378 Appendix: Anthropometric Data Tables TABLE A.3.5a Fifty-Percentile (50%) Female Body Segment Origin Coordinates Relative to the Reference Frame of the Adjacent Lower Numbered Body Segment (in Feet) Body Segment Coordinates (ft) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.308 3 Upper torso (chest) 0.0 0.0 0.617 4 Upper left arm 0.0 0.635 0.442 5 Lower left arm 0.0 0.0 À0.892 6 Left hand 0.0 0.0 À0.892 7 Neck 0.0 0.0 0.600 8 Head 0.0 0.0 0.357 9 Upper right arm 0.0 À0.635 0.442 10 Lower right arm 0.0 0.0 À0.892 11 Right hand 0.0 0.0 À0.892 12 Upper right leg 0.0 À0.233 À0.049 13 Lower right leg 0.0 0.0 À1.417 14 Right foot 0.0 0.0 À1.283 15 Upper left leg 0.0 0.233 À0.049 16 Lower left leg 0.0 0.0 À1.417 17 Left foot 0.0 0.0 À1.283 Note: See Section 6.2 and Chapter 10, Refs. [3,4]. TABLE A.3.5b Ninety-Fifth-Percentile (95%) Female Body Segment Origin Coordinates Relative to the Reference Frame of the Adjacent Lower Numbered Body Segment (in Meters) Body Segment Coordinates (m) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.093 3 Upper torso (chest) 0.0 0.0 0.188 4 Upper left arm 0.0 0.194 0.135 5 Lower left arm 0.0 0.0 À0.272 6 Left hand 0.0 0.0 À0.272 7 Neck 0.0 0.0 0.183 8 Head 0.0 0.0 0.109 9 Upper right arm 0.0 À0.194 0.135 10 Lower right arm 0.0 0.0 À0.272 11 Right hand 0.0 0.0 À0.272 12 Upper right leg 0.0 À0.071 À0.015 13 Lower right leg 0.0 0.0 À0.432 14 Right foot 0.0 0.0 À0.391 15 Upper left leg 0.0 0.071 À0.015 16 Lower left leg 0.0 0.0 À0.432 17 Left foot 0.0 0.0 À0.391 Note: See Section 6.2 and Chapter 10, Refs. [3,4].
Appendix: Anthropometric Data Tables 379 TABLE A.3.6a Ninety-Fifth-Percentile (95%) Female Body Segment Origin Coordinates Relative to the Reference Frame of the Adjacent Lower Numbered Body Segment (in Feet) Body Segment Coordinates (ft) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.327 3 Upper torso (chest) 0.0 0.0 0.654 4 Upper left arm 0.0 0.634 0.469 5 Lower left arm 0.0 0.0 À0.946 6 Left hand 0.0 0.0 À0.946 7 Neck 0.0 0.0 0.637 8 Head 0.0 0.0 0.379 9 Upper right arm 0.0 À0.674 0.469 10 Lower right arm 0.0 0.0 À0.946 11 Right hand 0.0 0.0 À0.946 12 Upper right leg 0.0 À0.247 À0.052 13 Lower right leg 0.0 0.0 À1.503 14 Right foot 0.0 0.0 À1.361 15 Upper left leg 0.0 0.247 À0.052 16 Lower left leg 0.0 0.0 À1.503 17 Left foot 0.0 0.0 À1.361 Note: See Section 6.2 and Chapter 10, Refs. [3,4]. TABLE A.3.6b Ninety-Fifth-Percentile (95%) Female Body Segment Origin Coordinates Relative to the Reference Frame of the Adjacent Lower Numbered Body Segment (in Meters) Body Segment Coordinates (m) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.099 3 Upper torso (chest) 0.0 0.0 0.199 4 Upper left arm 0.0 0.206 0.143 5 Lower left arm 0.0 0.0 À0.289 6 Left hand 0.0 0.0 À0.289 7 Neck 0.0 0.0 0.194 8 Head 0.0 0.0 0.116 9 Upper right arm 0.0 À0.206 0.143 10 Lower right arm 0.0 0.0 À0.289 11 Right hand 0.0 0.0 À0.289 12 Upper right leg 0.0 À0.075 À0.016 13 Lower right leg 0.0 0.0 À0.458 14 Right foot 0.0 0.0 À0.415 15 Upper left leg 0.0 0.075 À0.016 16 Lower left leg 0.0 0.0 À0.458 17 Left foot 0.0 0.0 À0.415 Note: See Section 6.2 and Chapter 10, Refs. [3,4].
380 Appendix: Anthropometric Data Tables TABLE A.4.1a Five-Percentile (5%) Male Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Feet) Body Segment Coordinates (ft) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.319 3 Upper torso (chest) 0.0 0.0 0.310 4 Upper left arm 0.0 0.0 À0.351 5 Lower left arm 0.0 0.0 À0.455 6 Left hand 0.0 0.0 À0.267 7 Neck 0.0 0.0 0.185 8 Head 0.0 0.0 0.314 9 Upper right arm 0.0 À0.674 À0.351 10 Lower right arm 0.0 0.0 À0.455 11 Right hand 0.0 0.0 À0.267 12 Upper right leg 0.0 0.0 À0.776 13 Lower right leg 0.0 0.0 À0.653 14 Right foot 0.314 0.0 À0.157 15 Upper left leg 0.0 0.0 À0.776 16 Lower left leg 0.0 0.0 À0.653 17 Left foot 0.314 0.0 À0.157 TABLE A.4.1b Five-Percentile (5%) Male Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Meters) Body Segment Coordinates (m) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.097 3 Upper torso (chest) 0.0 0.0 0.094 4 Upper left arm 0.0 0.0 À0.107 5 Lower left arm 0.0 0.0 À0.139 6 Left hand 0.0 0.0 À0.081 7 Neck 0.0 0.0 0.057 8 Head 0.0 0.0 0.095 9 Upper right arm 0.0 0.0 À0.107 10 Lower right arm 0.0 0.0 À0.139 11 Right hand 0.0 0.0 À0.081 12 Upper right leg 0.0 0.0 À0.237 13 Lower right leg 0.0 0.0 À0.199 14 Right foot 0.095 0.0 À0.048 15 Upper left leg 0.0 0.0 À0.237 16 Lower left leg 0.0 0.0 À0.199 17 Left foot 0.095 0.0 À0.048
Appendix: Anthropometric Data Tables 381 TABLE A.4.2a Fifty-Percentile (50%) Male Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Feet) Body Segment Coordinates (ft) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.338 3 Upper torso (chest) 0.0 0.0 0.329 4 Upper left arm 0.0 0.0 À0.372 5 Lower left arm 0.0 0.0 À0.483 6 Left hand 0.0 0.0 À0.283 7 Neck 0.0 0.0 0.196 8 Head 0.0 0.0 0.333 9 Upper right arm 0.0 0.0 À0.372 10 Lower right arm 0.0 0.0 À0.483 11 Right hand 0.0 0.0 À0.283 12 Upper right leg 0.0 0.0 À0.823 13 Lower right leg 0.0 0.0 À0.692 14 Right foot 0.333 0.0 À0.167 15 Upper left leg 0.0 0.0 À0.823 16 Lower left leg 0.0 0.0 À0.692 17 Left foot 0.333 0.0 À0.167 TABLE A.4.2b Fifty-Percentile (50%) Male Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Meters) Body Segment Coordinates (m) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.103 3 Upper torso (chest) 0.0 0.0 0.100 4 Upper left arm 0.0 0.0 À0.113 5 Lower left arm 0.0 0.0 À0.147 6 Left hand 0.0 0.0 À0.086 7 Neck 0.0 0.0 0.060 8 Head 0.0 0.0 0.101 9 Upper right arm 0.0 0.0 À0.113 10 Lower right arm 0.0 0.0 À0.147 11 Right hand 0.0 0.0 À0.086 12 Upper right leg 0.0 0.0 À0.251 13 Lower right leg 0.0 0.0 À0.211 14 Right foot 0.095 0.0 À0.057 15 Upper left leg 0.0 0.247 À0.251 16 Lower left leg 0.0 0.0 À0.211 17 Left foot 0.095 0.0 À0.048
382 Appendix: Anthropometric Data Tables TABLE A.4.3a Ninety-Fifth-Percentile (95%) Male Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Feet) Body Segment Coordinates (ft) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.358 3 Upper torso (chest) 0.0 0.0 0.348 4 Upper left arm 0.0 0.0 À0.394 5 Lower left arm 0.0 0.0 À0.511 6 Left hand 0.0 0.0 À0.300 7 Neck 0.0 0.0 0.207 8 Head 0.0 0.0 0.352 9 Upper right arm 0.0 0.0 À0.394 10 Lower right arm 0.0 0.0 À0.511 11 Right hand 0.0 0.0 À0.300 12 Upper right leg 0.0 0.0 À0.871 13 Lower right leg 0.0 0.0 À0.732 14 Right foot 0.352 0.0 À0.177 15 Upper left leg 0.0 0.0 À0.871 16 Lower left leg 0.0 0.0 À0.732 17 Left foot 0.352 0.0 À0.177 TABLE A.4.3b Ninety-Fifth-Percentile (95%) Male Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Meters) Body Segment Coordinates (m) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.109 3 Upper torso (chest) 0.0 0.0 0.106 4 Upper left arm 0.0 0.0 À0.120 5 Lower left arm 0.0 0.0 À0.156 6 Left hand 0.0 0.0 À0.091 7 Neck 0.0 0.0 0.064 8 Head 0.0 0.0 0.107 9 Upper right arm 0.0 0.0 À0.120 10 Lower right arm 0.0 0.0 À0.156 11 Right hand 0.0 0.0 À0.091 12 Upper right leg 0.0 0.0 À0.266 13 Lower right leg 0.0 0.0 À0.223 14 Right foot 0.107 0.0 À0.054 15 Upper left leg 0.0 0.0 À0.266 16 Lower left leg 0.0 0.0 À0.223 17 Left foot 0.107 0.0 À0.054
Appendix: Anthropometric Data Tables 383 TABLE A.4.4a Five-Percentile (5%) Female Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Feet) Body Segment Coordinates (ft) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.288 3 Upper torso (chest) 0.0 0.0 0.281 4 Upper left arm 0.0 0.0 À0.317 5 Lower left arm 0.0 0.0 À0.414 6 Left hand 0.0 0.0 À0.241 7 Neck 0.0 0.0 0.168 8 Head 0.0 0.0 0.285 9 Upper right arm 0.0 0.0 À0.317 10 Lower right arm 0.0 0.0 À0.414 11 Right hand 0.0 0.0 À0.214 12 Upper right leg 0.0 0.0 À0.702 13 Lower right leg 0.0 0.0 À0.592 14 Right foot 0.285 0.0 À0.143 15 Upper left leg 0.0 0.0 À0.702 16 Lower left leg 0.0 0.0 À0.592 17 Left foot 0.285 0.0 À0.143 TABLE A.4.4b Five-Percentile (5%) Female Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Meters) Body Segment Coordinates (m) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.088 3 Upper torso (chest) 0.0 0.0 0.085 4 Upper left arm 0.0 0.0 À0.096 5 Lower left arm 0.0 0.0 À0.126 6 Left hand 0.0 0.0 À0.074 7 Neck 0.0 0.0 0.051 8 Head 0.0 0.0 0.087 9 Upper right arm 0.0 0.0 À0.096 10 Lower right arm 0.0 0.0 À0.126 11 Right hand 0.0 0.0 À0.074 12 Upper right leg 0.0 0.0 À0.214 13 Lower right leg 0.0 0.0 À0.181 14 Right foot 0.087 0.0 À0.044 15 Upper left leg 0.0 0.0 À0.214 16 Lower left leg 0.0 0.0 À0.181 17 Left foot 0.087 0.0 À0.044
384 Appendix: Anthropometric Data Tables TABLE A.4.5a Fifty-Percentile (50%) Female Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Feet) Body Segment Coordinates (ft) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.308 3 Upper torso (chest) 0.0 0.0 0.300 4 Upper left arm 0.0 0.0 À0.339 5 Lower left arm 0.0 0.0 À0.442 6 Left hand 0.0 0.0 À0.258 7 Neck 0.0 0.0 0.179 8 Head 0.0 0.0 0.304 9 Upper right arm 0.0 0.0 À0.339 10 Lower right arm 0.0 0.0 À0.442 11 Right hand 0.0 0.0 À0.258 12 Upper right leg 0.0 0.0 À0.750 13 Lower right leg 0.0 0.0 À0.632 14 Right foot 0.304 0.0 À0.153 15 Upper left leg 0.0 0.0 À0.750 16 Lower left leg 0.0 0.0 À0.632 17 Left foot 0.304 0.0 À0.153 TABLE A.4.5b Fifty-Percentile (50%) Female Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Meters) Body Segment Coordinates (m) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.094 3 Upper torso (chest) 0.0 0.0 0.091 4 Upper left arm 0.0 0.0 À0.103 5 Lower left arm 0.0 0.0 À0.135 6 Left hand 0.0 0.0 À0.079 7 Neck 0.0 0.0 0.055 8 Head 0.0 0.0 0.093 9 Upper right arm 0.0 0.0 À0.103 10 Lower right arm 0.0 0.0 À0.135 11 Right hand 0.0 0.0 À0.079 12 Upper right leg 0.0 0.0 À0.229 13 Lower right leg 0.0 0.0 À0.193 14 Right foot 0.093 0.0 À0.047 15 Upper left leg 0.0 0.0 À0.229 16 Lower left leg 0.0 0.0 À0.193 17 Left foot 0.093 0.0 À0.047
