Cams and Followers

Why it matters

Cams and followers are essential components in mechanical systems, used to convert rotary motion into linear motion. They are widely used in internal combustion engines, automated machinery, and various industrial applications to achieve precise motion control and timing.

Key ideas

• Cam: A rotating or sliding piece in a mechanical linkage used especially in transforming rotary motion into linear motion or vice versa.
• Follower: A component that moves in response to the cam's motion, typically translating the cam's rotary motion into linear motion.
• Types of Cams:
  • Disk or Plate Cam: A flat, disk-shaped cam with a profile cut into its edge.
  • Cylindrical Cam: A cam with a cylindrical shape, where the follower moves parallel to the axis of the cylinder.
  • Translating Cam: A cam that moves in a straight line, with the follower moving in a corresponding linear path.
• Types of Followers:
  • Knife-edge Follower: A follower with a sharp edge that contacts the cam surface.
  • Roller Follower: A follower with a rolling element to reduce friction.
  • Flat-faced Follower: A follower with a flat surface in contact with the cam.
  • Spherical Follower: A follower with a spherical surface in contact with the cam.
• Cam Profile: The actual shape of the cam surface that dictates the motion of the follower.
• Lift or Stroke: The maximum displacement of the follower from its lowest position.
• Dwell: A period during which the follower remains stationary while the cam continues to rotate.

Motion law

Follower lift is set by the prescribed displacement law and cam profile. It cannot be found by subtracting roller radius from base-circle radius. Followers may translate or oscillate.

For constant cam speed ω, v = ω ds/dθ and a = ω² d²s/dθ², with θ in radians. If ω varies, add α ds/dθ to acceleration. For simple harmonic rise of height h over cam angle β:

s = (h/2)[1 − cos(πθ/β)], 0 ≤ θ ≤ β.

v = (hπω/(2β)) sin(πθ/β).

Worked example

A roller follower is specified to rise 40 mm with simple harmonic motion during 120° of cam rotation. The cam turns at a constant 600 rpm. Find displacement and velocity halfway through the rise.

ω = 2π(600)/60 = 62.8319 rad/s, β = 2π/3 rad, and θ = β/2.

s = h/2 = 20 mm and v = hπω/(2β) = 1.885 m/s. Acceleration at that midpoint is zero for this ideal motion law. A 50 mm base circle and a 10 mm roller alone would provide insufficient information to determine the lift.

At rise/dwell boundaries, assess velocity, acceleration, and jerk continuity; an SHM rise adjoining a dwell has an acceleration discontinuity.

Common mistakes

• Confusing the types of followers and their applications.
• Inferring stroke from the base circle and roller radius without a motion law or profile.
• Forgetting to convert RPM to rad/s when calculating angular velocity.

For GATE ME

Questions on cams and followers often involve calculating the displacement, velocity, and acceleration of the follower, as well as understanding the cam profile and its effects on motion. Practicing problems involving different types of cams and followers, and their kinematic analysis, is crucial.

Quick check

1. What is the primary function of a cam in a mechanical system?
2. Name two types of followers used in cam mechanisms.
3. How is the angular velocity of a cam calculated from its RPM?

Answers: 1. To convert rotary motion into linear motion. 2. Knife-edge follower, Roller follower. 3. ω = 2πN / 60.