Mechanical torsors

[XDN]

Hi

I want to solve a mechanical torsors problem, but I don't know how to go about it with Mathcad

I have a circular platform. on this platforme i have 3 point B1,B2,B3

on each point i have a forces, respectively F1,F2,F3. About it i know directional vector for each forces.

My platform have a spherical joint in this center (point C).

And i have a torsor which define exterior mechanical load applied on platform at C point.

1°/ i write mechanical component:

obviously expressed respectively at each point

 Now, i want to solve it find FB1,FB2,FB3,X,Y,Z

For this, i want to make a torsors transportation on C point!

And now! i am stuck😥

I make a light mc file for add to this post

[XDN]

And after all torsors transportation, i want to solve the system like this example:

Resultant theorem:
/ X : -0,9911.FB1 -0,9911.FB2 -0,9911.FB3 +XO = 0
/ Y : 0,1152.FB2 -0,1152.FB3 +YO = 0
/ Z : -0,1330.FB1 +0,0665.FB2 +0,0665.FB3 +ZO -12000 = 0
resultant moment theorem :
/ X : 0,0669.FB2 -0,0003.FB3 -1115 = 0
/ Y : 188,3112.FB1 -94,1556.FB2 -94,1556.FB3 +66000 = 0
/ Z : 164,0736.FB2 -163,0825.FB3 = 0

and finally:

FB1 = 16463,46
FB2 = 16763
FB3 = 16864,87
XO = 49646,1
YO = 11,74
ZO = 11953,37

I can to solve it with pen and paper, but i can't do it with mathcad

I can see that there is a problem with symbolic evaluations

😥

[LucMeekes]

My answers are different from yours. I may have made an error somewhere...

Anyway, you should be able to do this in Prime.

Success!
Luc

[XDN]

great! for different value,

it comes from me because the values of the points have changed slightly

[XDN]

It is possible to keep the formalism of mechanical load, because it's clearer for mechanical readers

[XDN]

I rewrite first matrix, in second equation , with correct values

 

But i see a problem in first line

if i solve that

 the calculation does not converge ...😓

[LucMeekes]

Please attach your worksheet.

Success!
Luc

[XDN]

it's strange

if i rewrite the vector value: i modify the red point value

The matrix is now:

And the calculation is done

[LucMeekes]

 I don't see a compelling reason for these programs of yours. You can just write:

and

to get the two matrices.

Success!
Luc

[XDN]

see attached file

it's strange, i copy paste in new sheet.

If i switch this matrix

The calculus run but it's wrong

if i use the matrix as in picture, the calculus is good

if i switch , it's wrong

[LucMeekes]

For the upper left matrix, the determinant is 0, it means the matrix is singular, or in other words, it cannot be inverted.

 That means that lsolve cannot find a solution.

For the lower left matrix that's not the sae, and lsolve can find a solution.

Success!
Luc

[LucMeekes]

Maybe this helps..?

Success!
Luc

[XDN]

in fact from a mechanical point of view, this means that the forces go towards infinity in the singular geometric position ?🙄

in your new calculation, if i use initial geometrical configuration the result are:

obviously this is absurd

If i slip a bit the geometrical value, the result are conform to your screenshot in you precedent post.

these values seem correct to me.

For mechanical design, these values do not need to be very precise

Perhaps it is possible to evaluate the geometrical parameter just before singularity 🤔

I don't know how to do that

in any case thank you very much for your very precious help🙂

and I understand better your first approach

[XDN]

however there are other things that don't work

If i move the Bpoints the geometrical value was changed.

The calculation run

but key result are curious ?

If i calculate this manually, i find approximately:

FB1 = -202569,41
FB2 = -194324,39
FB3 = -194325,75
XO = 584902,22
YO = 0,16
ZO = 13455,71

and the worksheet give

see attached full worksheet (sorry it is written in french)

[LucMeekes]

I have only a vague idea of what your calculations are about.

My responses have been from a(n almost pure) mathematical viewpoint, and knowledge of Mathcad/Prime,

just trying to streamline your calculations and potentially reducing the amount of typing (which is a general source of error).

Success!

Luc