Index Of: Mechanical Tolerance Stackup and Analysis

Accuracy and precision   8-9
Advanced Dimensional Management   14, 21, 78, 118, 208, 251, 286, 329-366
Ambiguity   4, 8-14
ASME B89   48
ASME Y14.5M-1994   5, 19, 22, 23, 54, 181, 187, 188, 207, 226, 271, 384
  fundamental rules 54
  rule #1 5
  simultaneous requirements and 187, 188
Assembly shift   49, 68-74, 87-90, 93, 96-99, 102-103, 288, 293-296, 303-327, 378-383, 388
  calculations 70-71
    fastener diameters used in 70
  chain of dimensions and tolerances and 70, 99-104
  clearance and 68-69
  definition of 68
  dimension values and 70
  direction of 70, 288, 293-296
    labeling in the tolerance stackup 70
  directional bias in 68
  effect of assembly forces on 68, 303
    effect of gravity 68, 87-90, 127-129, 378-383
  effect of assembly process on 68-73, 233-234, 378-383, 388
    adds to total predicted variation 68
    default condition in this text 73
    options for including in tolerance stackup 72-74
    reduces total predicted variation 72
  effect of mating features on 68
    features of size 68
    threaded fasteners 71-72, 74
  fixed-fastener calculations and 70-72, 74, 161-164, 167, 168, 228
  floating-fastener calculations and 70, 73, 100, 161-164, 167, 168, 228
  including in the tolerance stackup 70, 73-74
  rotational assembly shift 303-304, 304-327
    formulas and calculations 313, 315, 323-324, 326
    reporting in a tolerance stackup report 309, 311, 316, 322, 323, 327
  rules for 74-75
  sources of 68
  worst-case 69-70
Assumptions   74-78, 99, 120, 393
  default conditions in this text 77-78, 99
    specified temperature(s) 77
    static state 77
  framing the problem 77-78, 99, 393
  guesses and estimates 76
    labeling 76
  importance of stating 120
  reasons for 74-76, 120
    catalog and purchased parts 75-76
    incomplete drawings 74-75
    missing information 74-76
    plus/minus 74-76
    relying on manufacturing process tolerances 74-76
  role of 74-76
Calculating part tolerances from a final assembly tolerance   367-372
  adjusted RSS part allocation formula 370-372
  in complex assemblies 367
  iteration 367-369
    spreadsheets and 369
  RSS part allocation formula 371-372
  what-if tolerancing 367-369
Central limit theorem   30-31
  Gaussian distribution and 31, 106
Chain of dimensions and tolerances   53, 54, 57, 61, 63-64, 67, 78-104, 287-289
  definition of 53, 104
  moving from one interface to another in 99-104
  reason for term 104
Complete Dimensioning and Tolerancing   4, 6, 8-14
Converting plus/minus dimensions and tolerances into equal bilateral format   33-37, 37-41, 65
  limit dimensions 33-34
  and mean shift 37-41
  unequal bilateral 34-35
  unilateral negative 36-37
  unilateral positive 35-36
Coordinate measuring machine (CMM)   6, 386
Coordinates and coordinate systems   5, 137
  Cartesian 5
  and datum reference frames 137
  and dimensions 5
  polar 5
  rectangular 5
Datum feature shift   48, 100-103, 147, 151, 180-187, 264, 270-286, 288, 293-296
  calculations for 182-186
  and datum feature simulation rules 181, 182-187
    datum features of size simulated at MMC size 182-184
    datum features of size simulated at MMC virtual condition size 184-187
  and datum features of size 182
  definition of 180
  direction of 288, 293-296
  geometric tolerances and 181
  material condition modifiers and 181, 268, 270-271
  rules for 190-192
  separate requirements and 187, 192-195
  similarity to assembly shift 183
  simultaneous requirements and 147, 151, 187-192
  sources of 180-181
Datum reference frames   107, 137, 139-140, 146-149, 160, 171-172, 394
  coordinate systems defined by 107, 137
  functional 137, 171-172, 394
  more than one 137-138
Dimension    
  types of  
    angular (polar) 15-16
    basic 18, 100-103, 141-145
    chained 15-16
    diametral 15-16
    linear 15-16
    math-data based, model-based 6, 10-12, 18-20
    radial 15-16
    rectangular coordinate 15, 17-18
Dimensioning and tolerancing philosophy   4-6, 8-14, 17-18, 57, 137, 154, 158-159, 171-172, 194, 201, 204, 216, 225-231, 330, 394
  avoiding ambiguity 57, 216
  functional dimensioning and tolerancing 17-18, 57, 137, 154, 158-159, 171-172, 194, 201, 204, 216, 225-231, 330, 394
