PSI - Issue 8

F. Caputo et al. / Procedia Structural Integrity 8 (2018) 297–308 Author name / Structural Integrity Procedia 00 (2017) 000 – 000 Where = [ 1 , 2 , 3 , 4 ] is the quaternion vector and is the rotation matrix defined as follows: ( ) = [ 12 − 22 − 32 + 02 2( 1 2 − 3 0 ) 2( 1 3 + 2 0 ) 2( 1 2 + 3 0 ) − 12 + 22 − 32 + 02 2( 2 3 − 1 0 ) 2( 1 3 − 2 0 ) 2( 2 3 + 1 0 ) − 12 − 22 + 32 + 02 ] (4) The transformation between q and the Euler angles is:

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= tan −1 ( 2( 1 2 − 0 3 ) 1−2( 22 + 32 ) ) = tan −1 ( 2( 2 3 − 0 1 ) 1−2( 12 + 22 ) ) = sin −1 (−2( 1 3 + 0 2 )) 01 = (q 1 ) ( ( 0 )) 02 = ( 2 ) ( ( 0 )) 12 = ( 2 ) ( ( 1 ))

(5)

The upper limb pose is composed of an absolute orientation of the trunk, plus the relative orientation of arms about shoulder and the relative orientation of forearm about elbow. Given the symmetry of the arm problem, generally speaking, let’s call the orientation of trunk, the orientation of arm and the orientation of forearm, the relative transformation matrices can be written as follows:

(6)

Where is the transformation matrix between trunk and arm, 02 is the transformation matrix between trunk and forearm and 12 is the transformation matrix between arm and forearm. 2.5 Test cases In order to test the goodness of the presented method, two test cases in industrial environment have been carried out. In particular, the same activity, for two different cars, has been analysed in two different plants of FCA (Fiat Chrysler Automobiles): central tunnel assembly for Alfa Romeo MiTo, at Mirafiori Plant, and Jeep Renegade, at Melfi Plant. The two mentioned plant have different production volumes: at Mirafiori Plant 80 cars per day are produced, instead at Melfi plant the production cycle foresees 405 cars per day. About Alfa Romeo MiTo, central tunnel assembly needs one worker, in a cycle time of 360 s (6 minutes), while for Jeep Renegade the same activity need two workers in a cycle time of 60 s. In order to validate the iterative method proposed in this research, for both activities, virtual simulations have been realized and postural data have been acquired in assembly lines by means of the inertial motion capture, described above, and analysed in post-processing.