APT4 SCULPTURED SURFACES
PART PROGRAMMERS MANUAL
VOLUME II
Issue 3
September, 1989
CONTENTS
INDEX
PREFACE
This volume of the APT4 + Scupltured Surfaces part-programmers
manual was written by staff of the Department of Applied
Computing and Mathematics at Cranfield Institute of
Technology. The authors' intention is to provide a simple
text which will introduce part-programmers to all the
parametric geometry features of the Sculptured Surfaces System
and related machining concepts.
The many examples included in the text have been chosen
principally to illustrate the definitions. All results shown
with these examples were obtained using a VAX computer,
results obtained from other computers may differ in detail,
due to variations in computer word length.
PREFACE
CHAPTER 1 INTRODUCTION 1
1.1 PARAMETRIC GEOMETRY 1
1.2 VECTOR GEOMETRY 7
1.2.1 Vector Geometry of Parametric Curves 9
1.2.2 Vector Geometry of Parametric Surfaces 9
1.3 HOMOGENEOUS COORDINATES 11
1.4 EXAMPLES IN THIS MANUAL 12
CHAPTER 2 PARAMETRIC CURVES 13
2.1 CONIC ARCS (CURSEG DEFINITION) 13
2.1.1 Parametric Line 13
2.1.2 Circular Arcs 15
2.1.3 General Conic defined by 5 conditions 21
2.1.4 Conic Arcs defined by 4 conditions 27
2.2 SPLINE CURVES 29
2.2.1 Simple Example 29
2.2.2 Spline Curves with Vector constraints 33
2.2.3 Segments of Lines and Circles - 37
The SEG Defintion
2.2.4 Retrieval of Geometric Data from 41
Curves
2.3 COMBIN CURVES 45
2.3.1 Simple Example 45
2.3.2 Applications of COMBIN curves 46
2.4 CANONICAL ARRAYS USED FOR SCURV 47
2.4.1 Interim SCURV Array 47
2.4.2 Final SCURV Array 49
2.4.3 CURSEG Canonical Form 52
CHAPTER 3 MODIFICATION OF PARAMETRIC CURVES 53
3.1 SMOOTHING 53
3.1.1 WEIGHT Constraint 53
3.1.2 LIMIT Constraint 59
3.1.3 VECTOR Constraints in smoothing 63
3.1.4 Smoothing Information in the 65
Canonical Arrays
3.1.5 Smoothed curves in Surface Definition 67
3.2 FLOW OF PARAMETRIC CURVES 69
3.2.1 Arc length FLOW 69
3.2.2 Canonical Array for a FLOW curve 72
3.2.3 ANGLE specification of FLOW 75
3.2.4 CHORD specification of FLOW 81
3.2.5 PARAM specification of FLOW 85
3.3 DIVISION OF PARAMETRIC CURVES INTO 85
SEGMENTS
3.3.1 Segmentation Examples 87
3.4 ALTERNATIVE SPLINING ALGORITHM 91
3.4.1 Example 93
3.5 APPLICATION OF GEOMETRIC 97
TRANSFORMATIONS
3.5.1 Example 97
CHAPTER 4 SCULPTURED SURFACES DEFINED IN TERMS 99
OF A SINGLE CURVE
4.1 RULED CYLINDRICAL SURFACES 99
4.2 SURFACES OF REVOLUTION 102
4.3 DEFINITION ERRORS FOR RULED AND REVOLV 105
SURFACES
4.4 A SUGGESTED APPLICATION FOR REVOLV 106
SURFACES
4.5 VERIFICATION LISTINGS FOR RULED AND 106
REVOLV SURFACES
CHAPTER 5 SCULPTURED SURFACES DEFINED BY TWO 107
CURVES
5.1 RULED SURFACES 107
5.1.1 Ruled Surface Examples 108
5.1.2 Mesh Type Ruled Surfaces 115
5.1.3 Canonical Form for a Sculptured 120
Surface
5.2 'TRANSL' TYPE CROSS PRODUCT SURFACE 123
5.2.1 Torus Example 123
5.2.2 Spline Curve Example 127
5.3 ROTATIONAL TYPES OR CROSS PRODUCT 129
SURFACE
