Gabriel Chilli Case Study Solution

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Over the discussions we had with Gabriel LAPILLI, it was pretty obvious that to make the calculations of three rotation angles, we would use three markers at each node in order to create a coordinate system at each of them. I did that part by myself while Aymerick ROUSSEY was involved on the other project to make the drawings of the sloshing machine. I worked on the possible solutions for some months and my work is presented in annex 6. When Gabriel LAPILLI had important updates on his part of the project, we restored the weekly teleconferences that had stopped between the 13th of April and the 8th of June. During these teleconferences, we discussed about the optimal solution we could set up for the static testing. He actually presented his …show more content…

I found several ways to easily calculate plane angles thanks to Matlab, but most of them were inaccurate because the angle was flipping around of 180 degrees between two frames. The solution I chose was not to calculate the angle between a reference vector and a current vector, but to calculate the angle between the segment created by the two markers and one of the absolute axis of the Optitrack system, and then compare it to the one that was calculated during the reference frame. After a subtraction, we have the relative angle that is the torsion angle. Moreover, this process takes in account the errors in the alignment of the markers, and eliminates it. If at the reference, the torsion value is “0 + error” and at the current frame we calculate “torsion + error”, at the end, torsion + error –error = torsion. The formula I used was: Torsion=〖tan〗^(-1)⁡〖( (x_B-x_A)/(y_B-y_A ) ) 〗 The interesting property of the formula is that it works even if you invert the position in the substation, which was my issue at the beginning: when this is automated, you don’t know the order in the operation because it depends on the order in which the markers are

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