Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank Calculator

✖Angular velocity of cam refers to how fast an object rotates or revolves relative to another point.ⓘ Angular Velocity of Cam [ω]			+10% -10%
✖Radius of circular flank is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.ⓘ Radius of Circular Flank [R]			+10% -10%
✖Radius of the base circle is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.ⓘ Radius of the Base Circle [r₁]			+10% -10%
✖The total angle of action of cam is the total angle moved by the cam during the time between the beginning of rising and the end of return of the follower.ⓘ Total Angle of Action of Cam [α₂]			+10% -10%

✖Acceleration of follower is the rate of change in velocity to the change in time.ⓘ Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank [a]

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Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Total Angle of Action of Cam)
a = ω^2*(R-r₁)*cos(α₂)
This formula uses 1 Functions, 5 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

Acceleration of Follower - (Measured in Meter per Square Second) - Acceleration of follower is the rate of change in velocity to the change in time.
Angular Velocity of Cam - (Measured in Radian per Second) - Angular velocity of cam refers to how fast an object rotates or revolves relative to another point.
Radius of Circular Flank - (Measured in Meter) - Radius of circular flank is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
Radius of the Base Circle - (Measured in Meter) - Radius of the base circle is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
Total Angle of Action of Cam - (Measured in Radian) - The total angle of action of cam is the total angle moved by the cam during the time between the beginning of rising and the end of return of the follower.

STEP 1: Convert Input(s) to Base Unit

Angular Velocity of Cam: 27 Radian per Second --> 27 Radian per Second No Conversion Required
Radius of Circular Flank: 4.955 Meter --> 4.955 Meter No Conversion Required
Radius of the Base Circle: 4.98 Meter --> 4.98 Meter No Conversion Required
Total Angle of Action of Cam: 9.5 Radian --> 9.5 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = ω^2*(R-r₁)*cos(α₂) --> 27^2*(4.955-4.98)*cos(9.5)

Evaluating ... ...

a = 18.1734625466793

STEP 3: Convert Result to Output's Unit

18.1734625466793 Meter per Square Second --> No Conversion Required

FINAL ANSWER

18.1734625466793 ≈ 18.17346 Meter per Square Second <-- Acceleration of Follower

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Cams » Mechanical » Acceleration of the Follower » Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank

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National Institute Of Technology (NIT), Hamirpur

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< Acceleration of the Follower Calculators

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

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*Distance b/w Cam Center and Nose Center*(cos(Angle Turned by Cam When Roller is at Nose Top)+(Distance b/w Roller Centre and Nose Centre^2*Distance b/w Cam Center and Nose Center*cos(2*Angle Turned by Cam When Roller is at Nose Top)+Distance b/w Cam Center and Nose Center^3*(sin(Angle Turned by Cam When Roller is at Nose Top))^4)/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))

Acceleration of Follower after Time t for Cycloidal Motion

LaTeX Go Acceleration of Follower = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2)*sin((2*pi*Angle Through Which Cam Rotates)/(Angular Displacement of Cam During Out Stroke))

Acceleration of Follower for Roller Follower Tangent Cam, there's Contact with Straight Flanks

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*(Radius of the Base Circle+Radius of Roller)*(2-cos(Angle Turned by Cam from Beginning of Roller))^2/((cos(Angle Turned by Cam from Beginning of Roller))^3)

Acceleration of Follower for Circular Arc Cam if there's Contact on Circular Flank

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Angle Turned by Cam)

Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank Formula

LaTeX Go

Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Total Angle of Action of Cam)
a = ω^2*(R-r₁)*cos(α₂)

what is circular arc cam?

When the flanks of the cam connecting the nose and base circles are of a convex circular arc, such cams are referred to as circular arc cams.

How to Calculate Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank?

Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank calculator uses Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Total Angle of Action of Cam) to calculate the Acceleration of Follower, Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank formula is defined as the acceleration of the follower in a circular arc cam contacting with a circular flank, which is a critical parameter in cam design, affecting the smoothness and efficiency of the motion. Acceleration of Follower is denoted by a symbol.

How to calculate Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank using this online calculator? To use this online calculator for Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank, enter Angular Velocity of Cam (ω), Radius of Circular Flank (R), Radius of the Base Circle (r₁) & Total Angle of Action of Cam (α₂) and hit the calculate button. Here is how the Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank calculation can be explained with given input values -> -3.634693 = 27^2*(4.955-4.98)*cos(9.5).

FAQ

What is Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank?

Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank formula is defined as the acceleration of the follower in a circular arc cam contacting with a circular flank, which is a critical parameter in cam design, affecting the smoothness and efficiency of the motion and is represented as a = ω^2*(R-r₁)*cos(α₂) or Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Total Angle of Action of Cam). Angular velocity of cam refers to how fast an object rotates or revolves relative to another point, Radius of circular flank is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length, Radius of the base circle is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length & The total angle of action of cam is the total angle moved by the cam during the time between the beginning of rising and the end of return of the follower.

How to calculate Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank?

Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank formula is defined as the acceleration of the follower in a circular arc cam contacting with a circular flank, which is a critical parameter in cam design, affecting the smoothness and efficiency of the motion is calculated using Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Total Angle of Action of Cam). To calculate Minimum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank, you need Angular Velocity of Cam (ω), Radius of Circular Flank (R), Radius of the Base Circle (r₁) & Total Angle of Action of Cam (α₂). With our tool, you need to enter the respective value for Angular Velocity of Cam, Radius of Circular Flank, Radius of the Base Circle & Total Angle of Action of Cam and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Acceleration of Follower?

In this formula, Acceleration of Follower uses Angular Velocity of Cam, Radius of Circular Flank, Radius of the Base Circle & Total Angle of Action of Cam. We can use 3 other way(s) to calculate the same, which is/are as follows -

Acceleration of Follower = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2)*sin((2*pi*Angle Through Which Cam Rotates)/(Angular Displacement of Cam During Out Stroke))
Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Angle Turned by Cam)
Acceleration of Follower = Angular Velocity of Cam^2*(Radius of the Base Circle+Radius of Roller)*(2-cos(Angle Turned by Cam from Beginning of Roller))^2/((cos(Angle Turned by Cam from Beginning of Roller))^3)

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