Appendix: Anthropometric Data Tables 385 TABLE A.4.6a Ninety-Fifth-Percentile (95%) Female Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Feet) Body Segment Coordinates (ft) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.327 3 Upper torso (chest) 0.0 0.0 0.318 4 Upper left arm 0.0 0.634 À0.360 5 Lower left arm 0.0 0.0 À0.469 6 Left hand 0.0 0.0 À0.274 7 Neck 0.0 0.0 0.190 8 Head 0.0 0.0 0.322 9 Upper right arm 0.0 0.0 À0.360 10 Lower right arm 0.0 0.0 À0.469 11 Right hand 0.0 0.0 À0.274 12 Upper right leg 0.0 0.0 À0.796 13 Lower right leg 0.0 0.0 À0.670 14 Right foot 0.322 0.0 À0.162 15 Upper left leg 0.0 0.0 À0.796 16 Lower left leg 0.0 0.0 À0.670 17 Left foot 0.322 0.0 À0.162 TABLE A.4.6b Ninety-Fifth-Percentile (95%) Female Body Segment Mass Center Coordinates Relative to the Reference Frame of the Body Segment (in Meters) Body Segment Coordinates (m) Number Name XY Z 1 Lower torso (pelvis) 0.0 0.0 0.0 2 Middle torso (lumbar) 0.0 0.0 0.100 3 Upper torso (chest) 0.0 0.0 0.097 4 Upper left arm 0.0 0.0 À0.109 5 Lower left arm 0.0 0.0 À0.143 6 Left hand 0.0 0.0 À0.084 7 Neck 0.0 0.0 0.058 8 Head 0.0 0.0 0.099 9 Upper right arm 0.0 0.0 À0.109 10 Lower right arm 0.0 0.0 À0.143 11 Right hand 0.0 0.0 À0.084 12 Upper right leg 0.0 0.0 À0.243 13 Lower right leg 0.0 0.0 À0.205 14 Right foot 0.099 0.0 À0.050 15 Upper left leg 0.0 0.0 À0.243 16 Lower left leg 0.0 0.0 À0.205 17 Left foot 0.099 0.0 À0.050
386 Appendix: Anthropometric Data Tables TABLE A.5.1a Five-Percentile (5%) Male Body Segment Principal Inertia Matrices (in Slug ft2) Body Inertia Matrix (in Slug ft2) Segment Number Relative to Body Frame 1 Name Principal Directions Lower torso (pelvis) 2 Middle torso (lumbar) 2 0:078 0:0 0:0 3 Upper torso (chest) 64 0:0 0:048 0:0 75 3 Upper left arm Lower left arm 0:0 0:0 0:075 4 Left hand 2 0:078 0:0 0:0 3 Neck 46 0:0 0:048 0:0 75 5 Head Upper right arm 0:0 0:0 0:075 6 Lower right arm 2 0:055 0:0 0:0 3 Right hand 46 0:0 0:038 0:0 75 7 Upper right leg 0:0 0:0 0:055 8 2 0:014 0:0 0:0 3 64 0:0 0:014 0:0 57 9 0:0 0:0 0:001 10 2 0:011 0:0 0:0 3 64 0:0 0:011 0:0 57 11 0:0 0:0 0:001 12 2 0:002 0:0 0:0 3 46 0:0 0:001 0:0 75 0:0 0:0 0:001 2 0:008 0:0 0:0 3 46 0:0 0:008 0:0 75 0:0 0:0 0:001 2 0:020 0:0 0:0 3 46 0:0 0:020 0:0 57 0:0 0:0 0:010 2 0:014 0:0 0:0 3 64 0:0 0:014 0:0 75 0:0 0:0 0:001 2 0:011 0:0 0:0 3 64 0:0 0:011 0:0 57 0:0 0:0 0:001 2 0:002 0:0 0:0 3 46 0:0 0:001 0:0 57 0:0 0:0 0:001 2 0:050 0:0 0:0 3 46 0:0 0:050 0:0 75 0:0 0:0 0:013
Appendix: Anthropometric Data Tables 387 TABLE A.5.1a (continued) Five-Percentile (5%) Male Body Segment Principal Inertia Matrices (in Slug ft2) Body Inertia Matrix (in Slug ft2) Segment Number Relative to Body Frame 13 Name Principal Directions 14 Lower right leg Right foot 2 0:004 0:0 0:0 3 15 Upper left leg 46 0:0 0:004 0:0 57 Lower left leg 16 Left foot 0:0 0:0 0:001 2 0:001 0:0 0:0 3 17 64 0:0 0:004 0:0 75 0:0 0:0 0:004 2 0:050 0:0 0:0 3 64 0:0 0:050 0:0 57 0:0 0:0 0:013 2 0:004 0:0 0:0 3 64 0:0 0:004 0:0 75 0:0 0:0 0:001 2 0:001 0:0 0:0 3 46 0:0 0:004 0:0 57 0:0 0:0 0:004 TABLE A.5.1b Five-Percentile (5%) Male Body Segment Principal Inertia Matrices (in kg m2) Body Inertia Matrix (in kg m2) Segment Number Relative to Body Frame 1 Name Principal Directions 2 Lower torso (pelvis) 2 0:105 0:0 0:0 3 3 Middle torso (lumbar) 46 0:0 0:065 0:0 75 4 Upper torso (chest) 0:0 0:0 0:105 2 0:105 0:0 0:0 3 Upper left arm 46 0:0 0:065 0:0 75 0:0 0:0 0:105 2 0:075 0:0 0:0 3 64 0:0 0:052 0:0 75 0:0 0:0 0:075 2 0:019 0:0 0:0 3 46 0:0 0:019 0:0 57 0:0 0:0 0:002 (continued)
388 Appendix: Anthropometric Data Tables TABLE A.5.1b (continued) Five-Percentile (5%) Male Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Lower left arm Relative to Body Frame Number Left hand Neck Principal Directions 5 Head 2 0:014 0:0 0:0 3 Upper right arm 4 0:0 0:014 0:0 5 6 Lower right arm Right hand 0:0 0:0 0:001 7 Upper right leg 2 0:003 0:0 0:0 3 Lower right leg 4 0:0 0:001 0:0 5 8 Right foot Upper left leg 0:0 0:0 0:001 9 Lower left leg 2 0:011 0:0 0:0 3 Left foot 4 0:0 0:011 0:0 5 10 0:0 0:0 0:002 11 2 0:027 0:0 0:0 3 4 0:0 0:027 0:0 5 12 0:0 0:0 0:014 13 2 0:019 0:0 0:0 3 4 0:0 0:019 0:0 5 14 0:0 0:0 0:002 15 2 0:014 0:0 0:0 3 4 0:0 0:014 0:0 5 16 0:0 0:0 0:001 17 2 0:003 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:069 0:0 0:0 3 4 0:0 0:069 0:0 5 0:0 0:0 0:017 2 0:006 0:0 0:0 3 4 0:0 0:006 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:005 0:0 5 0:0 0:0 0:005 2 0:069 0:0 0:0 3 4 0:0 0:069 0:0 5 0:0 0:0 0:017 2 0:006 0:0 0:0 3 4 0:0 0:006 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:005 0:0 5 0:0 0:0 0:005
Appendix: Anthropometric Data Tables 389 TABLE A.5.2a Fifty-Percentile (50%) Male Body Segment Principal Inertia Matrices (in Slug ft2) Body Inertia Matrix (in Slug ft2) Segment Number Relative to Body Frame 1 Name Principal Directions Lower torso (pelvis) 2 Middle torso (lumbar) 2 0:109 0:0 0:0 3 Upper torso (chest) 46 0:0 0:067 0:0 75 3 Upper left arm Lower left arm 0:0 0:0 0:106 4 Left hand 2 0:109 0:0 0:0 3 Neck 64 0:0 0:067 0:0 57 5 Head Upper right arm 0:0 0:0 0:106 6 Lower right arm 2 0:078 0:0 0:0 3 Right hand 46 0:0 0:054 0:0 57 7 Upper right leg 0:0 0:0 0:078 8 2 0:020 0:0 0:0 3 64 0:0 0:020 0:0 75 9 0:0 0:0 0:002 10 2 0:015 0:0 0:0 3 46 0:0 0:015 0:0 57 11 0:0 0:0 0:001 12 2 0:003 0:0 0:0 3 46 0:0 0:001 0:0 57 0:0 0:0 0:001 2 0:011 0:0 0:0 3 64 0:0 0:011 0:0 57 0:0 0:0 0:002 2 0:028 0:0 0:0 3 46 0:0 0:028 0:0 57 0:0 0:0 0:014 2 0:020 0:0 0:0 3 46 0:0 0:020 0:0 75 0:0 0:0 0:002 2 0:015 0:0 0:0 3 46 0:0 0:015 0:0 57 0:0 0:0 0:001 2 0:003 0:0 0:0 3 64 0:0 0:001 0:0 75 0:0 0:0 0:001 2 0:071 0:0 0:0 3 64 0:0 0:071 0:0 57 0:0 0:0 0:018 (continued)
390 Appendix: Anthropometric Data Tables TABLE A.5.2a (continued) Fifty-Percentile (50%) Male Body Segment Principal Inertia Matrices (in Slug ft2) Body Inertia Matrix (in Slug ft2) Segment Number Relative to Body Frame 13 Name Principal Directions 14 Lower right leg Right foot 2 0:006 0:0 0:0 3 15 Upper left leg 46 0:0 0:006 0:0 57 Lower left leg 16 Left foot 0:0 0:0 0:001 2 0:001 0:0 0:0 3 17 64 0:0 0:005 0:0 75 0:0 0:0 0:005 2 0:071 0:0 0:0 3 64 0:0 0:071 0:0 75 0:0 0:0 0:018 2 0:006 0:0 0:0 3 64 0:0 0:006 0:0 57 0:0 0:0 0:001 2 0:001 0:0 0:0 3 64 0:0 0:005 0:0 75 0:0 0:0 0:005 TABLE A.5.2b Fifty-Percentile (50%) Male Body Segment Principal Inertia Matrices (in kg m2) Body Inertia Matrix (in kg m2) Segment Number Relative to Body Frame 1 Name Principal Directions Lower torso (pelvis) 2 2 0:148 0:0 0:0 3 Middle torso (lumbar) 46 0:0 0:091 0:0 75 3 Upper torso (chest) 0:0 0:0 0:148 4 2 0:148 0:0 0:0 3 Upper left arm 64 0:0 0:091 0:0 75 0:0 0:0 0:148 2 0:106 0:0 0:0 3 46 0:0 0:073 0:0 75 0:0 0:0 0:106 2 0:027 0:0 0:0 3 64 0:0 0:027 0:0 75 0:0 0:0 0:003
Appendix: Anthropometric Data Tables 391 TABLE A.5.2b (continued) Fifty-Percentile (50%) Male Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Lower left arm Relative to Body Frame Number Left hand Neck Principal Directions 5 Head 2 0:020 0:0 0:0 3 Upper right arm 4 0:0 0:020 0:0 5 6 Lower right arm Right hand 0:0 0:0 0:001 7 Upper right leg 2 0:004 0:0 0:0 3 Lower right leg 4 0:0 0:001 0:0 5 8 Right foot Upper left leg 0:0 0:0 0:001 9 Lower left leg 2 0:015 0:0 0:0 3 Left foot 4 0:0 0:015 0:0 5 10 0:0 0:0 0:003 11 2 0:038 0:0 0:0 3 4 0:0 0:038 0:0 5 12 0:0 0:0 0:019 13 2 0:027 0:0 0:0 3 4 0:0 0:027 0:0 5 14 0:0 0:0 0:003 15 2 0:020 0:0 0:0 3 4 0:0 0:020 0:0 5 16 0:0 0:0 0:001 17 2 0:004 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:097 0:0 0:0 3 4 0:0 0:097 0:0 5 0:0 0:0 0:024 2 0:008 0:0 0:0 3 4 0:0 0:008 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:007 0:0 5 0:0 0:0 0:007 2 0:097 0:0 0:0 3 4 0:0 0:097 0:0 5 0:0 0:0 0:024 2 0:008 0:0 0:0 3 4 0:0 0:008 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:007 0:0 5 0:0 0:0 0:007
392 Appendix: Anthropometric Data Tables TABLE A.5.3a Ninety-Fifth-Percentile (95%) Male Body Segment Principal Inertia Matrices (in Slug ft2) Body Name Inertia Matrix (in Slug ft2) Segment Lower torso (pelvis) Number Middle torso (lumbar) Relative to Body Frame Upper torso (chest) 1 Upper left arm Principal Directions 2 Lower left arm 2 0:146 0:0 0:0 3 3 Left hand 4 0:0 0:090 0:0 5 4 Neck 5 Head 0:0 0:0 0:142 6 Upper right arm 2 0:146 0:0 0:0 3 7 Lower right arm 4 0:0 0:090 0:0 5 8 Right hand 9 Upper right leg 0:0 0:0 0:142 10 Lower right leg 2 0:105 0:0 0:0 3 11 Right foot 4 0:0 0:073 0:0 5 12 13 0:0 0:0 0:105 14 2 0:027 0:0 0:0 3 4 0:0 0:027 0:0 5 0:0 0:0 0:003 2 0:020 0:0 0:0 3 4 0:0 0:020 0:0 5 0:0 0:0 0:001 2 0:004 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:015 0:0 0:0 3 4 0:0 0:015 0:0 5 0:0 0:0 0:003 2 0:038 0:0 0:0 3 4 0:0 0:038 0:0 5 0:0 0:0 0:019 2 0:027 0:0 0:0 3 4 0:0 0:027 0:0 5 0:0 0:0 0:003 2 0:020 0:0 0:0 3 4 0:0 0:020 0:0 5 0:0 0:0 0:001 2 0:004 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:095 0:0 0:0 3 4 0:0 0:095 0:0 5 0:0 0:0 0:024 2 0:008 0:0 0:0 3 4 0:0 0:008 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:007 0:0 5 0:0 0:0 0:007
