Gough Stewart Platform

[XDN]

Hi

I want to use a hexapod (gough stewart platform)  in mechanical application.

The hexapode is formed with:

_ 1 base plate (ground)

_ 1 end effector (platform)

_ 6 leg (mechanical drive effector)

This system have 6 DoF for platform

For build this mechanical device, I need to calculate:

_ inverse kinematics : If i know the posture of platform, I find the leg lenght

  (the posture is : 3 positions : dX,dY,dZ and 3 rotations : dRX,dRY,dRZ)

_ Leg Forces (traction-compression only generated in leg)

For start, i build the geometrical model, for this, i define a ground mark : O with coordinates 0,0,0

1)

I define the hinge point of base : Ai

2)

I define the hinge point of platform : Bi

3)

I define the C point is the géometrical center of platform

Now the leg are AiBi vector

I define a user mark

The  user mark M ( 3 positions + 3 orientations) is define to mark O ( the origin of mark M is the point of interest)

For moving the platform, i define a new mark Mc from M

This mark is mark M augmented with strokes

And finally i calculate the AiBi vector, and i find the leg lenght.

I calculate AiBi at nominal position : not mouved platform

I calculate AiBi at mouved position

I find the stroke of effector (leg displacement)

Now I have a problem for Trajectory calculation

For know the stroke of effector, is necessary to compute leg lenght for trajectory.

The start point is define with stroke (in Mc)

dXmin  dRXmin

dYmin  dRYmin

dZmin dRZmin

The end point is

dXmax  dRXmax

dYmax  dRYmax

dZmax dRZmax

I use a lambda parameter for hash trajectory with 20 points for example

Now I find 20 group of position parameter.

I want to run my calculus for all position  group, and finally i make a graph with leg lenght for position parameter group.

My calculus is right for calculate leg lenght for one position of platforme in 3D space.

But i can’t calculate for trajectory ( group of parameter ) and i can’t make a graph

I’am a mechanical men, not a software programmer (lol)

Do you can to help me ?

[XDN]

Now for my problem

i try to write it

 But it's wrong, because it calculate only with  the last value of position parameter

[BA_8808696]

Hey @XDN,

I'm a student and need to do the same calculations as u do for a racing simulator. Did you manage to get the right calculations?

Kind regards

[XDN]

Hello

Yes , my calculation is right.

But, it is not applicable for simulation.

Because, for the stewart platform, i use the inverse kinematic model.

For simulation system, it is necessary use the direct kinematic model. Because, you need a coordinates plateform with length leg.

But for this calculation, we must resolve with Newton's algorithm. (because it's impossible to get a literal solution for this)

I don't make that, because i need only stewart platform for positionning system.

[BA_8808696]

@XDN Can you send me the mathcad file? I only need to calculate the inverse kinematics, for the simulations we use drives from Beckhoff so we don't need to calculate any direct kinematics

[XDN]

the control system has nothing to do with here.

But as you want...

i can't send my file because belongs my company

But, in my post you have lot of information for rebuild this.

i can help you, with light mathcad file, but, now i don't have time for this

if you have need only inverse kinematic, it's only vector calculation with Chasles relation

[BA_8808696]

Ok, thanks for the help! Much appreciated!