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

--- In CAD_CAM_EDM_DRO@yahoogroups.com, "Dennis Schmitz"
<denschmitz@...> wrote:

>
> 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.

Delta robots can also be 6-axis. The "deltaness" comes from the fact
they use rotational actuators. You can build three axis platforms
with either actuator type.

> This means for any x,y,z coordinate, you arrive at
> only one solution for leg-lengths to get to it.

Actually you will always get at least two but you can normally ignore
one of them. The second solution is when the whole mechanism is
toggled or turned inside out. You can remove the generalism of the
matrix form and "tell it" which way it is basically configured

> 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.

When using mach I set up secondary axes, these were the actuator
postitions which were defined in terms of the primary axes using the
equations function. The quantization error is no more of a problem
than it is for a normal machine thought the positional error will tend
to grow as you move from the sweetspot.

> 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.

What's your point?

>> 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

I sometimes wonder if I am talking to myself. I have posted a link to
my kinematics page at least twice. You don't need matrix maths you
can calculate the lengths or base positions directly using pythagorus.
For example if you take a triaglide, you know the position you want
the table to be in, the points on the rail where the carriage should
be are given by the intersection of a sphere with a line. i.e. the
possible positions of the struts other end with the rail. You will
get two solutions but you can ignore one. Also if you keep the
equation in its most general form you can account for rails not being
parallel etc.

>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.

PLEASE have a look at my page, you will see that ball joints aren't
even needed.

> 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.

Again see my page, there is a cool way of getting high gear ratios
using a belt.

Bottom line, I think triaglides and deltas have real homebrew
possibilities, I've done the ground work, please run with it. BUT
hexapods specifically don't fit the bill for reprap or most homebrew.

Cheers,

Graham

www.indoor.flyer.co.uk/kinematics.htm