Dimensioning strategy (see also Functional dimensioning and tolerancing)   17, 18, 57
  and arrangement of dimensions 18
  effect on Tolerance Stackups 17, 57
Direction of dimensions and tolerances in the tolerance stackup   58, 287-296, 302, 303-327
  rules for including 295-296
  tolerance stackup direction and 288, 295-296, 302
  in tolerance stackups solved as a combination of translational and rotational variation 293-296, 303-327
  in tolerance stackups solved as translational variation only 288-289, 293-296, 303-327
Drawings    
  history of 3-4
  limited dimension 6, 15
  math based, model based 6, 15, 267
Enclosure assembly    
  drawings 330-338
    assembly 330, 337
    cover 338
    enclosure: option 1 331
    enclosure: option 2 332
    enclosure: option 3 333
    ground plate: option 1 334
    ground plate: option 2 335
    ground plate: option 3 336
  tolerance stackup examples  
    cover fit along X axis 339-345
    cover fit along Y axis 342-349
    ground plate to enclosure: option 1 353-356
    ground plate to enclosure: option 2 356-360
    ground plate to enclosure: option 3 360-365
    screw head clearance 346-352
    screw thread depth 337-341
Feature   5, 18, 22, 102
  bounded 5
  characteristics of 22
    form 22, 23-24
    location 22, 24-25
    orientation 22, 24
    size 22-23
  complex 5, 102
    "blending" the surface of 6
    shape of 102
  definition of 5
  simple 5
Feature control frames   18, 146, 147, 148, 149, 159
Feature of size   5, 100-103
  rule #1 and 5
Fit classifications   389-391
  clearance fit 389, 390
  interference fit 389, 391
  transition fit 389, 390
Fixed fastener situation   383-388
  assembly process and 388
    assumptions 383, 384
  assembly shift and 388
  calculations 385, 387-388
  datum features and 386
  defined 373, 383
  examples of 383
  formula 384
    distribution of tolerances in 384, 385
    variables 384
  interrelationship between part tolerances 384, 386
  limitations of 388
  positional tolerance and 384-388
  projected tolerance zone and 384-386
  virtual condition and 388
Fixtures   53-54
  chain of dimensions and tolerances and 54
  tolerances of 54-55
Floating fastener situation   373-383
  assembly process and 378-383
    assumptions 378, 382
  assembly shift and 378-383
  calculations 375, 377-378
  datum features and 376
  defined 373-374
  effect of gravity and 379-380
  examples of 374
  formula 374, 375
    variables 374
  interrelationship between part tolerances 375-376
  limitations of 378
  positional tolerance and 374-378
  virtual condition and 376, 378
Form tolerances in tolerance stackups   285-286, 393-428
  assembly forces and 395, 402-412, 420-425
  datum feature form tolerances 394-395
  difference between inspection and assembly 394-402
  effect on tolerance stackup 395-412
    as rotational variation projected to a linear displacement 395, 402-412, 420-425
    as translational variation only 395-402, 412, 417-420
  examples of  
    as rotational variation projected to a linear displacement 402-412, 420-425
    as translational variation only 395-402, 417-420
  and idealization of the problem 393
    how to include form tolerances in the tolerance stackup 412, 414-425
    how to quantify the potential effect of the form tolerances 412, 425-427
    whether form tolerances should be included in the tolerance stackup 395, 412, 413
    whether variation allowed by form tolerances should be treated as translation or rotation 412, 413-414
  mating surfaces and 394-402
  mean shift and 417-424
  other sources of form error 428
  probability of occurrence 395, 401-402, 411-412, 425-427
  step-by-step instructions for including 417-425
Format, plus/minus tolerances    
  conversion of +/- into equal bilateral 33-37, 65
  conversion of GD&T into equal bilateral 138-139
    position 154, 178-180
    profile 139-145
  dimensional limits and 30
  effect on manufacturing process 29-31
  effect on target value 29-31
  equal bilateral 27
  examples of 28
  legal differences 29-31, 37
  limit dimensions 27
  rules for 28
    leading zeroes 28
    number of decimal places 28
    trailing zeroes 28
  SPC and 29-31
  unequal bilateral 27
  unilateral 27
