(CLICK HERE to view the math behind polynomial cam motion)

High speed cams are used in many machinery applications.  Today's stringent design requirements - coupled with ever-increasing machine speeds, has made the engineering of cam motions a very demanding science.  At Genesis Innovation the mathematics of Matrix Algebra is employed to give our customers control over their cam motions.

What do we mean by this?  Conventional trigonometric cams - modified sine, cycloidal, trapezoidal, etc. - are encumbered with natural restrictions, namely the inability to impose desired properties within each individual cam motion.  Essentially, a trigonometric curve accomplishes a displacement over a cam angle; the resulting velocity, acceleration, and pulse (derivative of acceleration) usually fall to natural values and cannot be changed without revising the displacement, the cam angle, or both.  Therefore one is left with cam parameters that "are what they are," such as pressure angle, radius of curvature, normal force, contact stress, and alternating shear stress.

Conversely, polynomials provide "control" over key points in a cam motion, allowing desired results to be built in, rather than occurring by "luck of the draw."

So what benefit does this bring to a machine's operation? 

- reduction in critical design "tradeoffs"

- reduced stress

- longer cam life

- longer follower life

- "smoother" motions

- kinetic energy where you need it

- inertial energy where you need it

- the exact displacement you need, where you need it

- highly proprietary designs

As an example, in all cams - no matter what type motion is used - velocity has an effect on all important parameters, including acceleration, pulse, pressure angle, radius of curvature, normal force, contact stress, and maximum alternating shear stress, as illustrated by the following flowchart:

 In a polynomial cam motion, these parameters may be "synthetically altered" via the velocity, with primary impact specifically upon the radius of curvature and pressure angle.  Secondary impact is had upon pulse and normal force; tertiary upon contact stress; and remote influence upon maximum alternating shear stress.

Acceleration, in turn, may be used to "fine tune" the pulse, normal force, radius of curvature, contact stress, and alternating shear stress, as illustrated below:

In this case, acceleration has a primary effect upon pulse, normal force, and radius of curvature; and secondary upon contact stress and alternating shear stress.

Lastly, the pulse may be used to "micro-tune" the normal force, contact stress, and maximum alternating shear stress:

In this last case, pulse has a primary effect upon normal force and a secondary upon both contact stress and maximum alternating shear stress.

The bottom line: With polynomial motion it is easier to take control of your designs by allowing for the "burying," if you will, of constraints necessary in desired cam properties, usually anywhere within the cam.

Contact us today to see how we can assist you with this crucial element in your design.