Re: Open (i think) design for a parallel robot (reprap may be interested)

I've been thinking about this quite a bit.

The problem breaks down to a couple of different issues. In a
cartesian positioner, everything is fairly simple. Calibration is
linear -- a step corresponds to a linear displacement in x,y, or z. Or
it corresponds to an angle in a rotary table.

On the other hand, calibration of a stewart platform, or delta robot
requires that for every movement in x,y, or z you have to adjust the
position of all the servos. 6 for hexapod platforms, and 3 for the
delta robots. And it's not linear -- you have a higher resolution in
the center sweet spot than you have at the limits of movement.

The inverse kinematic transform appears to be stable for both and have
unique solutions. This means for any x,y,z coordinate, you arrive at
only one solution for leg-lengths to get to it.

So what does this mean to the home-shop or hobbiest builder? There
would be a layer of software between the xyz and the motor positioner
that would be responsible for positioning. This transform also
introduces some quantization error and also decouples the g-code
interpreter from the actual motor positions.

I'd venture that most people who build machines don't really
understand the details of PID controllers, basically because most
people aren't required to learn calculus, but are more than capable of
using or even expertly tuning them. This level of abstraction doesn't
seem insurmountable.

On the other hand, you do need to develop a transform for your own
machine. It might seem daunting to delve into the matrix math, but the
functions used in them are all high-school trig and geometry. This
could be facilitated by a module that calculates it for you, I
suppose, taking parameters in the form of leg length and platform
size, and doing the transform for you.

Building a delta robot isn't all that difficult either, and it's a
fine platform to set a router on, especially if you're carving 3D
shapes. The accuracy of the ball and socket joints seems crucial, but
like I said, I think you could grind a ball on the end of a rod and
clamp a delrin socket around it. Since all three axes are identical,
you repeat it rather than have three different axis designs.

The other crucial thing is the gearbox for the servo arm. It's a lot
different than mill screws, and probably more expensive. I'm still
pondering that.

Anyway, that's it for my thinking on the matter. I did pull down a
couple of Matlab simulations on hexapods to play with. If I learn
anything useful to home CNC, I'll let y'all know.

On 8/28/06, Graham Stabler <eexgs@...> wrote:
>
> No way, a hexapod is a can of worms. Software, calibration, joint
> accuracy, singularities etc etc