Functional dimensioning and tolerancing   17-18, 57, 137, 154, 158-159, 171-172, 194, 201, 204, 216, 225-231, 330, 394
  justifications for 57
  tolerance stackups and 57
GD&T   5, 13-14, 16, 18-21, 22-25, 45, 48, 54, 74-75, 100-104, 137-200, 245-247, 264-266, 268-286
  basic dimensions 18, 100-103, 141-145
    measuring in CAD 142
  benefits of 4, 13-14, 17-21, 75, 107-108
  bonus tolerance 48, 102-103, 154, 158-159, 169, 171, 180, 227, 229-231, 264, 268, 270-286
    and material condition modifiers 154, 158-159, 169
  comparison with +/- 4, 13-14, 74, 75, 107-108, 138
  concentricity, limitations of 215
  converting +/- to positional tolerances 178, 201-207
    Pythagorean theorem 201-206
    right angle solution 205-206
  datum feature 100-103, 137, 353-365
    affect on tolerance stackups 100-103, 353-366
    complex 102
    feature of size 102-103
    planar 100-101
  datum feature shift 48, 100-103, 180-188, 264, 270-286
    calculations for 182-186
    and datum feature simulation rules 181
    and datum features of size 182-183
    datum features of size simulated at MMC size 182-184
    datum features of size simulated at MMC virtual condition size 184-188
    definition of 180
    geometric tolerances and 181
    material condition modifiers and 181, 268, 270-271
    rules for 190-192
    separate requirements and 187, 192-195
    similarity to assembly shift 183
    simultaneous requirements and 147, 151, 188-192
    sources of 180-181
    tolerance stackup direction and 293-296
  datum reference frames 137, 139-140, 146-149, 160
    coordinate systems defined by 107, 137
    functional 137, 171-172, 394
    more than one 137-138
  feature control frames 18, 146, 147, 148, 149, 159-163, 189, 207
    projected tolerance zones in 207, 384-386
  feature of size 5, 100-103
  form tolerances 101, 285-286, 393-428
  fundamental rules 54
  interfaces in the tolerance stackup and 99-104, 137
    functional datum features 137, 171-172, 394
  material condition modifiers 48, 69-71, 97, 153-154, 225-231, 268, 270-271
    alignment and 158-159
    bonus tolerance and 154, 158-159, 169, 227, 229-231, 264, 268, 270-286
    effect on tolerance zones 154, 158-159
    LMC 48, 69-71, 97, 153-154, 157, 158
    MMC 48, 153-154, 156, 158-159
    part cost and 159
    RFS 154, 155, 158
    symbols for 154, 226
    tolerance charts 155-157
    variation and 158-159
  orientation tolerances 101, 102, 104, 282-285
  positional tolerances 102-103, 153-180
    assembly shift, misalignment and 154, 158-165
    bonus tolerance and 48, 102-103, 169, 171, 180
    circumscribing a cylindrical zone for converting +/- to position 178, 201-207
    composite position 104, 160-173
    converting +/- to positional tolerances 178, 201-207
    converting to equal bilateral +/- 154, 178-180
    datum reference frames and 160, 267, 268, 270-286
    features of size and 153-154
    in fixed- and floating-fastener formulas 161-164, 167, 168, 373-388
    including upper and lower segment tolerances in the tolerance stackup 160-173
    inner and outer boundaries and 155
    material condition modifiers and 153-154
    projected tolerance zones 207-213, 384-386
    reporting in a tolerance stackup report 160, 178-180, 275-283
    simultaneous requirements and 161, 167
    tolerance zone 153-160, 201-207
    virtual and resultant condition and 156-157
  profile tolerances 100-101, 139-153, 271-277
    benefits of 139-140
    complex surfaces 141-142
    composite profile 101, 146-153
    converting to equal bilateral +/- 140-145
    datum reference frames and 139-140
    equal bilateral 140-142
    including upper and lower segment tolerances in the tolerance stackup 145-153
    planar surfaces 141
    reporting in a tolerance stackup report 141, 143, 145, 147, 149-152, 271-277
    similarities to +/- 139-140
    simultaneous requirements and 147, 151
    tolerance zone 139-147
    unequal bilateral 142-144
    unilateral 144-145
    universal applicability 140
  projected tolerance zones 207-213, 384-386
    automated tools for calculating 208
    and CMMs 208, 386
    effect inside and outside the part 210
    examples of 209-210
    in fixed fastener calculations 213, 384-386
    formulas to calculate equivalent tolerance when projected tolerance is not specified 211-213
