphery in a cam and follower mechanism, affecting the motion of the follower.ⓘ Radius of Roller [r_roller]			+10% -10%
✖Angle Turned by Cam from Beginning of Roller is the rotation of the cam from the starting point of the roller in a cam-follower mechanism.ⓘ Angle Turned by Cam from Beginning of Roller [θ]			+10% -10%

✖Displacement of Needle is the linear movement of the needle in a cam and follower mechanism, indicating the follower's oscillatory motion.ⓘ Displacement of Needle for Tangent Cam with Needle-Bearing Follower [d_needle]

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Formula

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Displacement of Needle for Tangent Cam with Needle-Bearing Follower

Formula

d needle = (r 1 + r roller) \cdot (\frac{1 - \cos (θ)}{\cos (θ)})

Example

2.404204 m = (3 m + 33.37 m) \cdot (\frac{1 - \cos (170 rad)}{\cos (170 rad)})

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Displacement of Needle for Tangent Cam with Needle-Bearing Follower Solution

STEP 0: Pre-Calculation Summary

Formula Used

Displacement of Needle = (Radius of the Base Circle+Radius of Roller)*((1-cos(Angle Turned by Cam from Beginning of Roller))/cos(Angle Turned by Cam from Beginning of Roller))
d_needle = (r₁+r_roller)*((1-cos(θ))/cos(θ))
This formula uses 1 Functions, 4 Variables

Functions Used

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

Variables Used

Displacement of Needle - (Measured in Meter) - Displacement of Needle is the linear movement of the needle in a cam and follower mechanism, indicating the follower's oscillatory motion.
Radius of the Base Circle - (Measured in Meter) - Radius of the Base Circle is the radius of the circular base of the cam follower, which is a crucial component in mechanical systems.
Radius of Roller - (Measured in Meter) - Radius of Roller is the distance from the center of the roller to its periphery in a cam and follower mechanism, affecting the motion of the follower.
Angle Turned by Cam from Beginning of Roller - (Measured in Radian) - Angle Turned by Cam from Beginning of Roller is the rotation of the cam from the starting point of the roller in a cam-follower mechanism.

STEP 1: Convert Input(s) to Base Unit

Radius of the Base Circle: 3 Meter --> 3 Meter No Conversion Required
Radius of Roller: 33.37 Meter --> 33.37 Meter No Conversion Required
Angle Turned by Cam from Beginning of Roller: 170 Radian --> 170 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_needle = (r₁+r_roller)*((1-cos(θ))/cos(θ)) --> (3+33.37)*((1-cos(170))/cos(170))

Evaluating ... ...

d_needle = 2.40420413901074

STEP 3: Convert Result to Output's Unit

2.40420413901074 Meter --> No Conversion Required

FINAL ANSWER

2.40420413901074 ≈ 2.404204 Meter <-- Displacement of Needle

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Cams » Cam and Follower » Mechanical » Tangent Cam » Displacement of Needle for Tangent Cam with Needle-Bearing Follower

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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 Needle for Tangent Cam with Needle-Bearing Follower 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 Needle for Tangent Cam with Needle-Bearing Follower?

Displacement of Needle for Tangent Cam with Needle-Bearing Follower calculator uses Displacement of Needle = (Radius of the Base Circle+Radius of Roller)*((1-cos(Angle Turned by Cam from Beginning of Roller))/cos(Angle Turned by Cam from Beginning of Roller)) to calculate the Displacement of Needle, Displacement of Needle for Tangent Cam with Needle-Bearing Follower formula is defined as the measure of the movement of the needle in a tangent cam with a needle-bearing follower, which is a critical component in mechanical systems, particularly in engines and gear mechanisms. Displacement of Needle is denoted by d_needle symbol.

How to calculate Displacement of Needle for Tangent Cam with Needle-Bearing Follower using this online calculator? To use this online calculator for Displacement of Needle for Tangent Cam with Needle-Bearing Follower, enter Radius of the Base Circle (r₁), Radius of Roller (r_roller) & Angle Turned by Cam from Beginning of Roller (θ) and hit the calculate button. Here is how the Displacement of Needle for Tangent Cam with Needle-Bearing Follower calculation can be explained with given input values -> 2.404204 = (3+33.37)*((1-cos(170))/cos(170)).

FAQ

What is Displacement of Needle for Tangent Cam with Needle-Bearing Follower?

Displacement of Needle for Tangent Cam with Needle-Bearing Follower formula is defined as the measure of the movement of the needle in a tangent cam with a needle-bearing follower, which is a critical component in mechanical systems, particularly in engines and gear mechanisms and is represented as d_needle = (r₁+r_roller)*((1-cos(θ))/cos(θ)) or Displacement of Needle = (Radius of the Base Circle+Radius of Roller)*((1-cos(Angle Turned by Cam from Beginning of Roller))/cos(Angle Turned by Cam from Beginning of Roller)). Radius of the Base Circle is the radius of the circular base of the cam follower, which is a crucial component in mechanical systems, Radius of Roller is the distance from the center of the roller to its periphery in a cam and follower mechanism, affecting the motion of the follower & Angle Turned by Cam from Beginning of Roller is the rotation of the cam from the starting point of the roller in a cam-follower mechanism.

How to calculate Displacement of Needle for Tangent Cam with Needle-Bearing Follower?

Displacement of Needle for Tangent Cam with Needle-Bearing Follower formula is defined as the measure of the movement of the needle in a tangent cam with a needle-bearing follower, which is a critical component in mechanical systems, particularly in engines and gear mechanisms is calculated using Displacement of Needle = (Radius of the Base Circle+Radius of Roller)*((1-cos(Angle Turned by Cam from Beginning of Roller))/cos(Angle Turned by Cam from Beginning of Roller)). To calculate Displacement of Needle for Tangent Cam with Needle-Bearing Follower, you need Radius of the Base Circle (r₁), Radius of Roller (r_roller) & Angle Turned by Cam from Beginning of Roller (θ). With our tool, you need to enter the respective value for Radius of the Base Circle, Radius of Roller & Angle Turned by Cam from Beginning of Roller 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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