Re: Tripod

--- In CAD_CAM_EDM_DRO@yahoogroups.com, "andrew777j2002"
<andrewj777@...> wrote:

>
> I want to build a three axis tripod 2D painting robot.
> I read your article about kinematics for Mach 3. My 3 motors will be
> placed 120 degrees apart with cable etc., could you explain and give
> the formula for the equations for a b and c. This will be cable,

wire > or toothed belt driven. I know a and b from your pdf I need to
know c.

>

So you will have three variable length cords going to a single point.
Using the same notation as the pdf and putting the third motor at X3
Y3 then the equation is simply:

r = sqrt((Y3 - Y) + (X - X3))

Draw it out and it should make sense.

> The next project would be 3-D.
> Wouldn't a 3-D tripod use (mathematically speaking) three spheres
> intersecting at 120 degrees, we then can use spherical coordinates

to determine the radiuii of the spheres for the end lengths of the

> cables.

You don't need to use sherical co-ordinates just pythagorus again but
this time in 3D

R = sqrt(x^2 + y^2 + z^2) the rest is just as in my pdf more or less,
I'll leave it as an exercise for you or I will do it for you but only
when you get the 2D version working :)

This should explain why the 3D pythagorus works:

http://www.education.vic.gov.au/images/content/studentlearning/mathscontinuum/drinkbox.gif

x^2+c^2 = d^2
but
a^2 + b^2 = x^2
so
a^2+b^2+c^2 = d^2
and hence
d = sqrt(a^2+b^2+c^2) (but use a=x, b=y, c=z)

Graham