    methods of specifying 207-209
    reasons for 207-208
    reluctance of companies to use 208
    in tolerance stackups 208
  rule #1 5
  runout tolerances 286
  separate requirements 187, 192-195
    compared with simultaneous requirements 192, 195-199
    and datum feature shift  
    and datum reference frames 192
    examples of 195-199
    and feature control frames 192
    and functional dimensioning and tolerancing 194
    and inspection 192
    rules for including datum feature shift in the tolerance stackup 192
  simultaneous requirements 147, 151, 188-192
    and the chain of dimensions and tolerances 190-192
    and datum feature shift 187, 189-192
    and datum reference frames 188-192
    default condition per ASME Y14.5M-1994 187-188
    examples of 195-199
    and feature control frames 188
    and inspection 188-192
    overriding 187, 193
    and patterns 189-190
    rules for including datum feature shift in the tolerance stackup 190-192
  use of +/- on drawings based on 138
Geometric characteristic symbols   21
History   3-4
  of design & manufacturing practices 3-4
  of engineering drawings 3-4
  of tolerance analysis 1-4
Interchangeability   2
Justification for GD&T   4, 137-138
Loop (see Chain of dimensions and tolerances)    
Manufacturing processes   7-8, 43-48
Material condition modifiers   48, 69-71, 97, 153-154, 155, 156, 158-159, 169, 225-231
  bonus tolerance and 154, 158-159, 169, 227, 229-231
  choosing the correct modifier 225, 227-231
    alignment 229-230
    combination of factors 230-231
    edge distance or wall thickness 229
    fit or clearance 228
    selection criteria 227-231
  difference between the material condition modifiers 226-227
  effect on datum feature shift 225
  effect on tolerance stackup 225
  effect on tolerance zone 153-154
  entering into the tolerance stackup report 225
  LMC 48, 69-71, 97, 153-154, 157, 158, 225, 227
    definition of 227
    effect on tolerance zones 154, 158-159
    and internal and external features 227
  MMC 48, 153-154, 156, 158-159, 226-227
    definition of 226-227
    effect on tolerance zones 154, 158-159
    and internal and external features 226-227
  part cost and 159
  positional tolerance and 153-154
  RFS 154, 155, 158, 225-226
    ANSI Y14.5M-1982 226
    definition of 226
    effect on tolerance zones 154, 158-159
    as a subset of MMC and LMC 227
  symbols for 154, 226
  tolerance charts 155-157
  variation and 158-159
Mean   39-40
  definition of 40
Mean shift   37-41, 150, 417-424
  calculation of 38-41
    limit dimensions 38
    unequal bilateral tolerances 38
    unilateral tolerances 38-39
  definition of 37
  effect on Tolerance Stackup 38-40
    form tolerances and 417-424
    with and without dimensions 38-39
  form and orientation tolerances and 150, 417-424
  and manufacturing 40
  sign and direction of 39
Mean, Arithmetic    
  definition of 40
Moving from one part to another in a tolerance stackup   99-104
  complex-curved interfaces 102
  disclaimer 104
  feature-of-size interface  
    for +/- dimensions and tolerances 102
    for GD&T - if it is a referenced datum feature 102-103
    for GD&T - if it is not a referenced datum feature 103-104
  guidelines for 99-104
  planar interface  
    for +/- dimensions and tolerances 100
    for GD&T - if it is a referenced datum feature 100-101
    for GD&T - if it is not a referenced datum feature 101
Nominal   4, 6, 15, 16, 27, 29, 37-41, 44, 102, 105, 107, 139
  dimension value and 4, 15, 16, 27, 29
  manufacturing nominal 30-31
  math-data/model-data and 6, 12, 44
  mean shift of 37-41
  statistical tolerance stackups and 105, 107
Orientation tolerances in tolerance stackups   393, 395
  (see also form tolerances in tolerance stackups) 393-428
Probability   30, 105-108
Rule #1   5
Separate requirements   187, 192-195
  compared with simultaneous requirements 192, 195-199
  and datum feature shift  
  and datum reference frames 192
  examples of 195-199
  and feature control frames 192
  and functional dimensioning and tolerancing 194
  and inspection 192
  rules for including datum feature shift in the tolerance stackup 192
Simultaneous requirements   147, 151, 187-192
