Wally Kinematics

Re: Wally Kinematics

Postby geristockreiter » Wed Feb 25, 2015 11:21 am

Hi,

the diagram above for the math is awsome. Are there a similar diagram for GUS?
Thanks,

Geri
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Re: Wally Kinematics

Postby Nicholas Seward » Wed Feb 25, 2015 11:28 am

GUS uses the pythagorean theorem. All you have to do is calculate the distance from the effector (x,y,z) to the reference z at a pivot (xp,yp,z_ref). The linear nature of the arms makes it easy.
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Re: Wally Kinematics

Postby bloodyshadow13 » Thu Feb 26, 2015 11:15 pm

I hope that you don't mind the minor threadjacking, but did anyone ever figure out where the dlcj version of Wally's wrist points to? Another way of putting it is where does the line perpendicular to the dlcj point to? I'm trying to figure out where that would put the hotend.
Thanks in advance.
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Re: Wally Kinematics

Postby Nicholas Seward » Fri Feb 27, 2015 12:07 am

bloodyshadow13 wrote:I hope that you don't mind the minor threadjacking, but did anyone ever figure out where the dlcj version of Wally's wrist points to? Another way of putting it is where does the line perpendicular to the dlcj point to? I'm trying to figure out where that would put the hotend.
Thanks in advance.

It is not a constant. The wrist stays parallel to the line from elbow to elbow. Fun fun math
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Re: Wally Kinematics

Postby bloodyshadow13 » Fri Feb 27, 2015 11:51 pm

That math is digusting. I think I'll keep the concentric mount unless anyone has a better idea for wally's wrist joint. Has no one tried putting Gus Simpson arms on wally? I'm trying to figure out if it would make the xy simpler maths for slightly more complex construction.
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Re: Wally Kinematics

Postby Nicholas Seward » Sat Feb 28, 2015 1:05 am

GUS arms would have super easy math. (Easy means no trig so it is easy to do on old hardware.). That is probably the best plan.
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Re: Wally Kinematics

Postby bloodyshadow13 » Mon Mar 02, 2015 12:28 am

-snip for bad maths-
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Re: Wally Kinematics

Postby bloodyshadow13 » Sat Mar 07, 2015 8:15 am

So my previous post had several significant math errors in it and has been deleted accordingly. :oops:
Hopefully this post will have no math errors. If you find any, please point them out.
My idea at some point is to build Bob Wally with a bit of a twist. I'm going back to the DLCJ on the wrist, as well as a DLCJ on each shoulder.
This approach is very one sided, so I have reassigned the variables.
The line between the shoulders is Y=0.
Prime marks designate the far side arm.
A is the arm length.
B is the distance from the shoulder to the wrist joint.
C is the angle between the shoulder line and B.
D is the angle between B and the upper arm.
E is the distance from the elbow to the point(x,0).
F is the angle between the shoulder line and E.
G is the y-height of the elbow.
H is the distance of x (l-x on the far side) plus the x-length of the elbow.
K is the angle between the y axis and the extruder stub arm.
L is the distance between the shoulders.
M is the length of the extruder stub arm.
Xe is the X offset of the extruder.
Ye is the Y offset of the extruder.

Image
Image derivative, not used
Image derivative, not used
Image
Image derivative, not used
Image
Image
Image derivative, not used
Image
Image

By my count (at 23:00 with work in the morning)
2 square roots, 4 multiplies, 2 addition that we have to do for free to drive the elbows. (B)
4 square roots, 12 multiplies, 2 addition, 2 subtraction (E) also gives us Image for later use.
2 square roots, 8 multiplies, 2 division, 2 addition, 2 subtraction (G) remember we haveImage already.
2 square roots, 4 multiplies, 2 subtraction (H)
1 square roots, 4 multiplies, 2 division, 2 addition (Xe & Ye) I only did H+Hprime and G^2+H+Hprime once each.
The total damage comes to :
11 square roots, 32 multiplies, 4 division, 8 addition, 6 subtraction
Using the figures in this blog: http://markdow.blogspot.com/2011/06/blink-of-eye-processing-on-arduino.html I calculate that this will take a grand total of 1.12 milliseconds, or 892 operations/second if we use floating point math. Is this fast enough? Or do I need to do all of this in integers to achieve 0.638 milliseconds, or 1,560 operations/second?
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Re: Wally Kinematics

Postby cdsteinkuehler » Sat Mar 07, 2015 12:15 pm

Over 1 millisecond for just the kinematics is probably too slow, but you could cheat (ie: do what the existing AVR delta firmwares do: run 100-200 kinematics calculations/s and linearly interpolate in between).

But I'd just recommend getting a faster CPU. If you don't want to jump to something as complex as Linux and a BeagleBone or x86 system running Machinekit (what I'm using), get one of the Cortex-M boards (Smoothie, Azteeg x5, R2C2, etc). Then you can (mostly) just write code, without having to carve out spare cycles from _somewhere_ to get it to run.
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Re: Wally Kinematics

Postby Doglo » Fri Mar 20, 2015 4:37 pm

Hello! :)

Is it possible to control a wally with LinuxCNC without going through a BEAGLEBONE, installing the Wallykins.c kinematics with sudo comp --install wallykins.c ?
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