One mystery is solved. Need to divide by 2 turned out to be lack of parenthesis.
Correct factor of 1/sqrt2 became *sqrt2. (1/sqrt2 = sqrt2/2).

Second mystery, the modulus needs to be k*k. (now certain:-)

Also got rid of my negative sign. Learned a long time ago that if the professor's equations seem wrong, they are not, my thinking is wrong.
Now the undulary and nodoid line up with each other, at proper R and r, and the x-axis is the roll and revolve axis line.

Values of R and r corresponding to parameters a, b, and c for ellipse and hyperbola also solved.

Will post CMC8 later tonight, and word doc, and example node.

Still need to check if sample roulettes match the profiles.

A formula for the widths of the nodary would be nice...

- Brian