Cam and Follower Mechanisms – Design and Motion Analysis

A cam and follower mechanism converts rotary or reciprocating motion into a prescribed follower movement. The shape of the cam controls the follower displacement and can provide accurately timed rise, dwell and return motion within a machine cycle.

Cam systems are widely used where a relatively simple input motion must produce a more complex, accurately timed output motion. Applications include automatic machinery, engines, textile machinery, sewing machines, printing machinery and other mechanical systems requiring repeatable motion control.

Cam and Follower Principles

A cam is a machine element that rotates or reciprocates and acts upon a contacting component known as the follower. The cam profile is designed to produce the required follower motion.

Cam-follower mechanisms are particularly useful when the motion of one part of a machine must be converted into a prescribed motion of another part. The motion can include periods during which the follower remains stationary, known as dwells.

Cam systems can therefore replace relatively complicated linkage arrangements when a specific motion cycle is required.

In a cam system it is important that the follower remains in contact with the cam surface throughout the required operating cycle. Depending upon the mechanism, follower contact may be maintained by:

• gravity;
• a mechanical constraint, such as a groove or conjugate arrangement;
• spring force; or
• pneumatic or hydraulic force.

Types of Cam

Cams can be produced in several forms according to the required motion and mechanical arrangement. Common forms include:

• Plate or disc cam – a rotating plate having the required radial profile.
• Wedge or translating cam – a shaped member moving linearly relative to the follower.
• Cylindrical or barrel cam – a rotating cylinder incorporating a profiled groove or track.
• End or face cam – a cam in which the required profile is formed on the end or face of a rotating member.

Cam Followers

Cam followers may move in a straight line or oscillate about a pivot. The contact between the cam and follower can also take several forms.

Common follower types include:

• knife-edge follower;
• flat-faced follower;
• roller follower; and
• curved or spherical-faced follower.

For a translating follower, the line of follower motion may pass through the camshaft centre, producing an in-line follower, or it may be displaced from the camshaft centre by an offset.

Design of Cam Systems

An important early stage in cam design is the definition of the required follower motion. This is commonly represented by a displacement diagram, in which follower displacement is plotted against cam rotation angle.

A typical plate cam with an in-line roller follower and its associated displacement diagram is shown below.

The principal features include:

• Rise – the portion of the cycle during which the follower moves away from its initial position.
• Dwell – a period during which follower displacement remains constant while the cam continues to rotate.
• Return – the portion of the cycle during which the follower moves back towards its initial position.
• Base circle – the smallest circle, centred on the cam axis, that is tangent to the cam profile.
• Prime circle – for a roller follower, the circle centred on the cam axis and passing through the roller centre when the follower is at its lowest position.
• Cam profile – the working surface of the cam that determines the follower motion.

The slope of the displacement diagram represents displacement change with cam angle and is therefore related to follower velocity. The shape of the motion curve also determines follower acceleration and the resulting dynamic forces.

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Cam Profile Construction

The following examples illustrate several basic follower arrangements and the construction of the corresponding cam profile.

Plate Cam with Flat-Faced Follower

The diagram below shows a plate cam with a flat-faced translating follower at twelve successive cam positions.

Plate Cam with Offset Roller Follower

The diagram below shows a plate cam with an offset roller follower at twelve successive cam positions.

Plate Cam with Oscillating Follower

The diagram below shows a plate cam with a pivoted oscillating follower at twelve successive cam positions.

Kinematic Relationships of Cam Motion

For a translating follower, the displacement diagram may be expressed as follower displacement y as a function of cam angle θ:

$$y=f\left(\theta \right)$$

Differentiating the displacement with respect to cam angle gives the kinematic coefficients used to determine follower velocity and acceleration.

First-Order Kinematic Relationship

$$f^{\prime }\left(\theta \right)=\frac{dy}{d\theta }$$

This is the rate of change of follower displacement with cam angle. If the cam rotates at angular velocity ω, the follower velocity is:

$$v=\frac{dy}{dt}=\omega \frac{dy}{d\theta }$$

Large values of displacement change over a small cam angle can require steep cam profiles and may lead to excessive pressure angles, side forces or unfavourable follower motion. These effects must be considered when selecting the cam geometry.

Second-Order Kinematic Relationship

$$f^{″}\left(\theta \right)=\frac{d^{2}y}{d{\theta }^2}$$

For a cam rotating at constant angular velocity, follower acceleration is:

$$a={\omega }^2\frac{d^{2}y}{d{\theta }^2}$$

Follower acceleration is important because it produces inertia forces within the follower system. Excessive acceleration can increase contact forces, vibration, noise and wear, and can contribute to loss of follower contact at higher operating speeds.

Cam design must therefore consider not only the required displacement but also the resulting velocity, acceleration, pressure angle, cam-profile curvature and contact stresses.

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