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software packages for, 561 in 3 D cams, 144 152 vs Bezier curves, 109 cubic, 187 189, 193 194, 197 198 de nition of, 187 nonparametric, 187 parametric, 187 quintic functions, 187 Spline collocation method nonrational splines, 109 117 in nonrigid systems, 128, 136 144 rational splines, 117 127 Sprag clutch, 470, 470f Spring(s) in automotive cams, 529 bottoming out of, 335 design of, 223 224 energy storage in, 333 334 equivalent weight of, 438 follower contact maintenance and, 309 force in, 222 223, 418 419 models of, 331 342 coil springs, 334 335, 335f combinations, 338 340, 338f, 339f equivalent springs, 340 341, 340f linear, usefulness of, 331 332 mass in, 341 342, 341f nonlinear, 333 stiffness (spring rate), 332, 337t of coil spring, 334 determination of, 333 334, 335 338 equivalent, 340 341, 340f of parallel springs, 339 of series springs, 339 340 SPRINGMASTER software, 540, 541, 564 Spring rate, 332, 337t of coil spring, 334 determination of, 333 334, 335 338 equivalent, 340 341, 340f of parallel springs, 339 of series springs, 339 340 Spring ratio constant, 437 438 Spring surge, 374, 540 541 Stamping mechanism, 489, 491f Startup forces, 224 Star-wheel cam, 489, 490f Star-wheel mechanism, 482 483, 483f Stationary cam, 14 Steels, hardened, 265f, 271 272, 532, 534 535 Stick-slip friction, 345 Stiction, 345, 360, 525 Stop forces, 224

/* An array name without an index yields a pointer to the start of the array */ using System; class PtrArray { unsafe static void Main() { int[] nums = new int[10]; fixed(int* p = &nums[0], p2 = nums) { if(p == p2) ConsoleWriteLine("p and p2 point to same address"); } } }

sin(2/x) sin(5/x)

The output is shown here:

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604 Straddle (yoke) mountings, 306, 307f Stress contact, 256 260, 257f, 258f in at-faced followers, 258, 258f minimization of, 419 420, 424 425 in nonrigid systems, 131 subsurface, industry standard for, 303 Stress corrosion, 264 Stribeck-Hersey curve, 273, 273f Structural errors, in manufacturing, 293 Stud mountings, 306, 307f Subsurface stress, industry standard for, 303 SUMMiT (Sandia Ultra-planar, Multi-level MEMS Technology), 509, 514, 524 Surface(s), cam and follower asperities on, 260 261, 261f contact stresses See Contact stresses design of factors in, 252 methodology, general, 252 wear and, 264 272 elastic contact theory, 253 255, 254f materials for See Materials roughness composite, 276 grinding to remove, 295 296 surface lms, 260 surface loads, 225 228 waviness in, 293 294, 294f, 295f wear See Wear Surface fatigue, 263 269, 263f causes of, 263 264 prevention through design, 264 269 testing on, 264 269, 265t 266t Surface loads, 225 228 Surface micromachining, 509, 509f Surging, 223 Swash plate cams, 479 480, 480f SWIRL METER software, 541, 564 Symmetrical dwell-rise-return-dwell cams, 53, 53f Synthesis of motion programs displacement programs, 193 194 overview of, 108 109 Tangent cam, translating roller follower, 466 467, 467f Tangent, determination of, 178 179, 178f 3-D cams, 12 13, 13f, 149f applications, 144 145 in computing mechanisms, 496f, 497 offset surface, expression for, 146 147

Part I:

&nums[0]

surface, expression for, 145 146 synthesis of motion, B-splines in, 144 152 Three-dimensional cams See 3-D cams 3-4-5 polynomial curves in dwell-rise-dwell cam, 58t, 91 92, 92f, 93, 94t, 95f dynamic characteristics of, 405f, 406f in polydyne design, 439, 440 443 3-4-5-6-7 polynomial curves, 102 Time charts in graphical layout method, 160, 161f uses of, 18, 18f Timing diagrams See Time charts TK Solver software, 563 Tolerances accumulated error and, 296 extreme, jerk and, 296 probabilistic error and, 294, 294f, 295f typical, 291 Toolmakers, input from, 25 Torque, 219 220, 228 236 in cycloidal curve, 230, 231f in at-faced followers, 230 232, 231f in roller followers, 228 230, 230f, 308 309 in simple harmonic curves, 230, 231f in sine curve, modi ed, 230, 231f Torque-controlled cams, 232 235, 233f, 234f Torque-controlled wrapping cams, 235 236 Torque curve, in cam-follower design, 21 Torsional ratcheting microactuator, 514 516, 516f, 517f Torsional springs, 334, 334f Trace point, 18, 19f, 162f Transition point, 17f, 18, 19 Translating cams characteristics of, 5f, 6, 7f linear ball bearings for, 222, 222f Translating at-faced followers curvature of, 190, 190f, 191f pressure angle forces in, 168 169, 168f, 189 190 torque in, 230 232, 231f Translating knife-edge follower curvature of, 191f, 192 pressure angle of, 191f, 192 relevance of, 190 192 Translating roller follower pressure angle forces in, 163 166, 164f, 166f torque in, 228 230, 230f, 308 309 Trapezoidal cam, acceleration DRS of, 402, 403f

SOLUTION We note that both numerator and denominator tend to 0, so the quotient is indeterminate at of the form 0/0 We may therefore apply l H pital s Rule Our limit equals ( 2/x 2 ) cos(2/x) x ( 5/x 2 ) cos(5/x) lim This in turn simpli es to 2 2 cos(2/x) = x 5 cos(5/x) 5 lim l H pital s Rule also applies to one-sided limits Here is an example EXAMPLE 56

Since the second form is shorter, most programmers use it when a pointer to the start of an array is needed

When a pointer refers to an array, the pointer can be indexed as if it were an array This syntax provides an alternative to pointer arithmetic that can be more convenient in some situations Here is an example:

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