Who Like Math

[Spartacus51]

Alright, as instructed I've decided to make my spiral waterblock. I have a problem/question first. WTF is the rectangular equation of a spiral in terms of y= so that I can program it in my milling machine?

I've tried figuring it out to no avail. I've tried envisioning it, but when I do I find I'm looking at multiple logarithms... that's when I quit.


Please help!

:) :confused: :mad: :( :burn: :beer:

[PsYko420]

Where in the hick filled lands of wisconsin do you live? I'm residing in good ol' titletown.

[Samurai_Punch]

Ummm i don't think you can actually enter an equation of a spiral in the form of a rectangular equation in terms of y(x)... Because you can only have one solution (y) for the variable (x). But if you could enter the equation for the spiral in a polar equation it should work... i think... (it'd help if i could find my TI-whatever the number is)

But then again it's been awhile since i've done math at this level... :D
i shoulda paid more attention in AP Calc... and in college...:eh?:

[Holst]

Using a polar system its easy.

But a X/Y equation is benond my ability, or to be more precice its late and I cant be arsed.

It would probably be simpler to figure out a easyer way to program the CNC than do the maths.

[ButcherUK]

Here's a parametric equation for a spiral, if you want something else you'll have to work it out :)
x = (t/2)cos(t)
y = (t/2)sin(t)
for t = 0...2np, where n is the number of full turns in the spiral.

EDIT: just had a think, it's not possible to form an equation of the form y = f(x) to get a spiral as that would be a one-to-many mapping.

[Ridenow]

Thank you ButcherUK. I was afraid I would have bust out a trig book.

[Spartacus51]

First, from Lake Mills, cold damp corner of Hell between Madison and Milwaukee.

Second, i understand that in terms y= the equation must be a function, except bear in mind that roots produce pos/neg answers. just not sure how it will all coincide.

Third, I'm beginning to agree, easier to find another way of programming the CNC, but now that I've started this fiasco of equation discovery I'm really quite determined to find out if it can be done.

[Spartacus51]

think of an x^(1/3) but the center needs to be twisted... somehow like making a parabola out of each of the arcs. Who knows, maybe it just plain can't be done. Keep looking and thinking though, I hope you're all as miserable as I am... ;)

[Ridenow]

I do not know if it is possible to program your machine, I do not what it's requirements are. I think that your prospects are good though. I remember programming a TI-81 calculator to convert cartesian to polar and graph it. I do not remember how I did it. I know where the trig anc calc books are, but not the calculator. I am cooking tonight for a party, so I will not have time to look for it today.

[Spartacus51]

Alright, so I figured out a way to make the spiral using something other than equations. I am a student of math though, so if anyone DOES know the equation, I'd still like to know. Also this saves any time that would be spent solving for y. Would just like to know how to conver polar -> rectangular

[Ridenow]

I found one calculator, but not the one with all the programs and the book. There is a program on it that graphs a polar equation. I know I wrote it, but it does not make sense to me today, it has been years. Here it is as near as I can type it:

lable 1
Polar function
rsin (theta) = y
rcos (theta) = x
Point on (x,y)
theta + .8 = theta
if theta < 4PI goto lable 1

[nihili]

Conversion equations can be found at

http://www.physics.udel.edu/~watson/phys345/class/07-convert.html

nihili