5.3.1 Simple XYROT Example 131
5.3.2 More General XYROT Example 132
5.3.3 YZROT and ZXROT Definitions 137
5.4 THE SCALE TYPE OF CROSS PRODUCT 137
SURFACE
5.4.1 Simple Scale Example 139
5.4.2 More General Examples 141
CHAPTER 6 MORE GENERAL SCULPTURED SURFACE TYPES 143
6.1 INDIVIDUAL 'PATCH' DEFINITIONS 143
6.1.1 The 'PNTVEC' Patch 145
6.1.2 The 'POLYGN' Patch 149
6.1.3 The 'PNTSON' Patch 153
6.2 'SMESH' SURFACES 156
6.2.1 General 'XYZ' Mesh 156
6.2.2 Specialised 'SMESH' Surfaces 164
- The 'XYPLAN', 'YZPLAN' and
'ZXPLAN' Options
6.3 'GENCUR' SURFACES 166
6.3.1 Spline-constrained 'GENCUR' Surfaces 167
6.3.2 Cross-constrained 'GENCUR' Surfaces 173
6.4 THE 'COMBIN' SURFACE 177
CHAPTER 7 TOOL PATH CONTROL USING SCULPTURED 181
SURFACES
7.1 SCULPTURED SURFACES USED AS APT 181
SURFACES
7.1.1 Sculptured Surfaces used as a Part 183
Surface
7.1.2 Sculptured Surfaces used as Drive 185
and Check Surfaces.
7.1.3 Sculptured Surfaces used as Part, 189
Drive and Check Surfaces
7.1.4 Use of THICK with Sculptured 193
Surfaces
7.1.5 Extension to Sculptured Surfaces 193
7.1.6 Factors Affecting Efficiency 195
7.2 SPECIAL ARELEM 197
7.3 MULTI-AXIS MACHINING OF SCULPTURED 198
SURFACES
7.3.1 Conventional Tool Axis Control 198
7.3.2 Special Tool Axis Control for 203
Sculptured Surfaces
7.4 TOOL PATH GENERATION BY GEOMETRIC 205
CONSTRUCTION
7.4.1 Tool Offset Calculation for a 205
Spherical Cutter
7.4.2 Tool Offset Calculation for a Corner 209
Radius Cutter
7.5 ARELEM PROBLEMS AND SOLUTIONS 210
7.5.1 Cutter starts up on wrong side of 210
surface
7.5.2 Cutter out of Tolerance with Drive 210
Surface at start of cut
7.5.3 Problems finding a surface during 211
start-up
7.5.4 Problems in moving off in the 211
correct direction after a satisfactory
start up to a sculptured drive surface
CHAPTER 8 REGIONAL MILLING OF SCULPTURED 213
SURFACES
8.1 BASIC REGIONAL MILLING ALGORITHM 213
8.2 CONTROL OF TOOL PATH BY A SYNTHETIC 217
CURVE
8.3 CONCEPT OF REGIONAL TOOL CONTROL 221
8.4 PROGRAMMING REGIONAL MILLING 221
8.4.1 Developing a Regional Milling 222
Program
8.4.2 Example of a Regional Milling 228
Program
8.4.3 Regional Milling Verification 229
Listing
8.4.4 Regional Milling CLFILE Format 230
8.5 GENERAL APT COMMANDS APPLICABLE IN 232
REGIONAL MILLING
8.6 SPECIFICATION OF REGIONAL MILLING 233
CONDITIONS
8.6.1 Part Surface Parameters 235
8.6.2 Drive Control Parameters 236
8.6.3 Tool Axis Orientation 239
8.6.4 Feedrate Selection 240
8.6.5 Stepover Control 241
8.6.6 Clearance Plane Specification 242
8.7 REGIONAL MILLING TOOL CONTROL 243
8.7.1 Tool Positioning 245
8.7.2 Single Tool Path 247
8.7.3 Zigzag Area Clearance 251
8.7.4 PICKFD Area Clearance 255
8.7.5 SMIL Pre-requisites 262
8.8 REGIONAL MILLING DIAGNOSTICS 263
8.8.1 Sample Diagnostic Output 264
8.8.2 SCON Error Messages 266
8.8.3 SMIL Error Messages 266
8.8.4 PATH Error Messages 267
CHAPTER 9 OTHER PROGRAMMING FEATURES 269
9.1 DEFINITION OF POINTS AND VECTORS FROM 269