  chain of dimensions and tolerances and 190-192
  and datum feature shift 187, 189-192
  and datum reference frames 188-192
  default condition per ASME Y14.5M-1994 187, 188
  examples of 195-199
  and feature control frames 188
  and inspection 188-192
  overriding 193
  and patterns 189-190
  rules for including datum feature shift in the tolerance stackup 190-192
Statistical Process Control (SPC)   13, 29-31, 105-107
Statistical tolerance stackup   99, 105-136
  adjusted statistical tolerance stackup 107-109, 120-136
  appropriateness of 105-106
    number of dimensions and tolerances and 105-106
  assembly tolerance and 108
  chain of dimensions and tolerances in 110-111, 120-136
  comparison with worst-case result 120-136
  conditional assumptions 99, 106
  examples using Advanced Dimensional Management method 119, 149, 150, 151, 152, 169, 170, 172, 173, 176, 196, 197, 198, 237-240, 241, 242, 244, 252, 253, 261, 290, 291, 308, 311, 319, 322, 329-366
  examples using GD&T - simplified  
    complex bolted assembly 168-178
  examples using plus/minus - simplified 120-136
    assembly with effect of gravity 127-129
    complex bolted assembly 133-136
    complex welded assembly 130-133
    simple assembly 125-127
    single part 121-125
  manufacturing process controls and 106
  Monte-Carlo 107
  probability and 105-108
  results 105-136
  root-sum-square (RSS) and 107-108, 114-117, 120-136
    definition of 107
    formula for 107
    process related assumptions and 108
    standards deviations (σ) and 108
  spreadsheets and 116-120
    benefits of 116-119
    preformatted tolerance stackup report format 116-119, 120
  statistical process control (SPC) and 106-109
    Cp & Cpk 107
  step-by-step procedure 109-118
    adjusted statistical result 116, 118
    converting the dimensions and tolerances into equal bilateral format 112-113
    determining the nominal distance being studied 115, 117
    determining the positive and negative directions 110-113
    determining the upper and lower limits 116-118
    entering data into the tolerance stackup report form 100-104, 114-118
    labeling positive and negative direction dimensions 110-113
    labeling the distance being studied 109-110
    root-sum-square (RSS) and 114-117
  tolerance distribution and 106
Tolerance    
  conversion of +/- 33-37, 65
  conversion of GD&T  
    position 154, 178-180
    profile 140-145
  definition of 7
  effects of not specifying 8-14
  format of 27-30
    effect on manufacturing process 29-31
    effect on target value 29-31
    equal bilateral 27
    examples of 28
    legal differences 29-31
    limit dimensions 27
    rules for 28
    SPC and 29-31
    unequal bilateral 27
    unilateral 27
  importance of 4, 6
  range 39
  types of 20-25
    +/- 16-20
    angular 20
    form 22, 24
    general note - default 20
    geometric 14, 16-21
    local 20
    location 22, 24-25
    orientation 22, 24
    size 22-23
    statistical 105-136
    title block - default 20
    worst-case 58
Tolerance analysis   2, 51-60
  assumptions in 74-78, 99, 120
  computer modeled 59
  of cumulative variation 51-52
  definition of 51
  design complexity and 2
  at different stages in a project  
    before and after production 52
  importance of specifications in 51
  of individual tolerances 51
  manually modeled 58
  methods and types of 58-59
  reasons for 51-53, 55-56, 58
    clearance and interference 53
  statistical 58, 105-136
    root-sum-square (RSS) 59, 107
  steps of performing 51-52
  three-dimensional 59, 62, 107
    Monte-Carlo 107
  worst-case (arithmetic) 58
Tolerance stackup    
  Advanced Dimensional Management method 119, 149, 150, 151, 152, 169, 170, 172, 173, 176, 196, 197, 198, 237-240, 241, 242, 244, 252, 253, 261, 290, 291, 308, 311, 319, 322, 329-366
  assumptions in 74-78, 107, 99, 120
  calculating part tolerances from a final assembly tolerance 367-372
    adjusted RSS part allocation formula 370-372
    RSS part allocation formula 371-372
  chain of dimensions and tolerances in 53, 54, 57, 61, 63, 99-104, 165
    including dimensions and tolerances in 56, 58, 287-288, 293-296
  and decision making 53, 303
  at different stages in a project  
    before and after production 52
