I need to understand how to set up an equation.
The problem is related to creating a curve to execute a 4th axis wrap solution for helical groove milling.
The situation is I want to create a variable helix which varies smoothly and uniformly along its length. This means the helix angle of the groove would begin at 0° when the groove is parallel to the indexer axis, and 90° would be the logical maximum when the groove is an annular ring around the part.
Now, the length of the part could be variable, and the rate of change of the helix angle/unit length would be another variable.
Now I've been told that the solution to this is a parabola, but that doesn't really help me set up an equation.
According to customer specifications, the helix angle at the beginning and at the end of the part is defined. So, I know two slopes, and can graph their locations.
My question is how to derive the correct equation for general application in this situation. I've googled quadratic equations and parabolas already, and recall the stuff about vertices, and intercepts, but that doesn't really clue me in on how the equation is derived to begin with. Anybody can solve the damn thing once you've got one
Help, pretty please?