Introduction to Sports Biomechanics: Analysing Human Movement ...

More documents

Recommendations

Info

Vector resolution and components QUANTITATIVE ANALYSIS OF MOVEMENT Figure 4.21 Vector addition: (a) with same direction; (b) in opposite directions; (c) using vector triangle; (d) using vector parallelogram; (e) using vector polygon; and (f) vector subtraction. Determining the perpendicular components of a vector is often useful in sports biomechanics. Examples include the normal and frictional components of ground reaction force, and the horizontal and vertical components of a projectile’s velocity vector. It is, therefore, sometimes necessary to resolve a single vector into two or three perpendicular components – a process known as vector resolution. This is essentially the reverse of 159
INTRODUCTION TO SPORTS BIOMECHANICS vector composition and can be achieved using a vector parallelogram or vector triangle. This is illustrated by the examples of Figure 4.22, where the blue arrows are the original vector and the black ones are its components. The vector parallelogram approach is more usual as the components then have a common origin, as in Figure 4.22(a). Most angular motion vectors obey the rules of resolution and composition, but this is not true for angular displacements. Figure 4.22 Vector resolution using: (a) vector parallelogram; (b) vector triangle. 160 Vector addition and subtraction using vector components Vector addition and subtraction can also be performed on the components of the vector using the rules of simple trigonometry. For example, consider the addition of the three vectors represented in Figure 4.23(a). Vector A is a horizontal vector with a magnitude (proportional to its length) of 1 unit. Vector B is a vertical vector of magnitude −2 units (it points vertically downwards, hence it is negative). Vector C has a magnitude of 3 units and is 120° measured anticlockwise from a right-facing horizontal line. The components of the three vectors are summarised below (see also Figure 4.23(b)). The components (Rx, Ry) of the resultant vector R = A + B + C are shown in Figure 4.23(c). The magnitude of the resultant is then obtained from the magnitudes of 2 1/2 ), as R = (0.25 + 0.36) its two components, using Pythagoras’ theorem (R 2 = R x 2 + Ry = 0.78. Its direction to the right horizontal is given by the angle θ, whose tangent is R y/R x. That is tan θ = −1.2, giving θ = 130°. The resultant R is rotated anticlockwise 130° from the right horizontal, as shown in Figure 4.25(d). (A second solution for tan θ = −1.2 is θ = −50°, which would have been the answer if R x had been + 0.5 and R y had been −0.6). Vector Horizontal component (x) Vertical component (y) A 1 0 B 0 −2 C 3 cos120° = −3 cos60° = −1.5 3 sin120° = 3 cos60° = 2.6 A + B + C −0.5 0.6
Page 2:
Introduction to Sports Biomechanics
Page 5 and 6:
First edition published 1997 This e
Page 8 and 9:
Contents List of figures x List of
Page 10 and 11:
Study tasks 216 Glossary of importa
Page 12 and 13:
FIGURES 1.26 Underarm throw - femal
Page 14 and 15:
FIGURES 5.9 Typical path of a swimm
Page 16 and 17:
Tables 2.1 Examples of slowest sati
Page 18 and 19:
Preface Why have I changed the cove
Page 20 and 21:
Introduction MISSING TEXT The first
Page 22:
INTRODUCTION principal movements in
Page 25 and 26:
INTRODUCTION TO SPORTS BIOMECHANICS
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Figure 2.2 ‘Principles’ approac
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Figure 2.13 Identifying critical fe
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132: INTRODUCTION TO SPORTS BIOMECHANICS
Page 181: INTRODUCTION TO SPORTS BIOMECHANICS
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Figure 6.8 Main skeletal muscles: (
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
INDEX 282 balls air flow past 173 b
Page 307 and 308:
INDEX 284 energy 219 kinetic 219 mi
Page 309 and 310:
INDEX 286 isokinetic contraction 24
Page 311 and 312:
INDEX 288 muscle length-tension rel
Page 313 and 314:
INDEX 290 three-dimensional 146-7,
Page 315:
INDEX 292 validity 220 vantage poin
show all

Introduction to Sports Biomechanics: Analysing Human Movement ...

Create successful ePaper yourself

Delete template?

Save as template?