  definition of 51, 53
  determining which dimensions and tolerances to include 56, 58, 287-288, 293-296, 303
  diametral and radial tolerance stackups 215-224
    calculating coaxiality error / misalignment in 216, 218-224
    coaxiality versus concentricity 215
    controlling coaxiality with GD&T 216
    datum feature shift and 219
    examples of 217-224
    formula with variables 218-218
    material condition modifiers and 216-224
  direction of 58, 287-289, 293-296
    dimensions, tolerances and other variables 293-296
    linear one-dimensional stackups 58, 77
  effect of assembly process on 57-58, 108, 233-234, 353-366
  effect of dimensioning and tolerancing schemes on 56-57, 236, 353-365
  effect of part and assembly geometry on 56, 287-327, 367-368
    effect of changing part and assembly geometry 367-368
    locating features closer together 316-327
    locating features farther apart 305-316
    rotation of parts in an assembly 303-327
  elimination of ambiguity in 107-108
  fixed fastener 383-388
  and fixtures 53-55
  floating fastener 373-383
  form tolerances in 285-286, 393-428
  importance of GD&T in 107-108
  iteration in 367-369
  moving from one part to another in 99-104
  purpose of 51-52, 55-56, 58, 303
  rotation of parts within a linear tolerance stackup 293, 303-327
    affect on the tolerance stackup 305
    comparisons of translational variation versus rotational variation in a linear tolerance stackup 293, 303-327
    importance of 305
    locating features closer together 316-327
    locating features farther apart 305-316
    reporting in a tolerance stackup report 309, 311, 316, 322, 323, 327
  separate requirements and 192-195, 196-199
  simultaneous requirements and 187-192, 195-199
  statistical 58, 105-136
    examples of 120-136
    root-sum-square (RSS) 59, 107
  steps of, general 55
  subjects of a 51-52, 303
    clearance and interference 53
    examples of 52
  as a subset of tolerance analysis 52
  units 302-303
    determining which units to report in a tolerance stackup 303
  without dimensions 142
  worst-case (arithmetic) 58, 61-104
    examples of 58, 61-104
Tolerance stackup report   62, 66-67, 80, 83, 86, 89, 93, 97, 100-104,  116-120, 169, 249-286, 329-366
  Advanced Dimensional Management tolerance stackup report form 119, 253, 261, 329-365
  as a communication tool 250-251
  consistency and 117-118, 250-251
  data entry in 62, 100-104, 111-118
  data fields in 120, 251-260
  decision making and 249-250
  examples of  
    Advanced Dimensional Management method 119, 150, 152, 170, 173, 196, 197, 241, 244, 252, 253, 261, 291, 308, 311, 319, 322, 329-366, 398, 419, 421, 424, 426
    simplified 67, 80, 83, 86, 89, 93, 97, 117, 118, 122, 124, 126, 129, 131, 135, 177
  format of 251
  general guidelines for description, part number and revision information 260-262
  guidelines for entering dimension and tolerance data 262-268
    +/- dimensions and tolerances 262-264
    basic dimensions 266-268
    bonus tolerance 264, 268, 270-286
    datum feature shift 264, 270-286
    datum reference frames 160, 267, 268, 270-286
    form tolerances 285-286, 393-428
    GD&T 264-266, 268-286
    material condition modifiers 268, 270-271
    orientation tolerances 282-285
    positional tolerances 160, 178-180, 275-283
    profile tolerances 141, 143, 145, 147, 149-152, 271-277
    runout tolerances 286
  importance of preformatted tolerance stackup report format 116-120, 250-251
  purpose of 249-251
  reasons for 249-250
  simplified examples for +/- 80, 83, 86, 89, 93, 97
  step-by-step instructions for completing a simplified tolerance stackup form 65-67
  step-by-step instructions for filling out the Advanced Dimensional Management tolerance stackup report form 251-260
    assumptions block 260
    data entry block 254-258
    notes block 259-260
    results block 258-259
    suggested action block 260
    tracking and title block data 253-254
  step-by-step simplified introduction for worst-case +/- 66-67
  tolerance stackup report form 116-120, 249-286
Tolerance stackup sketch   62-67, 80, 83, 86, 88, 92, 96, 169, 233-247, 287-288
  annotation in 238-247
    assembly shift 238-240, 243, 245, 246
    contributing dimensions and tolerances 238-239, 243, 246