Appendix: Anthropometric Data Tables 393 TABLE A.5.3a (continued) Ninety-Fifth-Percentile (95%) Male Body Segment Principal Inertia Matrices (in Slug ft2) Body Name Inertia Matrix (in Slug ft2) Segment Upper left leg Number Relative to Body Frame 15 Lower left leg Principal Directions 16 Left foot 2 0:095 0:0 0:0 3 4 0:0 0:095 0:0 5 17 0:0 0:0 0:024 2 0:008 0:0 0:0 3 4 0:0 0:008 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:007 0:0 5 0:0 0:0 0:007 TABLE A.5.3b Ninety-Fifth-Percentile (95%) Male Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Lower torso (pelvis) Number Middle torso (lumbar) Relative to Body Frame Upper torso (chest) 1 Upper left arm Principal Directions Lower left arm 2 0:199 0:0 0:0 3 2 Left hand 4 0:0 0:122 0:0 5 Neck 3 Head 0:0 0:0 0:199 2 0:199 0:0 0:0 3 4 4 0:0 0:122 0:0 5 5 0:0 0:0 0:199 2 0:142 0:0 0:0 3 6 4 0:0 0:098 0:0 5 7 0:0 0:0 0:142 2 0:036 0:0 0:0 3 8 4 0:0 0:036 0:0 5 0:0 0:0 0:004 2 0:027 0:0 0:0 3 4 0:0 0:027 0:0 5 0:0 0:0 0:001 2 0:005 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:020 0:0 0:0 3 4 0:0 0:020 0:0 5 0:0 0:0 0:004 2 0:051 0:0 0:0 3 4 0:0 0:051 0:0 5 0:0 0:0 0:026 (continued)
394 Appendix: Anthropometric Data Tables TABLE A.5.3b (continued) Ninety-Fifth-Percentile (95%) Male Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Upper right arm Number Lower right arm Relative to Body Frame Right hand 9 Upper right leg Principal Directions Lower right leg 2 0:036 0:0 0:0 3 10 Right foot 4 0:0 0:036 0:0 5 Upper left leg 11 Lower left leg 0:0 0:0 0:004 Left foot 2 0:027 0:0 0:0 3 12 4 0:0 0:027 0:0 5 13 0:0 0:0 0:001 2 0:005 0:0 0:0 3 14 4 0:0 0:001 0:0 5 15 0:0 0:0 0:001 2 0:130 0:0 0:0 3 16 4 0:0 0:130 0:0 5 17 0:0 0:0 0:032 2 0:011 0:0 0:0 3 4 0:0 0:011 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:009 0:0 5 0:0 0:0 0:009 2 0:130 0:0 0:0 3 4 0:0 0:130 0:0 5 0:0 0:0 0:032 2 0:011 0:0 0:0 3 4 0:0 0:011 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:009 0:0 5 0:0 0:0 0:009 TABLE A.5.4a Five-Percentile (5%) Female Body Segment Principal Inertia Matrices (in Slug ft2) Body Name Inertia Matrix (in Slug ft2) Segment Lower torso (pelvis) Number Relative to Body Frame 1 Middle torso (lumbar) Principal Directions 2 2 0:063 0:0 0:0 3 4 0:0 0:039 0:0 5 0:0 0:0 0:062 2 0:038 0:0 0:0 3 4 0:0 0:023 0:0 5 0:0 0:0 0:037
Appendix: Anthropometric Data Tables 395 TABLE A.5.4a (continued) Five-Percentile (5%) Female Body Segment Principal Inertia Matrices (in Slug ft2) Body Name Inertia Matrix (in Slug ft2) Segment Upper torso (chest) Number Upper left arm Relative to Body Frame Lower left arm 3 Left hand Principal Directions 4 Neck 2 0:023 0:0 0:0 3 5 Head 4 0:0 0:015 0:0 5 6 Upper right arm 7 Lower right arm 0:0 0:0 0:022 8 Right hand 2 0:008 0:0 0:0 3 9 Upper right leg 4 0:0 0:008 0:0 5 10 Lower right leg 11 Right foot 0:0 0:0 0:001 12 Upper left leg 2 0:007 0:0 0:0 3 13 Lower left leg 4 0:0 0:007 0:0 5 14 Left foot 15 0:0 0:0 0:001 16 23 17 0:001 0:0 0:0 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:013 0:0 0:0 3 4 0:0 0:013 0:0 5 0:0 0:0 0:006 2 0:008 0:0 0:0 3 4 0:0 0:008 0:0 5 0:0 0:0 0:001 2 0:007 0:0 0:0 3 4 0:0 0:007 0:0 5 0:0 0:0 0:001 23 0:001 0:0 0:0 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:037 0:0 0:0 3 4 0:0 0:037 0:0 5 0:0 0:0 0:009 23 0:003 0:0 0:0 4 0:0 0:003 0:0 5 0:0 0:0 0:001 23 0:001 0:0 0:0 4 0:0 0:003 0:0 5 0:0 0:0 0:003 2 0:037 0:0 0:0 3 4 0:0 0:037 0:0 5 0:0 0:0 0:009 2 0:003 0:0 0:0 3 4 0:0 0:003 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:002 0:0 5 0:0 0:0 0:003
396 Appendix: Anthropometric Data Tables TABLE A.5.4b Five-Percentile (5%) Female Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Lower torso (pelvis) Number Middle torso (lumbar) Relative to Body Frame 1 Upper torso (chest) Upper left arm Principal Directions 2 Lower left arm 2 0:086 0:0 0:0 3 Left hand 4 0:0 0:052 0:0 5 3 Neck 4 Head 0:0 0:0 0:083 5 Upper right arm 2 0:051 0:0 0:0 3 6 Lower right arm 4 0:0 0:031 0:0 5 Right hand 7 Upper right leg 0:0 0:0 0:050 8 Lower right leg 23 9 Right foot 10 0:031 0:0 0:0 11 4 0:0 0:021 0:0 5 12 0:0 0:0 0:031 13 23 14 0:012 0:0 0:0 4 0:0 0:012 0:0 5 0:0 0:0 0:001 23 0:009 0:0 0:0 4 0:0 0:009 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 23 0:007 0:0 0:0 4 0:0 0:007 0:0 5 0:0 0:0 0:001 23 0:017 0:0 0:0 4 0:0 0:017 0:0 5 0:0 0:0 0:009 23 0:012 0:0 0:0 4 0:0 0:012 0:0 5 0:0 0:0 0:001 23 0:009 0:0 0:0 4 0:0 0:009 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 23 0:049 0:0 0:0 4 0:0 0:049 0:0 5 0:0 0:0 0:013 2 0:003 0:0 0:0 3 4 0:0 0:003 0:0 5 0:0 0:0 0:001 23 0:001 0:0 0:0 4 0:0 0:003 0:0 5 0:0 0:0 0:003
Appendix: Anthropometric Data Tables 397 TABLE A.5.4b (continued) Five-Percentile (5%) Female Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Upper left leg Number Relative to Body Frame 15 Lower left leg Principal Directions 16 Left foot 23 17 0:049 0:0 0:0 4 0:0 0:049 0:0 5 0:0 0:0 0:013 23 0:003 0:0 0:0 4 0:0 0:003 0:0 5 0:0 0:0 0:001 23 0:001 0:0 0:0 4 0:0 0:003 0:0 5 0:0 0:0 0:003 TABLE A.5.5a Fifty-Percentile (50%) Female Body Segment Principal Inertia Matrices (in Slug ft2) Body Name Inertia Matrix (in Slug ft2) Segment Lower torso (pelvis) Number Middle torso (lumbar) Relative to Body Frame Upper torso (chest) 1 Upper left arm Principal Directions Lower left arm 2 0:091 0:0 0:0 3 2 Left hand 4 0:0 0:056 0:0 5 Neck 3 Head 0:0 0:0 0:089 2 0:055 0:0 0:0 3 4 4 0:0 0:033 0:0 5 5 0:0 0:0 0:053 2 0:033 0:0 0:0 3 6 4 0:0 0:022 0:0 5 7 0:0 0:0 0:032 2 0:012 0:0 0:0 3 8 4 0:0 0:012 0:0 5 0:0 0:0 0:001 2 0:010 0:0 0:0 3 4 0:0 0:010 0:0 5 0:0 0:0 0:001 2 0:002 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:008 0:0 0:0 3 4 0:0 0:008 0:0 5 0:0 0:0 0:001 2 0:019 0:0 0:0 3 4 0:0 0:019 0:0 5 0:0 0:0 0:009 (continued)
398 Appendix: Anthropometric Data Tables TABLE A.5.5a (continued) Fifty-Percentile (50%) Female Body Segment Principal Inertia Matrices (in Slug ft2) Body Name Inertia Matrix (in Slug ft2) Segment Upper right arm Number Lower right arm Relative to Body Frame 9 Right hand Upper right leg Principal Directions 10 Lower right leg 2 0:012 0:0 0:0 3 Right foot 4 0:0 0:012 0:0 5 11 Upper left leg Lower left leg 0:0 0:0 0:001 12 Left foot 2 0:010 0:0 0:0 3 4 0:0 0:010 0:0 5 13 0:0 0:0 0:001 14 2 0:002 0:0 0:0 3 4 0:0 0:001 0:0 5 15 0:0 0:0 0:001 16 2 0:053 0:0 0:0 3 4 0:0 0:053 0:0 5 17 0:0 0:0 0:013 2 0:004 0:0 0:0 3 4 0:0 0:004 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:003 0:0 5 0:0 0:0 0:004 2 0:053 0:0 0:0 3 4 0:0 0:053 0:0 5 0:0 0:0 0:013 2 0:004 0:0 0:0 3 4 0:0 0:004 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:003 0:0 5 0:0 0:0 0:004 TABLE A.5.5b Fifty-Percentile (50%) Female Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Lower torso (pelvis) Number Relative to Body Frame 1 Middle torso (lumbar) Principal Directions 2 2 0:123 0:0 0:0 3 4 0:0 0:075 0:0 5 0:0 0:0 0:120 2 0:074 0:0 0:0 3 4 0:0 0:045 0:0 5 0:0 0:0 0:072
Appendix: Anthropometric Data Tables 399 TABLE A.5.5b (continued) Fifty-Percentile (50%) Female Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Upper torso (chest) Number Upper left arm Relative to Body Frame Lower left arm 3 Left hand Principal Directions 4 Neck 23 5 Head 6 Upper right arm 0:044 0:0 0:0 7 Lower right arm 4 0:0 0:030 0:0 5 8 Right hand 9 Upper right leg 0:0 0:0 0:044 10 Lower right leg 23 11 Right foot 12 Upper left leg 0:017 0:0 0:0 13 Lower left leg 4 0:0 0:017 0:0 5 14 Left foot 15 0:0 0:0 0:002 16 23 17 0:013 0:0 0:0 4 0:0 0:013 0:0 5 0:0 0:0 0:001 23 0:002 0:0 0:0 4 0:0 0:001 0:0 5 0:0 0:0 0:001 23 0:010 0:0 0:0 4 0:0 0:010 0:0 5 0:0 0:0 0:002 23 0:025 0:0 0:0 4 0:0 0:025 0:0 5 0:0 0:0 0:013 23 0:017 0:0 0:0 4 0:0 0:017 0:0 5 0:0 0:0 0:002 23 0:013 0:0 0:0 4 0:0 0:013 0:0 5 0:0 0:0 0:001 23 0:002 0:0 0:0 4 0:0 0:001 0:0 5 0:0 0:0 0:001 23 0:071 0:0 0:0 4 0:0 0:071 0:0 5 0:0 0:0 0:018 23 0:005 0:0 0:0 4 0:0 0:005 0:0 5 0:0 0:0 0:001 23 0:001 0:0 0:0 4 0:0 0:004 0:0 5 0:0 0:0 0:005 23 0:071 0:0 0:0 4 0:0 0:071 0:0 5 0:0 0:0 0:018 23 0:005 0:0 0:0 4 0:0 0:005 0:0 5 0:0 0:0 0:001 23 0:001 0:0 0:0 4 0:0 0:004 0:0 5 0:0 0:0 0:005
400 Appendix: Anthropometric Data Tables TABLE A.5.6a Ninety-Fifth-Percentile (95%) Female Body Segment Principal Inertia Matrices (in Slug ft2) Body Name Inertia Matrix (in Slug ft2) Segment Lower torso (pelvis) Number Middle torso (lumbar) Relative to Body Frame 1 Upper torso (chest) 2 Upper left arm Principal Directions 3 Lower left arm 2 0:128 0:0 0:0 3 4 Left hand 4 0:0 0:079 0:0 5 5 Neck 6 Head 0:0 0:0 0:126 7 Upper right arm 2 0:078 0:0 0:0 3 8 Lower right arm 4 0:0 0:047 0:0 5 9 Right hand 10 Upper right leg 0:0 0:0 0:075 11 Lower right leg 2 0:047 0:0 0:0 3 12 Right foot 4 0:0 0:031 0:0 5 13 14 0:0 0:0 0:045 2 0:017 0:0 0:0 3 4 0:0 0:017 0:0 5 0:0 0:0 0:001 2 0:014 0:0 0:0 3 4 0:0 0:014 0:0 5 0:0 0:0 0:001 2 0:003 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:011 0:0 0:0 3 4 0:0 0:011 0:0 5 0:0 0:0 0:001 2 0:027 0:0 0:0 3 4 0:0 0:027 0:0 5 0:0 0:0 0:013 2 0:017 0:0 0:0 3 4 0:0 0:017 0:0 5 0:0 0:0 0:001 2 0:014 0:0 0:0 3 4 0:0 0:014 0:0 5 0:0 0:0 0:001 2 0:003 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:075 0:0 0:0 3 4 0:0 0:075 0:0 5 0:0 0:0 0:018 2 0:006 0:0 0:0 3 4 0:0 0:006 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:004 0:0 5 0:0 0:0 0:006
Appendix: Anthropometric Data Tables 401 TABLE A.5.6a (continued) Ninety-Fifth-Percentile (95%) Female Body Segment Principal Inertia Matrices (in Slug ft2) Body Name Inertia Matrix (in Slug ft2) Segment Upper left leg Number Relative to Body Frame 15 Lower left leg Principal Directions 16 Left foot 2 0:075 0:0 0:0 3 4 0:0 0:075 0:0 5 17 0:0 0:0 0:018 2 0:006 0:0 0:0 3 4 0:0 0:006 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:004 0:0 5 0:0 0:0 0:006 TABLE A.5.6b Ninety-Fifth-Percentile (95%) Female Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Lower torso (pelvis) Number Middle torso (lumbar) Relative to Body Frame Upper torso (chest) 1 Upper left arm Principal Directions Lower left arm 2 0:174 0:0 0:0 3 2 Left hand 4 0:0 0:106 0:0 5 Neck 3 Head 0:0 0:0 0:169 2 0:104 0:0 0:0 3 4 4 0:0 0:064 0:0 5 5 0:0 0:0 0:102 2 0:062 0:0 0:0 3 6 4 0:0 0:042 0:0 5 7 0:0 0:0 0:062 2 0:024 0:0 0:0 3 8 4 0:0 0:024 0:0 5 0:0 0:0 0:003 2 0:018 0:0 0:0 3 4 0:0 0:018 0:0 5 0:0 0:0 0:001 2 0:003 0:0 0:0 3 4 0:0 0:001 0:0 5 0:0 0:0 0:001 2 0:014 0:0 0:0 3 4 0:0 0:014 0:0 5 0:0 0:0 0:003 2 0:035 0:0 0:0 3 4 0:0 0:035 0:0 5 0:0 0:0 0:018 (continued)
