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Galling, 261 Gauss divergence theorem (GDT), 194, 200 201 GDT See Gauss divergence theorem Gear(s) epicyclic, cam-modulated, 492, 492f, 493f equivalent weight of, 438 439 in MEMS, 512 noncircular, cam-modulated, 493 494, 494f worm, cam-modulated, 490, 491f Gear cam, in computing mechanisms, 296, 296f Gear discriminator, in MEMS, 518 520, 519f Gear drive, roller, 10, 488 489, 488f Geneva mechanism, 482 483, 483f Geometric properties case studies, 204 215 computational schemes, 186 202 global, 184 186, 194 202 local, 177 184, 189 194 overview of, 177 of planar contours, 184 185, 194 198 software packages, 203, 561 562 of solid regions, 198 202 Globoidal cams, 10, 11f, 12f concave grooved, 486 487, 486f indexing, 10 11, 12f Grain ow, 302 303 Graphical layout of cam pro le graphical layout method, 160, 161f manual method, 15 16, 16f, 17f, 28 Graphical-slope differentiating method, 29, 31 Grease, 277 278, 278f Grinding, cam nish and, 295 296 Groove cams de ned, 4 5, 7f in micromechanical lock, 518, 518f, 519f Gutman 1 3 harmonic curve, 103, 405, 405f, 406f Hardening See Heat treatment Hardness recommended, 303 of roller follower, 306 and wear, 269 270 Harmonic content, minimization of, 103 Harmonic curves, 103 105 See also Double harmonic curves; Simple harmonic curves Berzak-Freudenstein 3-4-5-6-7, 405f, 406f factors for, 552t Freudenstein 1-3, 104, 405 Freudenstein 1-3-5, 104 105, 405f, 406f Gutman 1-3, 103, 405, 405f, 406f

Notice that the numerator tends to and the denominator tends to as x 0 Thus the quotient is indeterminate at 0 of the form / + So we may apply l H pital s Rule for in nite limits to see that the limit equals 1/x = lim x 3 /3 = 0 x 0 3x 4 x 0 Yet another version of l H pital s Rule, this time for unbounded intervals, is this: Let f and g be differentiable functions on an interval of the form [A, + ) If limx + f (x) = limx + g(x) = 0 or if limx + f (x) = and limx + g(x) = , then lim f (x) f (x) = lim x + g(x) x + g (x) lim provided that this last limit exists either as a nite or in nite limit The same result holds for f and g de ned on an interval of the form ( , B] and for the limit as x EXAMPLE 54

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int* p, q;

declares an int pointer called p and an int called q It is equivalent to the following two declarations:

shaft windup in, 383, 383f, 384f vibratory response characteristics, 400 Heat treatment distortions and, 291, 302 methods of, 302, 303f HEXIL, 510 High-speed cam-follower systems design of, 413, 448 449 (see also Polydyne design) vibration in, 447 (see also Vibration) Hub design, 173 174 Hydraulic cylinders, servo valve-controlled, 20 Hydrodynamic lubrication, 273, 273f Hyperbolic curves characteristics of, 546 548, 547f rolling in, 457, 458f Impact forces See Mechanical shock Implicit Runge-Kutta method, 137 IMSL software, 111 Increased stroke cams, 475, 476f Indexing cams See also Intermittent motion mechanisms globoidal, 10 11, 12f operating forces and, 225, 225f Industrial adjustable mechanisms, performance characteristics of, 20 Industrial production cams, most-popular, 6, 6f Inertia equivalent, 331 332 as force, 219 220 Inertia matrix in planar contours, 184 185, 194 198 in solid regions, 185 186, 198 202 Inspection methods of, 291, 297 301 real-world example, 566 572, 573f 583f Integrals, truncation errors and, 177, 187 Interior control, in DRRD curves, 97 98, 98f Intermittent motion mechanisms, 482f concave globoidal cams, grooved, 486 487, 486f cylindrical cam, 484 485, 485f multiple double-end cam, 488 489, 488f spider cams, 487, 487f star-wheel cam, 489, 490f types and uses of, 481 484 Interrupted drive forces, 224 225 Inverse cam, 13 14, 14f in microvibromotor, 520 521, 521f rotatable, 236 250 Involute cams, 459 460, 460f

20:

We compute g of any argument by doubling it and adding 1 Thus equation ( ) equals t2 2 +1 t +1 2t 2 4 +1 = t +1 2t 2 + t 3 = t +1 One of the main points of this example is to see that f g is different from g f We compute f g: 2 (f g)(t) = f (g(t)) = f (2t + 1) (2t + 1)2 2 (2t + 1) + 1 4t 2 + 4t 1 = 2t + 2 So f g and g f are different functions = You Try It: Let f (x) = |x| and g(x) = x/x Calculate f g(x) and g f (x)

U n s a f e C o d e , P o i n t e r s , N u l l a b l e Ty p e s , a n d M i s c e l l a n e o u s To p i c s

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