I really should charge for this, but........

When designing a cam, you must first decide whether to make it symmetrical, or unsymmetrical--opening and closing sides different. I have done unsymmetrical cam design only since 1977, although some of my symmetrical cam designs of the early 1970s are still being made today.

Each side needs at least 2 seperate equations, and I have used as many as 5 or 6, per side...... A design needs a ramp, and a flank, and all my work at Competition Cams was of this sort, what I call '4-Equation' cams, opening ramp, opening flank, closing flank, closing ramp.

Each equation has to have starting and ending conditions, at least 4 of each, and they are: Displacement, Velocity, Acceleration, and Jerk. Where 2 equations meet, they must meet in ALL 4 conditions, or you get infinite spikes in Jerk, at the least. This means the equation has to have 8 exponents, although some exponents may be 0, and some of the coefficients may be 0.

Exponents may vary from 0 to as high as 99, although I've never used any that high. Picking the right exponents is one of the major factors in good cam design. It is learned only through trial and a lot of error. As a point of interest, Displacement, ie---cam lift, always has the exponent 0.

Acceleration at the nose means there has to be an exponent of 2 present, to give a real 2nd derivative.

I have equations written to help design cams as far as the 4th derivative, Harvey's 'Snap'. Once you get into 5 or 6 0s before the 1st signifigant digit, ie---.000001", one-millionth of an inch, I wonder if there is any noticable benefit in further pursuit of derivatives. It's a very good cam grinder indeed that is more accurate than .0001".......

That's enough to get you thinking for the next year.....

UDHarold

BTW, I am self-taught in cam design, although I did get a B in Differential Equations in Jr. college....