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parallel scara inverse kinematics

Posted by ekaggrat 
parallel scara inverse kinematics
December 22, 2013 07:30AM
hi,
i am building a small robotic arm based on the parallel scara design ( some thing like the morgan ) , but i can't seem to find the equations for the inverse kinematics of this design... I know the equations for a serial scara robot..

Does anybody have any idea where i could find them ? Or any links to them

thanks

Edited 1 time(s). Last edit at 12/22/2013 07:31AM by ekaggrat.
Re: parallel scara inverse kinematics
December 22, 2013 03:44PM
if you share some images maybe I can solve it
Re: parallel scara inverse kinematics
December 22, 2013 06:14PM
hi gomez

thanks for the reply,,, the arm looks like this :



and the working diagram is like this :




i would be very grateful if you could provide me with a solution.. I am not a expert at this things...

thanks again


[imgur.com]
[imgur.com]

Edited 1 time(s). Last edit at 12/22/2013 06:15PM by ekaggrat.
Re: parallel scara inverse kinematics
December 22, 2013 08:51PM
Quote
ekaggrat
hi gomez

thanks for the reply,,, the arm looks like this :



and the working diagram is like this :




i would be very grateful if you could provide me with a solution.. I am not a expert at this things...

thanks again


[imgur.com]
[imgur.com]

We have x,y and we need two angles: one represents the height and the other the angle
first we need distance from x,y to axis :h= sqrt(x^2+y^2)
now angle between arms with law of cosines: angA= (L1^2+L2^2-h^2)/(2*L1*L2)
the angles of the parallelogram always add up to 360: angB=180-angA
calculate real height of arm: hA=sen(angB )*L2
height of arm's joint: hB=y-hA
ang2=asen(hB/L1)
ang1=angB+ang2

so to finish you have to do the next:
1°- angB=180-(L1^2+L2^2-x^2-y^2)/(2*L1*L2)
2°-ang2=asen(y-(sen(angB )*L2)/L1)
3°-ang1=angB+ang2

remember to copy the link finished at .jpg/.png/.* for the images

I like the arm design I'm going to use it at my printer

Edited 2 time(s). Last edit at 12/22/2013 11:36PM by Gomez.Marcos.
Re: parallel scara inverse kinematics
December 22, 2013 10:46PM
hi gomez..

thanks for the great solution ... I just couldn't understand what ang cool smiley is? is it ang B ?

assuming it is ang B i plugged the formulas into a excel and it doesn't seem to give a solution ... I think something is wrong....

Edited 1 time(s). Last edit at 12/22/2013 11:17PM by ekaggrat.
Attachments:
open | download - scara test.xls (17 KB)
Re: parallel scara inverse kinematics
December 22, 2013 11:17PM
yes, it is B

EDIT:
its true it have 2 errors one was of writing and the other is bigger lol
I used angB like ang1
give a me a minute

Edited 1 time(s). Last edit at 12/22/2013 11:36PM by Gomez.Marcos.
Re: parallel scara inverse kinematics
December 22, 2013 11:20PM
it gives a error when put into a excel...
Attachments:
open | download - scara test.xls (17 KB)
Re: parallel scara inverse kinematics
December 23, 2013 12:46AM
the formulas should be as follows :

1°- angB=180-Acos((L1^2+L2^2-sqrt(x^2+y^2))/(2*L1*L2))
2°-ang2=Asin(y-(sin(angB*L2)/L1)
3°-ang1=angB+ang2

but even with this the solution fails when angB > 90 degrees ..

so i think this approach might not work
Re: parallel scara inverse kinematics
December 23, 2013 12:49AM
now works fine test it

reduced:
angB=180-ACOS((L1^2+L2^2-x^2-y^2)/(2*L1*L2))
ang2=90-(ACOS((L1^2-L2^2+x^2+y^2)/(2*L1*RAIZ(x^2+y^2)))+(ATAN(x/y))
ang1=ang2+angB

Edited 1 time(s). Last edit at 12/23/2013 12:57AM by Gomez.Marcos.
Attachments:
open | download - scara test.xls (24 KB)
Re: parallel scara inverse kinematics
December 23, 2013 01:28AM
works like a charm

thanks a ton..........

time to build it



Edited 2 time(s). Last edit at 12/23/2013 08:13AM by ekaggrat.
Attachments:
open | download - Frame_00000.gif (64 KB)
Re: parallel scara inverse kinematics
October 07, 2015 02:18AM
Finally done

hackaday
Re: parallel scara inverse kinematics
March 11, 2016 01:44AM
Quote
ekaggrat
Finally done

hackaday

This is so cool ekaggrat, I love the doodle clock.

If I had that on my desk I'd watch it for hours lol. Are the plans to build it anywhere?
Re: parallel scara inverse kinematics
March 11, 2016 10:33PM
@tomso

thanks

most of the stuff is here
hackaday project
the hardest part is winding the coils so it is not a easy build..
Ambidextrous SCARA IK
September 04, 2016 09:27PM
Here's an OpenSCAD animatable demo of SCARA kinematics showing how an arm can change orientation in some situations.

[gist.github.com]


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