402 Appendix: Anthropometric Data Tables TABLE A.5.6b (continued) Ninety-Fifth-Percentile (95%) Female Body Segment Principal Inertia Matrices (in kg m2) Body Name Inertia Matrix (in kg m2) Segment Upper right arm Number Lower right arm Relative to Body Frame 9 Right hand Upper right leg Principal Directions 10 Lower right leg 2 0:024 0:0 0:0 3 Right foot 4 0:0 0:024 0:0 5 11 Upper left leg Lower left leg 0:0 0:0 0:003 12 Left foot 2 0:018 0:0 0:0 3 4 0:0 0:018 0:0 5 13 0:0 0:0 0:001 14 2 0:003 0:0 0:0 3 4 0:0 0:001 0:0 5 15 0:0 0:0 0:001 16 2 0:100 0:0 0:0 3 4 0:0 0:100 0:0 5 17 0:0 0:0 0:025 2 0:007 0:0 0:0 3 4 0:0 0:007 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:006 0:0 5 0:0 0:0 0:007 2 0:100 0:0 0:0 3 4 0:0 0:100 0:0 5 0:0 0:0 0:025 2 0:007 0:0 0:0 3 4 0:0 0:007 0:0 5 0:0 0:0 0:001 2 0:001 0:0 0:0 3 4 0:0 0:006 0:0 5 0:0 0:0 0:007
Glossary Abduction—spreading the legs apart (opposite of adduction; see Figure 2.18) Absolute velocity—velocity in a inertial reference frame Acceleration—see Section 8.4 Acetabulum—rounded socket supporting the head of the femur Acromion—a pointed projection forming the tip of the shoulder Active forces—forces exerted on a body such as gravity or contact forces; also called applied forces, as opposed to passive (or inertia) forces (see Section 12.1) Addition theorem for angular velocity—see Section 8.7.2 Adduction—bring the legs together from a spread position (opposite of abduction; see Figure 2.18) Afferent—leading to, as a nerve impulse to the brain or spinal cord Angular velocity—see Section 8.6 Angular velocity matrix—the matrix whose dual vector is the angular velo- city (see Equation 8.122) Anterior—toward the front (opposite of posterior) Aorta—the large blood vessel providing blood flow out of the heart to the body Applied forces—forces exerted on a body such as gravity or contact forces; also called active forces, as opposed to inertia (or passive) forces (see Section 12.1) Arachnoid—fibrous tissue between the brain and dura mater Avulsion—a traumatic tearing of body tissue Axilla—armpit Ball-and-socket joint—a spherical joint with three rotational degrees of freedom Barber poling—a vehicle occupant moving up relative to a seat belt, particu- larly a shoulder belt (see Section 15.7) Beltrami–Mitchell equations—see compatibility equations Biomechanics—mechanics applied with living systems Biosystem—a living system Block multiplication of matrices—multiplication of partitioned matrices with the submatrices treated as elements (see, for example, Equation 3.101) Bone maintenance—bone remodeling Bound vector—a vector acting along a specific line of action (also called a bound vector) Bryant angles—dextral rotation angles (1-2-3 rotation sequence angles) of a body relative to a reference frame (see Section 8.8) Cadence—in walking, the number of steps per unit time 403
404 Glossary Cancellous bone—soft, spongy bone, also called trabecular bone (see Sec- tion 7.2) Carpal—referring to the wrist Cartilage—a relatively stiff, fibrous connective tissue between bones as in the knees and chest (sternum) Caudal—referring to the tail Center of gravity—see mass center Central inertia dyadic—the dyadic of a body computed relative to the mass center G (see Section 10.4) Cerebrum—the largest portion of the brain Cervical—pertaining to the neck Characteristics of a vector—magnitude (length or norm) and direction (orien- tation and sense) Cockpit—vehicle occupant space Collagen—a tough, fibrous tissue providing strength to bone, ligament, tendon, and cartilage Column matrix, column array—a matrix with only one column Compact bone—hard or cortical bone (see Section 7.2) Compatibility equations—constraint equations to insure consistency in solu- tions of stress equilibrium equations (see Section 5.7) Component—a vector or scalar contributing to the sum (or resultant) of a vector (see Section 3.2.5) Component—one of the addends in a vector sum; a scalar coefficient of a unit vector where a vector is expressed in terms of unit vectors Compression—a force or stress tending to shorten or decrease the volume of a body Concussion—loss of consciousness Configuration graph—see Section 8.8 Conformable matrices—for two matrices, where the number of rows of the first is equal to the number of columns of the second Constraint equations—analytical expressions resulting from position, move- ment, or motion constraints on a multibody system (a human body model) (see Sections 13.5 and 13.6) Convulsion—violent erratic muscle contraction Coronal plane—a vertical plane dividing the human body into anterior and posterior parts, also called the frontal plane (see Figure 2.8) Cortical bone—hard or compact bone (see Section 7.2) Costal—referring to the ribs Coup=contra coup injury—head injury occurring at and opposite the site of traumatic impact Couple—a force system with a zero resultant but a nonzero moment about some point (see Section 4.5.2) Crash-victim simulator—a computer program or software to model the kinematics and dynamics of a vehicle occupant during a crash Cutaneous—referring to the skin
Glossary 405 D’Alembert’s principle—a variant of Newton’s second law stating simply that F þ F* ¼ 0 where F* is defined as Àma with F being an applied force on a particle, m is the mass of the particle, and a is the acceleration of the particle in an inertial (or Newtonian) reference frame Degloving—the traumatic tearing away of skin and flesh from the bones Degree of freedom—a measure of the manner of possible movement of a particle, body, or system Deltoid—shoulder muscle Dermis—the middle or central layer of skin Dextral rotation angles—so-called Bryant angles (1-2-3 rotation sequence angles) of a body relative to a reference frame (see Section 8.8.) Diagonal matrix—a square matrix with nonzero elements on its diagonal but zero elements off the diagonal Diaphysis—shaft of a long bone (see Figure 2.23) Diffuse axonal injury (DAI)—scattered microdamage to brain tissue Digits—fingers or toes Dimensions of a matrix—the number of rows and columns of a matrix Dorsiflexion—raising the toe of the foot upward (opposite of plantar flexion; see Figure 2.20) Double support—the condition in walking when two feet are on the walking surface, as opposed to single support, where only one foot is on the walking surface Dual vector—a vector forming the nondiagonal entries of a skew-symmetric matrix as in the angular velocity matrix of Equation 8.122 Dummy force method—applying a concentrated force in the strain energy method, at a point, to determine the displacement at that point, with the magnitude of the force being then set to zero Dura mater—thick outermost layer of the brain Dyad—the result of a dyadic product (see Section 3.4) Dyadic—a sum of dyads (see Equation 3.45) Dyadic product—a means of multiplying vectors resulting in dyads (see Equation 3.42) Dyadic transpose—a dyadic obtained by interchanging the rows and col- umns of the array of its components Dyadic=vector product—a product of a dyadic and a vector producing a vector (see Equations 3.72 and 3.78) Dynamics—combined study of kinematics, inertia, and kinetics Efferent—leading away from, as a nerve impulse away from the brain or spinal cord Eigenvalue—the parameter l in the expression Ax ¼ lx (see Equation 3.135); also called principal value Eigenvalues of inertia—see eigenvalues; the eigenvalues of the inertia matrix Eigenvector—the vector x in the expression Ax ¼ lx (see Equation 3.135); also called principal vector
406 Glossary Elastic modulus—proportionality constant in linear stress–strain equations; also known as Young’s modulus of elasticity (see Equation 5.64) Elements of a matrix—the numbers, or variables, making up a matrix (see Section 3.6) Engineering shear strain—see Equation 5.18 Epidermis—outermost layer of the skin Epiligament—a ligament sheath Epiphysis—rounded, enlarged end of a long bone (see Figure 2.23) Epitendon—a tendon sheath Equivalent force systems—force systems with equal resultants and equal moments about some point (see Section 4.5.3) Euler angles—angles generated by a 1-3-1 or a 3-1-3 rotation sequence of a body relative to a reference frame (see Section 8.8) Euler parameters—a set of four parameters defining the orientation of a body (see Section 8.16) Eversion—rotating the soles of the feet outward so as to cause a varus leg position (opposite of inversion; see Figure 2.21) Extension—the straightening of a limb, or the backward movement of the head=neck (opposite of flexion; see, for example, Figures 2.13, 2.14, and 2.15) Femur—thigh bone (see Figure 2.22) Fibrillation—erratic muscle contraction (see also twitching) Fibula—smaller of the two lower leg bones Finite-segment modeling—representing a system by lumped masses or indi- vidual bodies (see Figure 2.3); also called lumped-mass modeling First moment—the product of a particle mass and the position vector locating the particle. First moments are used to locate mass centers as in Section 9.2 Flexion—the bending of a limb, or the forward bending of the head=neck (chin to chest; opposite of extension; see, for example, Figures 2.13, 2.14, and 2.15) Flexural stress—stress arising due to bending of a structure Foramen—an opening through a bone Force—a push or pull (see Section 4.1) Free vector—a vector (such as a unit vector) which is not restricted to a specific line or point Frontal bone—the front and top of the skull (see Figure 2.24) Frontal plane—see coronal plane Gait—the procedure of walking; walking analysis Generalized coordinates—variables describing the degrees of freedom of multibody systems or of human body models Generalized forces—forces (and moments) projected onto partial velocity (and partial angular velocity) vectors (see Section 12.2) Generalized speed—a linear combination of generalized coordinate deriva- tives (see Section 11.6) Gross modeling—representing a system as a whole
