parallel scara inverse kinematics

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 10:31AM by ekaggrat.

if you share some images maybe I can solve it

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 09:15PM by ekaggrat.

Quote
ekaggrat
hi gomez

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

avl6lQX.jpg

and the working diagram is like this :

ZnWcO1W.jpg

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 12/23/2013 02:36AM by Gomez.Marcos.

hi gomez..

thanks for the great solution ... I just couldn't understand what ang 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 12/23/2013 02:17AM by ekaggrat.

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 12/23/2013 02:36AM by Gomez.Marcos.

it gives a error when put into a excel...

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

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 03:57AM by Gomez.Marcos.

works like a charm

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

time to build it



Edited 2 time(s). Last edit at 12/23/2013 11:13AM by ekaggrat.

Finally done

hackaday

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?

@tomso

thanks

most of the stuff is here
hackaday project
the hardest part is winding the coils so it is not a easy build..

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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I noticed that the firmware called the kinematic inverse solution of the SCARA robot before calling the plan_buffer_line function, and then assigns the calculated three joint angle values to the plan_buffer_line function.After reading the plan_buffer_line function in detail, I feel that this is wrong. 
This is because all the computational algorithmic processes in the function are directed to Cartesian Cartesian coordinate space, for example:

block->millimeters = sqrt(square(delta_mm[X_HEAD]) + square(delta_mm[Y_HEAD]) + square(delta_mm[Z_AXIS]));

This is to calculate the spatial moving distance through the three target coordinates of Cartesian space. If it is replaced by three joint angle values, is this wrong?
The latter algorithm has similar problems, especially the Breasham algorithm in ISR, which is completely an algorithm of Cartesian space. If the value passed to the algorithm is three joint angle values, I think it should be incorrect.
I looked at the code for the marlin 1.1 version and there are similar issues.
I hope that my doubts can be answered, thank you!
My email address: [email protected]