## Wally Kinematics

### Re: Wally Kinematics

Hi,

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

Geri
geristockreiter

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### Re: Wally Kinematics

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.
Nicholas Seward

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Joined: Mon Nov 25, 2013 10:41 pm

### Re: Wally Kinematics

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.

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Joined: Tue Feb 03, 2015 6:17 pm

### Re: Wally Kinematics

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.

It is not a constant. The wrist stays parallel to the line from elbow to elbow. Fun fun math
Nicholas Seward

Posts: 738
Joined: Mon Nov 25, 2013 10:41 pm

### Re: Wally Kinematics

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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Joined: Tue Feb 03, 2015 6:17 pm

### Re: Wally Kinematics

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.
Nicholas Seward

Posts: 738
Joined: Mon Nov 25, 2013 10:41 pm

### Re: Wally Kinematics

Posts: 5
Joined: Tue Feb 03, 2015 6:17 pm

### Re: Wally Kinematics

So my previous post had several significant math errors in it and has been deleted accordingly.
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.

$B = \sqrt{x^2+y^2}$
$C=arccos(\frac{x}{b})$ derivative, not used
$D=arccos(\frac{b}{2a})$ derivative, not used
$E=\sqrt{a^2+x^2-2ax\cdot cos(c+d)} = \sqrt{a^2+xy\sqrt{4a^2-b^2}}$
$F=arcsin(\frac{a\cdot sin(c+d)}{e})$ derivative, not used
$G=e\cdot sin(f)=\frac{b\sqrt{1-x^2}+x\sqrt{4a^2-b^2}}{2b}$
$H=e\cdot cos(f)=\sqrt{e^2-g^2}$
$K=arctan(\frac{g}{h+h{}'})$ derivative, not used
$X_{e}=\frac{mg}{\sqrt{g^2+(h+h{}')^2}}$
$Y_{e}=\frac{m(h+h{}')}{\sqrt{g^2+(h+h{}')^2}}$

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 $\sqrt{4a^2-b^2}$ for later use.
2 square roots, 8 multiplies, 2 division, 2 addition, 2 subtraction (G) remember we have$\sqrt{4a^2-b^2}$ 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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Joined: Tue Feb 03, 2015 6:17 pm

### Re: Wally Kinematics

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.
cdsteinkuehler

Posts: 74
Joined: Tue Nov 26, 2013 1:53 am

### Re: Wally Kinematics

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 ?
Doglo

Posts: 1
Joined: Fri Mar 20, 2015 4:29 pm

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