1. Date of download: 6/8/2016 Copyright © ASME. All rights reserved. From: Optimal Restraint for the Thoracic Compression of the SID-IIs Crash Dummy Using a Linear Spring- Mass Model J. Dyn. Sys., Meas., Control. 2013;135(3):031007-031007-8. doi:10.1115/1.4023397 The SID-IIs dummy and the optimal restraint model containing spring-mass representation of the dummy Figure Legend:

2. Date of download: 6/8/2016 Copyright © ASME. All rights reserved. From: Optimal Restraint for the Thoracic Compression of the SID-IIs Crash Dummy Using a Linear Spring- Mass Model J. Dyn. Sys., Meas., Control. 2013;135(3):031007-031007-8. doi:10.1115/1.4023397 Thoracic compression time history of optimization runs with different number of discretization in a 50 ms interval. Impactor has constant velocity of 9 m/s, and the allowable space between the impactor and the control points is 8 cm. Figure Legend:

3. Date of download: 6/8/2016 Copyright © ASME. All rights reserved. From: Optimal Restraint for the Thoracic Compression of the SID-IIs Crash Dummy Using a Linear Spring- Mass Model J. Dyn. Sys., Meas., Control. 2013;135(3):031007-031007-8. doi:10.1115/1.4023397 (a) The optimal control acceleration time history. u 1 : thoracic control point; u 2 pelvic control point. (b) Velocity time history for the impactor (z 1v ), the control points (y 1v for thoracic, y 2v for pelvic), and the thoracic mass (x 1v ) and pelvic mass (x 2v ). The control point velocity time histories correspond to the accelerations shown in Fig. 3(a). (c) Thoracic compression (y 1 -x 1 ), pelvic compression (y 2 - x 2 ) and lumbar spine shear deformation (x 2 -x 1 ) with the optimal solution. (d) Constrained responses normalized by their individual limits. z 1 -y 1 : space at thorax (limit: 10 cm); z 2 -y 2 : space at pelvis (limit: 10 cm); x 1acc : thoracic mass acceleration (limit: 650 m/s 2 ); f 2 : external pelvic load (limit: 8.8 kN). (e) thoracic control point force (f 1 ) and pelvic control point force (f 2 ) time history. (f) Thoracic control point force versus the relative motion between the impactor and the control point at thoracic location (f 1 ) and pelvic location (f 2 ). Figure Legend:

4. Date of download: 6/8/2016 Copyright © ASME. All rights reserved. From: Optimal Restraint for the Thoracic Compression of the SID-IIs Crash Dummy Using a Linear Spring- Mass Model J. Dyn. Sys., Meas., Control. 2013;135(3):031007-031007-8. doi:10.1115/1.4023397 (a) Velocity time history for impactor (z 1v ), the control points (y 1v for thoracic, y 2v for pelvic), and the thoracic mass (x 1v ) and pelvic mass (x 2v ). The control point velocity time histories correspond to the accelerations shown in Fig. 4(a). (b) Thoracic compression (y 1 -x 1 ), pelvic compression (y 2 -x 2 ) and lumbar spine shear deformation (x 2 -x 1 ) with the optimal solution. (c) Constrained responses normalized by their individual limits. z 1 -y 1 : space at thorax (limit: 6 cm); z 2 -y 2 : space at pelvis (limit: 8 cm); x 1acc : thoracic mass acceleration (limit: 650 m/s 2 ); f 2 : external pelvic load (limit: 8.8 kN). All constraints are satisfied within numerical tolerances. (d) Thoracic control point force (f 1 ) and pelvic control point force (f 2 ) time history. Figure Legend:

5. Date of download: 6/8/2016 Copyright © ASME. All rights reserved. From: Optimal Restraint for the Thoracic Compression of the SID-IIs Crash Dummy Using a Linear Spring- Mass Model J. Dyn. Sys., Meas., Control. 2013;135(3):031007-031007-8. doi:10.1115/1.4023397 The minimum thoracic compression theoretically possible as a function of the allowable space. Initial velocity is as shown, and −14 g deceleration is assigned to the impactor. Figure Legend:

6. Date of download: 6/8/2016 Copyright © ASME. All rights reserved. From: Optimal Restraint for the Thoracic Compression of the SID-IIs Crash Dummy Using a Linear Spring- Mass Model J. Dyn. Sys., Meas., Control. 2013;135(3):031007-031007-8. doi:10.1115/1.4023397 (a) Control point acceleration time history (u 1 : thoracic control point; u 2 : pelvic control point). The 100 g limit on the accelerations is clearly reflected. (b) Control point velocity time history (y 1v for thoracic, y 2v for pelvic), and the thoracic mass (x 1v ) and pelvic mass (x 2v ). The control point velocity time histories correspond to the accelerations shown in Fig. 6(a). (c) Thoracic compression (y 1 -x 1 ), pelvic compression (y 2 -x 2 ) and lumbar spine shear deformation (x 2 -x 1 ) with the optimal solution. (d) Constrained responses normalized by their individual limits. z 1 -y 1 : space at thorax (limit: 10 cm); z 2 -y 2 : space at pelvis (limit: 10 cm); x 1acc : thoracic mass acceleration (limit: 650 m/s 2 ); f 2 : external pelvic load (limit: 8.8 kN). (e) Thoracic control point force (f 1 ) and pelvic control point force (f 2 ) time history. Figure Legend: