Re: Tripod

Dear Graham Stabler:

Thank You. You're my Hero. I knew that you would have a simpler
solution for my problem based on the article that you wrote.

Thank you again.

Best regards,

Andrew





--- In CAD_CAM_EDM_DRO@yahoogroups.com, "Graham Stabler"
<grezmos@...> wrote:

>
> --- 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/mathsco
ntinuum/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
>