Principles of Biomechanics Mechanical Engineering - Ronald L. Huston

428 Index Recursive formulation, for Saint Venant’s principle, 76–77 transformation matrices, SAS, see Supplemental restraint systems 270–273 Scalar product, 37–39, 45–46, 227, 411 Scalars Reference configuration, 11–12, 410 for vehicle operation, 12 matrices, 50 stress, 80 Reference frames vectors, 31–32 coordinate axes Scalar triple product, 45–46, 227, 411 female, 377–379 Scalp, 161–162 male, 374–376 Seat belts, 351–352, 407 inertial reference, 9, 166, 407 Second moment of area, 411 Newtonian, 78, 151, 215–216, 409 Second moment vector, 225–229, 411 vector differentiation of, 176–178 Semilinear springs and dampers, 10 Shear displacement, 111 Reference points, forces, 72 Shear loading, 85–86, 95–96, 110 Rehabilitation, 1, 410 sign conventions for, 105–106 Relative angular velocity, 146, 177, 263 Shear modulus, 96, 411 Shear strain, 85, 87 generalized speeds, 316 engineering, 87, 406 Relative velocity, 145, 169–171 mathematical, 87, 408 Shear stress, 83, 111–113, 411 acceleration, 199–200 transverse, 129–130 Remodeling, 155, 410 Shoulders, 23 Repeated index summation convention, Simple angular velocity, 172, 411 Simple couple, 74, 411 274 Simple rotation, 14 Resultant, 32, 410 Simple strain, 85, 86, 411 Revolute joint, 22, 410 Simple stress, 80, 411 Ribs, 114 Simulation, 337–362; see also Crash- cartilage, 159 victim simulator; Gross-motion thoracic, 22 simulator Rigid bodies, 75 with ball-and-socket joint, 10 Rise function, 342 lifting, 342–344 Roll motion, 341, 410 Single support, 345, 411 Rollover accidents, neck injuries in, 362 Singular matrix, 50, 411 Rotation, 19 Singularity functions, 115–117, 200–201 axial, 14 Sinistral configuration, 40 dyadic, 201–206, 411 Sitting dimensions, 25, 369 forearm, 16 Skeletal anatomy, 19–22 pitch motion, 340–341 Skeletal muscle, 23, 158 roll motion, 341 Skew-symmetric matrices, 50 simple, 14 Skin tissue, 162–163 spine, 23 Skull, 19, 20, 161–162 yaw motion, 339–340 Slider joint, 411 Row-column rule, 51 Sliding vector, 69, 411 Row matrix, row array, 411 Smooth muscle, 23 Rows and columns, of matrix, 49 Soapfilm analogy, 411 Runge-Kutta methods, 335, 353–354 Soft tissue, 10, 153–154 Spacewalk, 339–341, 411 S Sphenoid bone, 20, 411 Sacrum, 20, 411 Sagittal plane, 11–12, 411 lateral, 13