Glossary 407 Gross-motion simulator—a whole-body model as in Figure 6.1 Haversian system—a set of concentric cylindrical layers of bone containing an inner blood supply; also called an osteon Heel strike—in walking, the beginning of the support phase of a leg Hematoma—bruising or bleeding between the brain and skull, or elsewhere in the body Hinge joint—a pin or revolute joint with one rotational degree of freedom (see Figure 2.28) Horizontal plane—see transverse plane Humerus—upper arm bone (see Figure 2.22) Identity dyadic—a dyadic whose scalar components are the same as the values of the Kronecker delta function (see Equations 3.48 and 3.49) Identity matrix—a matrix whose diagonal elements are one and whose off-diagonal elements are zero (see Section 3.6.2) Inertia—mass and mass distribution; resistance to movement Inertia dyadic—a dyadic composed from inertia vectors and unit vectors (see Equation 10.17) Inertia forces—forces due to accelerations; also called passive forces, as opposed to applied (or active) forces (see Section 12.1) Inertia matrix—a matrix whose elements are moments and products of inertia (see Equation 10.18); also, the matrix whose elements are components of an inertia dyadic Inertia vector—a vector useful in determining inertia properties of particles and rigid bodies, as defined by Equation 10.3; also called second moment vector Inertial reference frame—a reference frame where Newton’s laws are valid; also called a Newtonian reference frame Inferior—toward the feet, or downward (opposite of superior) Injury—failure or damage of the tissue of a biosystem Integrated seat belt—a seat belt webbing with the shoulder belt portion anchored to the seat backrest Inverse dyadics—dyadics which multiplied together produce the identity dyadic (see Equations 3.57 through 3.60) Inverse matrix—a matrix whose product with a matrix produces an identity matrix (see Equation 3.95) Inversion—rotating the soles of the feet inward so as to cause a valgus leg position (opposite eversion; see Figure 2.21) Isometric—a muscle contraction which does not produce movement Isotonic—a constant force muscle contraction Isotropic material—a material having the same properties in all directions Kane’s equations—equations (analogous to Lagrange’s equations or Newton’s laws) which are ideally suited for dynamic analyses of human body models (see Section 13.1) Kinematics—a study of motion and movement
408 Glossary Kinesiology—the study of human movement and the associated mechanics thereof Kinetics—a study of forces and force systems Kronecker delta function—a double index function with values 1 and 0 depending on whether the indices are equal or not equal (see Equa- tion 3.23); also, elements of the identity matrix Lateral—toward the outside, away from the median (or saggital) plane (opposite of medial) Lateral collateral ligament—a ligament on the lateral side of the knee between the femur and fibula Ligament—cord or cable connecting bone to bone Load limiter—a device or seat belt design intended to limit peak seat belt forces during a vehicle crash Lower body array—an array of numbers defining the connection configu- rations of a multibody system (see Section 6.2) Lumbar—lower back Lumped-mass modeling—representing a system by finite segments or indi- vidual bodies (lumped masses) (see, for example, Figure 10.1); also called finite-segment modeling Mandible—jaw bone Mass center—a point of a body, or within a set of particles, for which the sum of the first moments of the particles of the body, or set, is zero; also called center of gravity Mathematical shear strain—see Equation 5.17 Matrix—a structured array of numbers (see Section 3.6) Matrix transpose—a matrix resulting from the interchange of the rows and columns of a given matrix (see Section 3.6.3) Maxilla—upper jaw bone Medial—toward the middle or median (saggital) plane (opposite of lateral) Medial collateral ligament—a ligament on the medial side of the knee between the femur and tibia Median plane—see saggital plane Melanin—a dark pigment providing color to the skin Membrane analogy—a means of modeling the torsional response of noncircular cross-section rods; also called soapfilm analogy (see Section 5.17) Metacarpal—refers to the bones of the hand Metatarsal—refers to the bones of the feet Modeling—bone formation, or bone growth Modeling—mathematical representation of a physical body or system; a simplified, and usually reduced size, object or structure representing a body or system Modulus of rigidity—see shear modulus Moment of inertia—the projection of the second moment vector (inertia vector) along the direction used to form the second moment vector, as defined by Equation 10.5 (see also Equation 10.14 for a geometric interpretation)
Glossary 409 Negative force system—if two force systems S1 and S2 when superimposed result in a zero system, then S1 and S2 are said to be negative to each other Neutral axis—a median axis of a beam which is neither in tension nor compression as the beam is bent Newtonian reference frame—a reference frame where Newton’s laws are valid; also called an inertial reference frame Normal strain—a strain component normal to or perpendicular to a surface (see also simple strain) Normal stress—a stress component at a point of a surface directed normal to or along the perpendicular to the surface Occipital—refers to the back of the head Occipital bone—the rear part of the skull (see Figure 2.24) Orbital—refers to the eye socket Order—dimension of a matrix. For a square matrix, the order is the number of rows (or columns) of the matrix Orthogonal complement array—an array C which when premultiplied by a given array B produces a zero array, that is, BC ¼ 0; orthogonal complement arrays are used in processing constraint equation arrays (see Sections 13.7 and 13.8) Orthogonal dyadic—a dyadic whose inverse is equal to its transpose (see Equation 3.61) Orthogonal matrix—a matrix whose inverse is equal to its transpose Osteoblast—a bone-forming cell Osteoclast—a bone-resorbing cell Osteocyte—bone cell Osteon—the primary structural component of cortical (compact) bone; also called the Haversian system Osteoporosis—a bone disease (porous bones) characterized by low bone mineral density Parallelogram law—geometric representation of a vector addition (see Figure 3.5) Parietal bone—the side and rear upper part of the skull (see Figure 2.24) Partial angular velocity—the vector coefficient in an angular velocity vector of a generalized coordinate derivative or of a generalized speed (see Section 11.4) Partial velocity—the vector coefficient in a velocity vector of a generalized coordinate derivative or of a generalized speed (see Section 11.10) Partitioned matrix—a matrix divided into submatrices Passive forces—forces due to accelerations; also called inertia forces, as opposed to ‘‘active’’ (or applied) forces (see Section 12.1) Pectoral—refers to the breast or chest Performance—activity of a living system Permutation symbol—a three index function having values 1, À1, and 0, depending upon whether the indices are cyclic, anticyclic, or non- distinct (see Equation 3.36)
410 Glossary Pia mater—fibrous membrane beneath the arachnoid and on the outer sur- face of the brain Pin joint—a hinge or revolute joint with one rotational degree of freedom (see Figure 2.28) Pitch motion—leaning or tilting forward or backward (see Section 15.2) Plantar flexion—pushing the toe of the foot downward, as in accelerating a vehicle (opposite of dorsiflexion; see Figure 2.20) Poisson’s ratio—an elastic constant which is a measure of the transverse contraction of a body being elongated or transverse expansion of a body being shortened; also known as the transverse contraction ratio (see Equation 5.69) Porpoising—a vehicle occupant moving up relative to a seat belt, particularly a lap belt (see Section 15.7) Posterior—toward the rear or back (opposite of anterior) Pretensioner—a device for eliminating slack and for tightening a seat belt in the beginning of a motor vehicle crash Principal direction—the direction of an eigenvector or of a principal vector Principal value—the parameter l in the expression Ax ¼ lx (see Equation 3.135) Principal vector—the vector x in the expression Ax ¼ lx (see Equation 3.135) Product of inertia—the projection of the second moment vector (inertia vector) along a direction different than that used to form the second moment vector, as defined by Equation 10.4 (see also Equation 10.15 for a geometric interpretation) Pronation—axial rotation of the forearm so that the palm of the hand faces downward (opposite of supination; see Figure 2.17) Prone—lying on the stomach Pseudoinverse of a matrix—a matrix which for a singular matrix has pro- perties analogous to that of an inverse (see Section 3.6.18) Quasicoordinate—a variable (generally nonexisting) whose derivative is a generalized speed (see Section 11.6) Radius—anterior lower arm bone Radius of gyration—a geometric quantity (a length) used for determining moment of inertia (see Section 10.5) Rank—the dimension of the largest nonsingular submatrix of a matrix Reference configuration—an orientation and positioning of the bodies of the human frame so that the local coordinate axes are all mutually aligned and also aligned with the global axes of the torso Rehabilitation—recovery from injury or disease Remodeling—bone resorption and subsequent reformation, sometimes called bone maintenance Resultant—the sum of vectors (see Section 3.2.5) Revolute joint—a pin, or hinge, joint with one rotational degree of freedom (see Figure 2.28) Roll motion—rotation about a spinal axis (see Section 15.2)
