How to Convert the Unit Vector of "ijk" to Roll, Pitch, and Yaw ???

[The SAINTaholic]

We make canopys for aircraft. Some of these canopys need to have different types of coatings on their concaved surfaces. We have a robot that has the capability to do this but it needs the roll pitch and yaw values to be able to program it correctly. We do have all the "points" of the surfaces on CAD..... The idea is to be able to simply open up an Excel sheet with this formulation and type in the "ijk" values ("points" in CAD) which will pop up the Roll Pitch and Yaw values.....

Incase anybody is wondering; the formulation is:

Z″(α)oX′(β)oZ(γ) = [ (X′(β)z(γ)) o z(α) o (X′(β)z(γ))−1 ] o X′(β) o z(γ)

= [ {z(γ)x(β)z(−γ) z(γ)} o z(α) o {z(−γ) z(γ)x(−β)z(−γ)} ] o [ z(γ)x(β)z(−γ) ] o z(γ)

= z(γ)x(β)z(α)x(−β)x(β) = z(γ)x(β)z(α) .

http://en.wikipedia.org/wiki/Tait-Bryan_angles


We just dont know how to insert this formula into Excel so that all we have to do is type in the ijk unit vectors......


Thank you in advanced....
Ron

 

[ThePaladinGuild]

SAINT,

In what format does your CAD program export the data points (e.g. comma deliminated text file)?

-- Matthew

 

[The SAINTaholic]

SAINT,

In what format does your CAD program export the data points (e.g. comma deliminated text file)?

-- Matthew

Yes, its Comma Deliminated......

 

[ThePaladinGuild]

I still need a little more to go on...

How many values in the list? Will it always be the same number of values? Does your CAD program do all the Calculus you listed, or are you needing Excel to run the derivatives?


-- Matthew

 

[The SAINTaholic]

I still need a little more to go on...

How many values in the list? Will it always be the same number of values? Does your CAD program do all the Calculus you listed, or are you needing Excel to run the derivatives?


-- Matthew

Matthew,

I really dont know right now. Im asking this question thru one of our other engineers; and actually Im now at home.... It will be Monday when I can answer your question....... Thank you so much for your interest thus far, I really hope you can help us!!! Apparently this is something that our engineer has been literally "banging" his head on and about for quite sometime now...
Thanks again, and I will be posting the answer to your question sometime Monday...

FYI: Our company: www.texstars.com


Ron

 

[The SAINTaholic]

I still need a little more to go on...

How many values in the list? Will it always be the same number of values? Does your CAD program do all the Calculus you listed, or are you needing Excel to run the derivatives?


-- Matthew

Matthew,
Ok, here's the answers to the questions you are needing (I hope.... Remember, I'm asking these thru another engineer):

Your Questions:

"How many values in the list?" ---- X,Y,Z,I,J,K.
"Will it always be the same number of values?" ---- Yes.
"Does your CAD program do all the Calc?" ---- No, it doesn't; we do need Excel to run the derivatives.

Once again Matthew, I totally appreciate you and others in here on your help in this.

Ron