Index 429 Spherical coordinates, 103–105, 266 Stride, 345, 412 Spherical joint, 22, 23, 411 Stride length, 345, 412 Spine, 20, 21 Subcutaneous, 162, 412 Submarining, 352, 412 cervical, 9, 20, 404 Submatrix, 52, 412 foramen of, 22 Substitution symbol, 38 head and neck, 21–22 Summation convention, 198, 412 vertebrae, 21 Summation notation, 36, 98 Superimposed force systems, 77 joints, 23 Superior, 13, 14, 412 lumbar, 20, 408 Supination, 15, 19, 412 Supinators, 24 injury to, 22 Supine, 412 rotation, 23 Supplemental restraint systems (SAS), sacrum, 20, 411 thoracic, 20, 412 352 Swimming, 347–350 ribs, 22 Swing, 345, 412 translation, 23 Symmetrical bodies, eigenvalues of Sprain, 160, 411 Springs and dampers, vehicle seats, 352 inertia, 241–242 Square matrix, 49, 411 Symmetric dyadic, 43, 412 Standing dimensions, 25, 369 Symmetric matrix, 49, 412 Static analysis, 73 Synovial fluid, 159, 412 Stature, 25 Step length, 345, 412 T Sternum, 19, 20, 412 Strain, 84–88, 412 Temporal bone, 20, 412 dyadics, 42 Tendons, 20, 160–161, 412 elongation, 84–86 normal, 86, 409 forces of, 302–304 principal values of, 88–89 Tension, 412 simple, 85 stress, 94–99 bones, 156 uniaxial, 96, 413 Tetanic, 159, 412 Strain-curvature relations, 107–109 Thick beams, 111–113 Strain energy, 133 Thoracic, 20, 412 Stress, 79–84, 412 bending moment, 109–110 ribs, 22 burden bearing, 354 3X3 determinants, 55–58 cross section, 111 Three-anchor system, 352 dyadics, 42, 84 Tibia, 19, 412 flexural, 111, 406 Tissue, 412 normal, 80, 83, 409 Tissue biomechanics, 152–163 principal values of, 88–89 Toe off, 345, 412 scalars, 80 Torque, 412 shear, 83, 111–113, 411 of couples, 74 transverse, 129–130 Torsion, 14, 130–133 simple, 80, 411 Trabecula, 154, 412 strain, 94–99 Trabecular bone, 20, 154, 412 uniaxial, 96, 413 Trace, 50, 412 uniform muscle stress criterion, Transformation matrices, 92, 205, 209, 412 356–357 derivatives, 197–199 Stress vector, 412 recursive formulation for, 270–273

430 Index Transition movement, 361, 412 magnitude of, 30 Translation, spine, 23 multiple products of, 44–48 Transverse contraction ratio, 96, 413 multiplication, 37–41, 172 Transverse plane, 11, 413 scalars, 31–32 Transverse shear stress, 129–130 Vector triple product, 46 Trapezius, 24 Vector-vector, 229, 413 Triceps, 23, 24 Vehicle environment model, crash-victim Triple scalar product, 45–46, 227, 411 Triple vector product, 58, 413 simulator, 351–353 Twisting, 14 Vehicle operation, reference for crash victims, 352 configuration for, 12 head and neck, 16 Vehicle seats, springs and dampers, 352 Twitching, 159, 413 Velocity, 413 U mass center, 288–290 of particles, 166–167 Ulna, 19, 413 Vertebrae, 21 Uniaxial strain, 96, 413 cervical, 21 Uniaxial stress, 96, 413 Vertical foot reaction force, 343 Uniform muscle stress criterion, W 356–357 Unit eigenvectors, 237, 239–240 Waist height, 25 Waitron and tray, 357–359 inertia matrix, 240–241 Unit vector, 30–31, 171, 413 constraint equations for, 359 forces for, 358 configuration graph for, 186–187, 193 orientation for, 358 vector addition, 34 Walking, 344–347 Upward direction, 13 gyroscopic effects in, 361–362 Water forces, 347–348 V Weight, see Gravity Weight lift, 342–344, 357 Valgus, 19, 413 Whole body models, 146–149 inversion, 18 injury, 149 legs, 17 Windshield, 352–353 Wolff’s law, 156–157, 413 Variational techniques, 134 Work-energy method, 133 Varus, 19, 413 Y eversion, 18 legs, 17 Yaw motion, 339–340, 413 Vector product, 37, 39–41, 58, 413 Young’s modulus of elasticity, 95, 413 Vectors, 29–41, 413; see also Specific vector Z types addition, 32–36 Zero dyadic, 42, 413 Zero force system, 73, 413 unit vector, 34 Zero matrix, 49, 413 angles, 37 Zero vector, 30–31, 413 characteristics of, 30, 404 differentiation, 171–176 of reference frames, 176–178 equality of, 30 forces, 69