Glossary 411 Rotation dyadic—a dyadic which when multiplied with a vector rotates the vector about a given line through a specified angle (see Sec- tion 8.15) Row matrix, row array—a matrix with any one row Sacrum—a fusion of five vertebrae at the base of the spine; the tailbone Saggital plane—the midplane dividing the human body into its left and right parts, also called the median plane (see Figure 2.8) Scalar product—a means of multiplying vectors resulting in a scalar (see Equation 3.19) Scalar triple product—a product of three vectors producing a scalar (see Equation 3.63) Second moment of area—a geometric property of beam cross sections, some- times regarded as an area moment of inertia (see Equation 5.105) Second moment vector—a vector useful in determining inertia properties of particles and bodies, as defined by Equation 10.3; also called inertia vector Shear modulus—proportionality constant in linear shear stress–shear strain relations (see Equation 5.68); also known as the modulus of elasticity in shear or the modulus of rigidity Shear stress—a stress component at a point of a surface directed tangent to the surface Simple angular velocity—the angular velocity of a body rotating about a fixed axis (see Equation 8.19) Simple couple—a couple with only two forces (equal in magnitude, but oppositely directed; see Section 4.5.2) Simple strain—intuitively an average deformation, or a change in length per unit length; see also normal strain (see Section 5.2 and Equa- tion 5.18) Simple stress—uniaxial or normal stress (see Section 5.1) Single support—the condition in walking where only one foot is on the walking surface, as opposed to ‘‘double support,’’ where two feet are on the walking surface Singular matrix—a matrix whose determinant is zero Slider joint—a simple translation joint (see Figure 2.29) Sliding vector—a vector acting along a specific line of action (also called a bound vector) Soapfilm analogy—a means of modeling the torsional response of non- circular cross-section rods; also called membrane analogy (see Sec- tion 5.17) Spacewalk—an astronaut moving in space outside a satellite Sphenoid bone—the frontal base of the skull (see Figure 2.24) Spherical joint—a ball-and-socket joint with three rotational degrees of freedom Sprain—the stretching or yielding of a ligament or tendon Square matrix—a matrix with the same numbers of rows and columns
412 Glossary Step length—in walking, the distance in the direction of walking of two successive footprints (one from each foot) Sternum—cartilage forming the breastbone Strain—see Section 5.2 Stress—the limiting value of a force component per unit area as the area shrinks to zero (see Section 5.1) Stress vector—the vector of stress components acting at a point of a given surface (see Section 5.1) Stride—in walking, the time required to complete both the support phase and the swing phase for a leg Stride length—in walking, the distance between two successive footprints of the same leg Subcutaneous—beneath the dermis (skin) Submarining—a vehicle occupant sliding under a seat belt, particularly a lap belt; alternatively, a lap belt moving up on an occupant’s torso (see Section 15.7) Submatrix—a matrix formed by eliminating rows and=or columns from a given matrix Summation convention—a rule that repeated indices represents a sum over the range of the index (see Equations 3.16 and 3.17) Superior—toward the head, or upward (opposite of inferior) Supination—axial rotation of the forearm so that the palm of the hand faces upward (opposite of pronation; see Figure 2.17) Supine—lying on the back Swing—in walking, the movement of a nonsupporting leg (see Section 15.4.1) Symmetric dyadic—a dyadic equal to its transpose (see Equation 3.52) Symmetric matrix—a matrix which is equal to its transpose (see Section 3.6.5) Synovial fluid—a lubricating fluid in joints and tendon sheaths Temporal bone—the side and base of the skull (see Figure 2.24) Tendon—cord or cable connecting muscle to bone Tension—a force or stress tending to elongate or enlarge a body Tetanic—erratic muscle contraction or spasm Thoracic—referring to the chest Tibia—largest of the two lower leg bones (see Figure 2.22) Tissue—biological material (see Section 7.1) Toe off—in walking, the ending of the support phase of a leg Torque—the moment of a couple (see Section 4.5.2) Trabecula—a ‘‘little beam’’ bone structure in cancellous or soft bone Trabecular bone—soft or spongy bone; also called cancellous bone (see Section 7.2) Trace—the sum of the diagonal elements of a square matrix Transformation matrix—a matrix whose elements are used to relate vector components referred to different unit vector bases, as defined and illustrated in Equations 3.160 through 3.168 Transition movement—a movement successively employing different muscle groups
Glossary 413 Transverse contraction ratio—see Poisson’s ratio Transverse plane—a horizontal plane dividing the human body into its upper and lower parts (see Figure 2.8) Triple vector product—a product of three vectors producing a vector (see Equations 3.69 and 3.70) Twitching—erratic muscle contraction or spasm Ulna—posterior lower arm bone Uniaxial strain—one-dimensional strain Uniaxial stress—one-dimensional stress Unit vector—a vector with magnitude one (see Section 3.2.2) Valgus—leg position with the knees separated more than the feet (bow- legged; opposite of varus; see Figure 2.19) Varus—leg position with the knees close together (knock-kneed; opposite of valgus; see Figure 2.19) Vector—intuitively, a directed line segment with the characteristics of magnitude, orientation, and sense (see Section 3.1). More formally, vectors are elements of vector spaces [12,15,20] Vector product—a means of multiplying vectors resulting in a vector (see Equation 3.31) Vector–vector—a dyadic (see Section 3.4) Velocity—see Section 8.3 Wolff’s law—in short: form follows function (see Section 7.1) Yaw motion—leaning or tilting side-to-side (see Section 15.2) Young’s modulus of elasticity—see elastic modulus Zero dyadic—a dyadic whose scalar components are zero Zero force system—a force system with a zero resultant and a zero moment about some point (see Section 4.5.1) Zero matrix—a matrix, all of whose elements are zero (see Section 3.6.1) Zero vector—a vector with magnitude zero (see Section 3.2.3)
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Bibliography 417 D. R. Peterson and J. D. Bronzino (Eds.), Biomechanics Principles and Applications, CRC Press, Boca Raton, FL, 2008. J. A. Pike, Automotive Safety—Anatomy, Injury, Testing, and Regulation, Society of Automotive Engineers, Warrendale, PA, 1990. B. O. Polsson and S. N. Bhatia, Tissue Engineering, Pearson=Prentice Hall, Upper Saddle River, NJ, 2004. V. Putz-Anderson (Ed.), Cumulative Trauma Disorders—A Manual for Musculoskeletal Diseases of the Upper Limbs, Taylor & Francis, London, 1994. H. Reul, D. N. Ghista, and G. Rau (Eds.), Perspectives in Biomechanics, Harwood Academic Publishers, London, England, 1978. A. B. Ritter, S. Reisman and B. B. Michnaik, Biomedical Engineering Principles, CRC, Taylor & Francis, Boca Raton, FL, 2005. J. A. Roebuck Jr., K. H. E. Kroemer, and W. G. Thompson, Engineering Anthropometry Methods, John Wiley & Sons, New York, NY, 1975. J. A. Roebuck Jr., Anthropometric Methods: Designing to Fit the Human Body, Human Factors and Ergonomics Society, Santa Monica, CA, 1995. A. Seireg and R. Arvikar, Biomechanical Analysis of the Musculoskeletal Structure for Medicine and Sports, Hemisphere Publishing Corporation, New York, 1989. S. L. Stover, J. A. DeLisa, and G. G. Whiteneck (Eds.), Spinal Cord Injury—Clinical Outcomes from the Model Systems, Aspen, Gaithersburg, MD, 1995. A. R. Tilley, The Measure of Man and Woman, Henry Dreyfuss Associates, New York, 1993. C. L. Vaughan, G. N. Murphy, and L. L. du Toit, Biomechanics of Human Gait— Annotated Bibliography, 2nd edn., Human Kinetics Publishers, Champaign, IL, 1987. A. A. White III and M. M. Panjabi, Clinical Biomechanics of the Spine, J. B. Lippincott Company, Philadelphia, PA, 1978. W. C. Whiting and R. F. Zernicke, Biomechanics of Musculoskeletal Injury, Human Kinetics, Champaign, IL, 1998. D. A. Winter, Biomechanics of Motor Control of Human Movement, 2nd edn., John Wiley & Sons, New York, 1990. R. Wirhed, Athletic Ability and the Anatomy of Motion, Wolfe Medical Publications, London, England, 1989. W. E. Woodson, B. Tillman, and P. Tillman, Human Factors Design Handbook, 2nd edn., New York, McGraw-Hill, 1992. N. Yoganandan, F. A. Pintar, S. J. Larson, and A. Sances Jr. (Eds.), Frontiers in Head and Neck Trauma—Clinical and Biomechanical, IOS Press, Amsterdam, the Netherlands, 1998. D. Zacharkow, Posture: Sitting, Standing, Chair Design and Exercise, Springfield, IL, Charles C Thomas Publishers, 1987.
