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XDN14-Alexandrite
14-Alexandrite
January 17, 2023
Solved

Equation solving

  • January 17, 2023
  • 3 replies
  • 8495 views

Hi community

I don't know how to use prime to find solutions to a robotic problem this problem is based on matrix calculus for a serial type robot it is easy to determine the direct geometry, i.e. to express the generalized coordinates according to the joint coordinates The difficulty is to solve the inverse geometry, that is to say determine the coordinates of the joints according to the generalized coordinates usually this uses Paul's iterative method I don't know how to solve these equations with Mathcad see the attached sheet

Best answer by Werner_E

Prime does not have a "do ... while" or "REPEAT ... UNTIL" kind of loop which would be more appropriate for this task.

Nonetheless here a shorter version which avoids doubling the calculation of X.

It makes one additional iteration step at the end, though!

Werner_E_3-1701815870247.png

 

3 replies

X
XDN14-AlexandriteAuthor
14-Alexandrite
January 17, 2023

1.png2.png3.png4.png

L
LucMeekes23-Emerald IV
23-Emerald IV
January 17, 2023

From your description it is not clear to me how q is used in producing Uo. That makes it difficult to find q from a given Uo.

 

Here's your file in Prime 6, for a broader audience.

 

Success!

Luc

W
Werner_E25-Diamond I
25-Diamond I
January 18, 2023

Werner_E_0-1674002254227.png

 

X
XDN14-AlexandriteAuthor
14-Alexandrite
January 18, 2023

the joint variable q is (in this example)  RZ1 and RZ2

to show the variables,  is necessary to rewrite TG with symbolic parameter

symbolic TJ1:

5.png

symbolic TJ2:

6.png

Symbolic TG

7.png

 

And finally

8.png

sorry it was true that it was not clear

 

 

 

W
Werner_E25-Diamond I
25-Diamond I
January 18, 2023

The reason for the "solve" command failing could be because you end up with much more single equations compared to just two unknowns.

Furthermore the symbolics doesn't know "deg". You may try to define deg:=pi/180 at the top of the sheet (deg must be labelled as unit) or you use radians throughout.

 

And I just notice that you demand the impossible:

Werner_E_0-1674034147939.png

 

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