CAM Follower-II

Terminology of Radial Cam

Base Circle

It is the smallest circle tangent to the cam profile drawn from the centre of rotation of the radial cam. The base circle decides the overall size of the cam and thus is fundamental feature.

Trace Point

The points on the follower which is required to trace the cam profile is known as trace point. For a roller follower, the trace point is at the roller centre.

Pitch Curve

The curve traced by trace point is known as pitch curve. It is parallel to the cam profile.

Prime Circle

It is the smallest circle that can be drawn so as to be tangential to the pitch curve, with its centre at the cam centre.

Pressure Angle

The angle between the direction of the follower movement and the normal to the pitch curve at any point is called pressure angle. It represents the steepness of the cam profile. Higher the pressure angle higher is side thrust and higher the chances of jamming the translating follower in its guide ways.

Pitch Point

It is the point on pitch curve at which pressure angle is maximum.

Lift (or) stroke

It is the maximum travel of the follower from its lowest position to the topmost position.

Follower Displacement Diagram

Angle of Ascent

It is the angle through which the cam turns during the time the follower rises.

Angle of Dwell

It is the angle through which the cam turns while the follower remains stationary at the highest or the lowest position.

Angle of Descent

It is the angle through which the cam turns while follower returns to the initial position.

Angle of Action

It is the total angle moved by the cam during the time between the beginning of rise and the end of return of the follower.

Force Exerted by Cam

The force exerted by a cam on the follower is always normal to the surface of the cam at the point of contact. The vertical component (F cosα) lifts the follower whereas the horizontal component(F sinα) exerts lateral pressure on the bearing. To reduce the lateral pressure, α has to be decreased which means making the cam surface more convex or longer but that reduces the velocity of follower. The minimum value of α can not be reduced from a certain value.

Kinematics:

Let's say s is the displacement of the follower and θ is cam angle.

Velocity of the follower = \( \dot s = \frac{ds}{dt} = w\frac{ds}{dθ}\)

Where $\frac{ds}{dθ}$ represents the slope or the steepness of the displacement curve at each position of cam angle.

Acceleration of the follower = \( \ddot s = \frac{d^2 s}{dt^2} = w^2\frac{d^2s}{dθ^2}\)

• Higher value of acceleration means a higher inertia force.
• The value of $\frac{d^2s}{dθ^2}$ is inversely proportional to the radius of curvature of the cam at different points along its profile. 

Third derivative is known as 'Jerk' and higher values of jerk are undesirable.

\[Jerk = \dddot s = = \frac{d^3 s}{dt^3} = w^3\frac{d^3s}{dθ^3}\]

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Reference:

1. Theory of Machines By SS Rattan