Index A generalized speeds, 276–279 kinematics, 261–266 Abduction, 17, 19, 403 matrices, 403 Abductors, 24 relative, 146, 177, 263, 316 Absolute angular velocity, 145–146, 263 simple, 172, 411 Absolute velocity, 145, 169–171, 403 singularities with, 200–201 Acceleration, 169–171, 403 Annular bones, 21 Anterior, 11–12, 14, 403 angular, 195–197, 279–282 coronal plane, 13 mass center, 290–291 Anterior cruciate ligament, 161 of particles, 167–169 Anthropometric data, 24–26, 370 relative velocity, 199–200 Aorta, 403 Acetabulum, 403 Applications, 337–362 Achilles tendon, 161 Applied forces, 215–217, 295–296, 403 Acromion, 403 Arachnoid, 161, 162, 403 Actin, 158 Arms Action-reaction, 77–78 extension, 15 Active forces, 215–217, 295–296, 403 flexion, 15 Addition length, 25 of matrices, 50–51 Arrays, 48–53; see also Lower body array; of vectors, 32–36 Addition theorem, for angular velocity, Orthogonal complement arrays 178–179, 193, 403 constraint force, 321 Adduction, 15, 17, 19, 403 row matrix, row, 411 Adductors, 24 Articulation moments, joints, 304–306 Adenosine diphosphate (ADP), 159 ATP, see Adenosine triphosphate Adenosine triphosphate (ATP), 159 Avulsion, 403 ADP, see Adenosine diphosphate Axial rotation, 14 Afferent, 403 Axilla, 403 Air bags, 352 Angles B Bryant, 188, 403 Ball-and-socket joint, 22, 23, 403 dextral rotation, 188, 405 simulation with, 10 Euler, 188, 189, 259, 406 orientation, 200–201, 274 Barber poling, 352, 403 vectors, 37 Base vectors, 297 Angular acceleration, 195–197, 279–282 Beam theory, 105–111 Angular bracket functions, 115–117 Beltrami-Mitchell equations, 403 Angular velocity, 145–146, 171–176, 403; Bending moment, 111 see also Partial angular velocity cantilever beam, 128–129 absolute, 145–146, 263 displacement, 111 addition theorem for, 178–179, 193, 403 positive, 114 configuration graph for, 190–192 stress, 109–110 dextral configuration, 262 Biceps, 23, 24 Euler parameters, 208–210 inverse relations of, 210–212 419
420 Index Biomechanics, 403 C principal areas of, 1–2 Cadence, 345, 403 Biosystem, 1, 59, 403 Cancellous bone, 154, 404 forces, 71 Cantilever beam, 76, 117–129 Block multiplication of matrices, bending moment, 128–129 52, 403 displacement, 128–129 Cardiac muscle, 23, 158 Bodies, 165 Carpal, 404 position and direction, 10–14 Cartesian coordinate system, 10, 90, 166, Body segments, 8, 9, 312 266 coordinate axes, 12 Cartilage, 159–160, 404 female, 377–379 male, 374–376 compression, 160 inertia dyadic for ribs, 159 female, 255 Caudal, 404 male, 252–253 Center of gravity, 215–217, 404 inertia matrices Central inertia dyadic, 236, 338, 404 female, 394–402 Cerebrum, 404 male, 386–394 Cervical, 9, 20, 404 mass foramen of, 22 female, 253, 372–373 head and neck, 21–22 male, 250, 371–372 vertebrae, 21 mass center Characteristics of a vector, 404 female, 254, 383–385 Chest, 9 male, 251, 380–382 Clavicle, 19 particles of, 232–234 Cockpit, 353, 404 reference points Collagen, 159, 404 female, 254 Column matrix, 404 male, 250–251 Compact bone, 154, 404 Compatibility equations, 99–102, 404 Bone, 20–21, 154 Complementary energy, 133 cells, 154–155 Component, 32, 404 compression, 156, 157 Compression, 404 development of, 156–157 bones, 156, 157 failure of, 157–158 cartilage, 160 fracture, 157–158 Concussion, 162, 404 maintenance, 403 Configuration graph, 180–190, 404 mass density of, 155 for angular velocity, 190–192 physical properties of, for unit vector, 186–187, 193 155–156 Conformable matrices, 404 strengthening of, 158 Constrained system dynamics, 322–324 tension, 156 Constraint equations, 317–319, 331, 404 generalized speeds, 318 Boundary element methods, 134 for waitron tray, 359 Bound vector, 69, 403 Constraint forces, 319–321 Brain array, 321 equivalent force systems, 320 injury, 161–162 on movements, 330 tissue, 161–162 on multibody system, 319, 322–324 Breast stroke, 349–350 orthogonal complement array, 323 Bryant angles, 188, 403 Bulk modulus, 99 Burden bearing, 354–359 Buttocks height, 25
Index 421 Contact forces, across joints, 301–302 Degloving, 161, 405 Convulsion, 159, 404 Degrees of freedom, 405 Coordinate axes in crash-victim simulator, 353 body segments, 12 generalized speeds, 275, 316, 337 female, 377–379 of human body model, 312 male, 374–376 for kinematics, 257–261 variables with, 259 Cartesian, 10, 90, 166, 266 Deltoid, 24, 405 curvilinear, 102–105 Dermis, 162, 405 cylindrical, 102–103, 266 Determinants, 45, 50, 53–55 generalized, 266–268, 406 properties of, 55 for human body model, 249 Dextral configuration, 40, 211, 259, for kinematics, 257–261 reference frames 271–272 angular velocity, 262 female, 377–379 Dextral rotation angles, 188, 405 male, 374–376 Diagonal matrix, 50, 405 spherical, 103–105, 266 Diaphysis, 20, 405 Coordinate axes of body, 11 Diffuse axonal injury (DAI), 162, 405 Coordinate planes, 14 Digits, 405 Coronal plane, 11–12, 404 kinematics of, 10 anterior, 13 Dilatation, 99 Cortical bone, 154, 404 Dimensions of a matrix, 405 elastic modulus for, 156 Direction, 14; see also Principal direction Costal, 404 upward, 13 Coup=contra coup injury, 162, 404 Discs, 21 Couples, 74, 404 Displacement, 101, 316 simple, 74, 411 bending moment, 111 torque of, 74 cantilever beam, 128–129 Cramer’s rule, 53 Distal, 13, 14 Crash-victim simulator, 404 Dorsiflexion, 19, 405 degrees of freedom in, 353 foot, 18 human body model, 350–351 Dot product, 43–44 kinematics, 353 Double support, 345, 405 kinetics, 353 Dual vector, 199, 405 numerical analysis, 353–354 Dummy force method, 405 vehicle environment model, 351–353 Dura mater, 161, 405 Cross product, 39 Dyad, 42, 405 Cross section stress, 111 Dyadic, 42–44, 405 Curved beams, 114–115 central inertia, 236, 338, 404 Curvilinear coordinates, 102–105 identity, 42–43, 206, 407 Cutaneous, 404 inertia, 229–230 Cylindrical coordinates, 102–103, 266 for body segments, 252–253, 255 D inverse, 44, 407 multiplication of, 43–44 DAI, see Diffuse axonal injury orthogonal, 44, 409 D’Alembert’s principle, 215, 405 rotation, 201–206, 411 Dampers, 9 strain, 42 Deformation, 84–85 stress, 42, 84 symmetric, 43, 412 sign conventions for, 105–106 zero, 42, 413
422 Index Dyadic product, 37, 41, 405 generalized speeds, 318 Dyadic transpose, 43, 405 governing dynamical equations, 314, Dyadic=vector product, 47–48, 405 Dynamical equations, see Governing 331–332 orientation, 201–202, 315 dynamical equations Eversion, 19, 406 Dynamics, 405 foot, 18 varus, 18 of human body model, 311–326 Evertors, 24 Kane’s equations for, 334 Extension, 14, 19, 406 modeling, 151 arm, 15 head and neck, 14, 16 E legs, 15 muscles, 23 Efferent, 405 Extensors, 24 Eigenvalues, 59–65, 405 Eye height, 25 maximum minimum, 65–66 F orthogonal complement arrays, Fatigue fracture, 157 324–325 Femur, 19, 406 Eigenvalues of inertia, 405 Fibrillation, 159, 406 Fibula, 19, 406 principal directions and, 237–241 Finite-element methods, 134 symmetrical bodies and, 241–242 Finite-segment modeling, 7, 406 Eigenvectors, 59–65, 90, 92, 405; see also First moment, 406 Flexion, 14, 19, 406 Unit eigenvectors orthogonal complement arrays, arm, 15 head and neck, 14, 16 324–325 legs, 15 Elastic modulus, 406 muscles, 23 Flexors, 24 for cortical bone, 156 Flexural stress, 111, 406 Elasticity theory, 101 Flutter kick, 349 Elastin, 161 Foot Elbows, 22–23 dorsiflexion, 18 Element faces, 83 eversion, 18 Elements of a matrix, 48, 406 horizontal foot reaction force, 343 Elongation inversion, 18 normalized foot force, 346 neck, 14 plantar flexion, 18 strain, 84–86 vertical foot reaction force, 343 Energy methods, 133–139 Foramen, 406 Engineering shear strain, 87, 406 of cervical, 22 Epidermis, 162, 406 Forces, 69–78, 406; see also Constraint Epiligament, 161, 406 Epiphysis, 20, 406 forces; Generalized forces Epitendon, 161, 406 active (applied), 215–217, 295–296, Equal matrices, 49 Equilibrium equations, 99–102 403 Equivalent force systems, 74–77, 221–224, biosystem, 71 horizontal foot reaction, 343 406 constraint forces, 320 Euler angles, 188, 189, 259, 406 Euler parameters, 206–208, 316, 406 angular velocity, 208–210 inverse relations of, 210–212
Index 423 interactive, 297 constraint equations, 318 on joints, 300–306 degrees of freedom, 275, 316, 337 of ligament, 302–304 Euler parameters, 318 lines, 70–71 in governing dynamical equations, nonworking, 297 normalized foot, 346 313 normalized hip, 347 for multibody systems, 276 normalized knee, 346 partial angular velocity, 280 object points, 72 relative angular velocity, 316 one-way, 352 Governing dynamical equations, 311, passive, 215, 295–296, 409 reference points, 72 313–314 systems of, 71–77 development of, 329–331 of tendons, 302–304 Euler parameters, 314, 331–332 vectors, 69 generalized speed, 313 vertical foot reaction, 343 Kane’s equations, 335 for waitron tray, 358 numerical integration, 212–213 water, 347–348 Gravity Forearm, rotation, 16 center of, 215–217, 404 Fractures, 157–158 generalized active forces, 306–307 Free-space on human body model, 306 human body model, 339–341 Gross modeling, 7–10, 406 swimming motion, 348–349 Gross-motion modeling, 150–151 Free vector, 69, 71, 406 Gross-motion simulator, 7, 337, 407 Frontal bone, 20, 406 human body model for, 333–334 Frontal plane, 11–12, 406 Gyroscopic effects, in walking, 361–362 G H Gait, 344, 406 Hamilton-Cayley equation, 88 Galerkin analyses, 134 Hamstrings, 23, 24 Generalized active forces Hand, kinematics of, 10 Hand and wrist model, 10, 146–149 generalized inertia forces, 334 Hard tissue, 153–154 gravity, 306–307 Haversian system, 155, 407 on human body model, 299–300 Head and neck Kane’s equations, 311 Generalized coordinates, 266–268, 406 brain, 161–162 Generalized forces, 297–299, 406 cervical, 21–22 for human body model, 312–313 extension, 14, 16 orthogonal complement array, 324 flexion, 14, 16 partial angular velocity, 335 lateral bending, 16 partial velocity, 335 model, 9, 146–149 Generalized force triangle, 322 orientation of, 12 Generalized inertia forces, 307–309 skull, 19, 20, 161–162 generalized active forces, 334 twisting, 16 Kane’s equations, 311 Heavy hanging cable, 354–356 Generalized mass, 330 Heel strike, 345, 407 Generalized speeds, 273–276, 406 Hematoma, 161, 407 angular velocity, 276–279 Hinge joint, 22, 407 Hip, 23 normalized hip force, 347