    datum feature shift 238-240 ,246
    dimension direction labels 238-240, 243, 246
    identification of the distance or gap being studied 238-239, 243, 245
    item numbers 238-240, 245, 246-247
    part identification 238-239, 243, 245
    title and reference information 238-239, 245, 247
    tolerance stackup direction 238-240, 243, 245-246
  chain of dimensions and tolerances and 233, 236, 240, 243, 246-247
  as a communication tool 233, 247
  content of 236-237
  correlating with the tolerance stackup report 239, 241-243, 245, 247
  dimensioning and tolerancing schemes and 236
  examples of  
    Advanced Dimensional Management method 119, 149, 151, 169, 172, 176, 198, 237-240, 242, 290, 329-366, 397, 418, 420, 423, 425
    for drawings based on +/- 240
    for drawings based on GD&T 242
    simplified 67, 80, 83, 86, 88, 92, 96, 117, 118, 122, 124, 126, 129, 131, 135
  form tolerances in 393-428
  importance of 233-236, 287-288
  part and assembly geometry in 237-239
    clarity and 238-239
    scale of 238-239
    sources of 238
  purpose of 236-237, 247
  reason for 233, 234-236, 247, 287-288
  required information 233-236
    assembly drawings 233, 236
    catalog and purchased item drawings 233, 235
    manufactured component drawings 233-234
    part and assembly model(s) 233
  simplified examples for +/- 80, 83, 86, 88, 92, 96
  step-by-step directions for completing 243-247
    for drawings based on +/- 243-245
    for drawings based on GD&T 245-247
    simplified 61-67
  step-by-step simplified introduction for worst-case +/- 62-67
  timing of 233
  visualization of the problem and 233, 236, 247, 287-288
Trigonometry   99-100, 141-142, 201, 287-327, 343-345, 347-349
  converting +/- to positional tolerance zone 201-207
    Pythagorean theorem 201-206
    right angle solution 205-206
  converting angular dimensions and tolerances into linear units 296-302
    +/- example 297-299
    GD&T example 300-302
  like triangles 304-305, 407-408, 422, 423
  projection into the tolerance stackup direction 99-100, 141-142, 287-302
  rotation of parts within a linear tolerance stackup 303-327
  tolerance stackup units and 302-303
    linear units 302
    polar units 302
Units   302-303
  determining which units to report in a tolerance stackup 303
Variation   43-49, 53-54, 58, 108, 233-234, 287, 293
  of actual parts versus models 44
  defining allowable 43-44
  definition of 43
  from a design point of view 43
  from a manufacturing point of view 43
  from a measurement point of view 43
  from a tolerance analysis point of view 44
  prediction of  
    by a tolerance stackup 53, 58
  reducing predicted 53-54
    fixturing 53-54
  sources of 45-49
    ambient conditions 46-47
    assembly process 48-49, 108, 233-234
    difference in process 47
    difference in processing equipment 47
    inspection process 48
    manufacturing process capability 45
    operator error and bias 46
    poor maintenance 47-48
    tool wear 46
    variations in material 46
  tolerances and 44
Worst-case tolerance stackup   61-104
  chain of dimensions and tolerances in 61, 63-64, 67, 78-104
  conditional assumptions 61, 77-78, 99
  examples using Advanced Dimensional Management method 119, 149, 150, 151, 152, 169, 170, 172, 173, 176, 196, 197, 198, 237-240, 241, 242, 244, 252, 253, 261, 290, 291, 308, 311, 319, 322, 329-366
  examples using GD&T - simplified  
    complex bolted assembly 168-178
  examples using plus/minus - simplified 78-99
    assembly with effect of gravity 87-90
    complex bolted assembly 93-99
    complex welded assembly 90-93
    simple assembly 84-87
    single part 79-84
  results 61
  step-by-step procedure 61-68
    converting the dimensions and tolerances into equal bilateral format 33-37, 65
    determining the nominal distance being studied 65-66
    determining the positive and negative directions 62-64
    determining the upper and lower limits 66, 67
    entering data into the tolerance stackup report form 65, 100-104
    labeling positive and negative direction dimensions 62-65, 68
    labeling the distance being studied 61-62
    summation of values 65
Mechanical Tolerance Stackup, Tolerance Analysis Book, Tolerance Analysis Terms