424 Index Hooke’s law, 94–96, 151 Inertia forces, 295–296, 407 Horizontal foot reaction force, 343 kinetics, 215–224 Horizontal plane, 11, 407 on particles, 223 Human anthropometric data, 369 Human body model, 8, 191–192; see also Inertial reference frames, 9, 166, 407 Inertia matrices, 407 Body segments body segments of, 312 body segments coordinate axes for, 249 female, 394–402 crash-victim simulator, 350–351 male, 386–394 degrees of freedom of, 312 dynamics of, 311–326 unit eigenvector, 240–241 free-space, 339–341 Inertia vectors, 227, 407 generalized active forces on, 299–300 Inferior, 13, 14, 407 generalized forces for, 312–313 Injury, 1, 407 gravity on, 306 for gross-motion simulator, 333–334 brain, 161–162 inertia in, 225–255 coup=contra coup, 162, 404 input data for, 332 DAI, 162, 405 kinematics of, 257–293 to lumbar, 22 kinetics of, 295–309 whole body model, 149 lower body array for, 265 Inside vectors, 184, 185, 187 mass center of, 221, 284, 287 Integrated seat belt, 351–352, 407 numbering labeling of, 194, 245–255 Interactive forces, at joints, 297 partial angular velocity for, 283 Inverse dyadic, 44, 407 particles, 222–223 Inverse matrices, 51–52, 407 position vectors for, 287 Inversion, 19, 407 variable names for, 261 foot, 18 Humerus, 19, 407 valgus, 18 Hydrostatic pressure, 99 Invertors, 24 Isometric, 159, 407 Isotonic, 407 Isotropic material, 1, 97, 155, 234, 407 I J Ideal geometry, 151 Jaw, 20 Identity dyadic, 42–43, 206, 407 Joints, 22–23 Identity matrix, 49, 407 Ilium, 19 articulation moments, 304–306 Index notations, 36 contact forces across, 301–302 Inertia, 407 forces on, 300–306 interactive forces at, 297 eigenvalues of, 237–242, 405 spine, 23 generalized inertia forces, 307–309 K generalized active forces, 334 Kane’s equations, 311 Kamman’s procedure, 329 in human body model, 225–255 Kane’s equations, 311–312, 322, 353–354, moment of, 225–229, 408 product of, 225–229, 410 407 Inertia dyadic, 229–230 for dynamics, 334 for body segments, 252–253 generalized inertia forces, 311 female, 255 for governing dynamical equations, male, 252–253 335
Index 425 Kick strokes, in swimming, 349–350 Load limiter, 408 Kinematics, 407 Load sharing, between muscle groups, angular velocity, 261–266 360 coordinate axes for, 257–261 Local unit vectors, 171 crash-victim simulator, 353 Long bones, 20, 154 degrees of freedom for, 257–261 Lower body array, 142–146, 195, digits, 10 hand, 10 244–245, 408 human body model, 257–293 for human body model, 265 lower body array for, 334 for kinematics, 334 notation for, 257–261 partial angular velocity, 278 Kinesiology, 14, 408 Lumbar, 20, 408 Kinetics, 408 injury to, 22 crash-victim simulator, 353 Lumped-mass modeling, 141–142, 408 fundamental equations for, 165–213 of human body model, 295–309 M inertia forces, 215–224 Knees, 22–23 Mandible, 20, 408 normalized knee force, 346 Mass, of body segments Kronecker delta function, 46, 55–58, 99, female, 253, 372–373 204, 408 male, 250, 371–372 Mass center, 217–221, 408 L acceleration, 290–291 for body segments Lagrange’s equations, 311–312, 335 Lateral, 13, 14, 408 female, 254, 383–385 male, 251, 380–382 sagittal plane, 13 of human body model, 221, 284, 287 Lateral bending, 14, 19 for multibody system, 285 partial angular velocity of, 338 head and neck, 16 partial velocity of, 338 Lateral collateral ligament, 161, 408 positions, 282–288 Law of cosines, 33 velocity, 288–290 Law of sines, 33 Mass density, of bones, 155 Least squares, 134 Mathematical shear strain, 87, 408 Legs Matrices, 44, 48–53, 408 addition of, 50–51 extension, 15 angular velocity, 403 flexion, 15 block multiplication of, 52, 403 length, 25 column, 404 valgus, 17 conformable, 404 varus, 17 diagonal, 50, 405 Lifting=lowering function, 343 dimensions of, 405 Lifting simulation, 342–344 elements of, 48 Ligament, 20, 160–161, 408 equal, 49 forces of, 302–304 identity, 49, 407 Limbs; see also Arms; Legs inertia, 407 orientation of, 13 body segments, 386–394 swimming motion, 348–349 unit eigenvector, 240–241 Line of action, 70 inverse, 51–52, 407 Lines, forces, 70–71 measures of, 50 Load displacement, 111
426 Index multiplication of, 51 Muscles orthogonal, 52, 205, 409 extension, 23 partitioned, 52, 409 flexion, 23 pseudoinverse of, 53 groups of, 23–24, 158 rows columns of, 49 load sharing between, 360 scalars, 50 strength of, 356 singular, 50 tissue, 158–159 skew-symmetric, 50 uniform muscle stress criterion, square, 49, 411 356–357 symmetric, 49 transformation, 92 Myosin, 158 zero, 49, 413 Matrix transpose, 49, 408 N Maxilla, 408 Medial, 14, 408 Neck; see also Head and neck Medial collateral ligament, 161, 408 elongation, 14 Median plane, 11–12, 408 injuries, in rollover accidents, 362 Melanin, 162, 408 Membrane analogy, 408 Negative force system, 77, 409 Meningeal tissue, 161 Neutral axis, 409 Metacarpal, 408 Newtonian reference frame, 78, 151, Metatarsal, 408 Midriff, 9 215–216, 409 Mid shoulder height, 25 Newton’s laws, 311 Modeling, 155, 408; see also Specific Models Newton’s second law, 215 Nonholonomic systems, 311 or modeling Nonlinear springs and dampers, 9, 10 dynamics, 151 Nonrigid bodies, 75 head and neck, 9 Nonworking forces, 297 of human frame, 8 Normalized foot force, 346 Modulus of rigidity, 96, 408 Normalized hip force, 347 Mohr’s circle, 89–94 Normalized knee force, 346 Moment of inertia, 225–229, 408 Normal strain, 86, 409 Moments of force, 69–70 Normal stress, 80, 83, 409 Movements, 14–19 Notation constraint forces on, 330 transition, 361, 412 index, 36 Multibody systems, 141–142 for kinematics, 257–261 constraint forces on, 319, 322–324 summation, 36 generalized speeds for, 276 Numerical integration, of governing mass center for, 285 partial angular velocity for, 282 dynamical equations, 212–213 position vectors for, 246, 285 Numerical methods, 329–335 Multiple products, of vectors, O 44–48 Multiplication Object points, forces, 72 Occipital, 409 block multiplication of matrices, 52, Occipital bone, 20, 409 403 Occupant kinematics, 350 One-way forces, 352 of dyadics, 43–44 Open-chain multibody system, 142, 244 of matrices, 51 Orbital, 20, 409 vectors, 37–41, 172 Order, 409
Index 427 Orientation Patella, 19 burden bearing, 354 Patellar tendon, 161 Euler parameters, 201–202, 315 Pectoral, 409 of head and neck, 12 Pelvis, 9 of limbs, 13 Performance, 1, 409 for waitron tray, 358 Permutation symbol, 55–58, 409 Perpendicular vectors, 230 Orientation angles, 200–201 derivatives, 274 addition of, 32–36 Pia mater, 161, 410 Orthogonal complement arrays, 409 Pin joint, 10, 22, 410 constraint forces, 323 Pitch motion, 340–341, 410 determination of, 324–325 Planes of body, 11–12 eigenvalues, 324–325 Plantar flexion, 19, 161, 410 eigenvectors, 324–325 generalized forces, 324 foot, 18 Points, 165 Orthogonal dyadic, 44, 409 Poisson’s ratio, 96, 410 Orthogonal matrix, 52, 205, 409 Porpoising, 352, 410 Osteoblast, 155, 409 Position vectors Osteoclast, 155, 409 Osteocyte, 155, 409 for human body model, 287 Osteon, 155, 409 for multibody systems, 246, 285 Osteoporosis, 157–158 Positive bending moment, 114 Outside vectors, 184, 185, 187 Posterior, 11–12, 13, 14, 410 Posterior cruciate ligament, 161 P Potential energy, 133 Pretensioner, 352, 410 Parallel axis theorem, 234–237 Principal direction, 59–65, 410 Parallelogram law, 32, 409 eigenvalues, of inertia, 237–241 Parietal bone, 20, 409 Principal values, 410 Partial angular velocity, 268–270, 273, of strain, 88–89 of stress, 88–89 409 Principal vector, 410 array, 331 Product of inertia, 225–229, 410 generalized forces, 335 Pronation, 15, 410 generalized speeds, 280 Pronators, 24 for human body model, 283 Prone, 349, 410 lower body array, 278 Proximal, 13, 14 of mass center, 338 Pseudoinverse of a matrix, 53, 410 for multibody system, 282 Partial velocity, 409 Q array, 331 generalized forces, 335 Quadriceps, 23, 24 of mass center, 338 Quasicoordinate, 276, 410 Particles, 165 acceleration of, 167–169 R of body segments, 232–234 human body model, 222–223 Radius, 19, 410 inertia force on, 223 Radius of gyration, 234, 410 sets of, 230–232 Rank, 410 velocity of, 166–167 Reaction force position, 344 Partitioned matrix, 52, 409 Passive forces, 215, 295–296, 409
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