PARAMETRIC CURVES AND SURFACES
9.1.1 By Parametric Reference from a 270
Synthetic Curve
9.1.2 By Intersection of a LINE or PLANE 273
with a Synthetic Curve
9.1.3 By Parametric Reference from a 274
Sculptured Surface
9.1.4 By Proximity to a POINT and on a 275
Sculptured Surface
9.1.5 By Intersection of a space line 276
defined by two POINTS and a
Sculptured Surface
9.1.6 By Intersection of a space line 277
defined by a VECTOR and a POINT and
a Sculptured Surface
9.2 STORING AND RETRIEVING CANONICAL 278
FORMS OF LARGE DATA ARRAY SURFACES
9.3 PRINTOUT CONTROL 280
9.4 FUNCTIONS 281
9.4.1 Trigonometric Functions 281
9.4.2 Mathematical Functions 282
9.4.3 Geometric Functions 283
9.4.4 Data Extraction Functions 284
CHAPTER 10 THE INTERACTIVE CASPA SYSTEM 289
10.1 GEOMETRY DEFINITIONS 289
10.1.1 Point and Polygon Definitions 289
10.1.2 Vector and Plane Definitions 290
10.1.3 Curve and Surfaces 292
10.2 GRAPHICS COMMANDS 293
10.2.1 Global Commands 293
10.2.2 Specific Commands 296
10.2.3 Example 299
10.3 OTHER CASPA COMMANDS 303
10.3.1 Output Control 303
10.3.2 File Handling Facilities 306
10.3.3 Editor Commands 309
10.3.4 Miscellaneous Commands 310
CHAPTER 11 THE NON NATIVE GEOMETRY FACILITY 312
11.1 SOFTWARE AND DATA REQUIREMENTS 312
11.1.1 Evaluator Specification 313
11.1.2 Transformation Specification 314
11.1.3 Data File Specification 314
11.2 TORUS EXAMPLE 316
11.2.1 Creation of a Torus 317
11.2.2 Use of Non Native Geometry 318
11.3 VDA-FS NON-NATIVE INTERFACE 319
11.3.1 VDA-FS Formatter, FVDAFS 319
11.3.2 VDA-FS Evaluator and Transformator 320
CHAPTER 12 ENHANCEMENTS TO APT4 321
12.1 ADDITIONAL CONDITIONAL TRANSFER 321
12.1.1 The Logical IF Statement 321
12.1.2 Use of logical IF in APT programs 323
12.1.3 The computed JUMPTO statement 324
12.2 ADDITIONAL PART PROGRAM STRUCTURING 325
12.2.1 The DO Statement 325
12.2.2 The CONTIN Statement 325
12.2.3 Considerations and Restrictions 326
in using a DO loop
12.3 ADDITIONAL ARITHMETIC AND VECTOR 327
EXPRESSIONS
12.3.1 Extended Number Definition 327
12.3.2 Vector Expressions 327
12.4 ADDITIONAL CANON/ STATEMENT 328
12.5 ADDITIONAL EXFILE OUTPUT MANIPULATION 329
12.5.1 EXFILE output CLDAT definitions 329
12.5.2 EXFILE output segments 330
12.5.3 Additional CLDATA location count 330
extraction
12.5.4 Additional Part Program Definitions 331
with EXFILE Data
12.5.4.1 Additional Point Definitions 331
12.5.4.2 Additional Vector Definitions 331
12.5.4.3 Additional Scalar Definitions 332
12.5.5 Programming Example 333
12.6 ADDITIONAL TLAXIS FEATURES 334
12.6.1 Existing /360APT and APT-AC language 334
12.6.2 Existing APT4 language 334
12.6.3 New TLAXIS Language 335
12.6.3.1 Additional Switch to 3-axis Mode 335
12.6.3.2 Additional Ruled Surface TLAXIS 335
Definition
12.6.3.3 Additional full TLAXIS Statement 336
12.7 ADDITIONAL PRINT CONTROL 337
CHAPTER 13 ISOPARAMETRIC PLOTTING AND MACHINING 338
13.1 THE PLOTFT STATEMENT 338
13.1.1 Single Curve Plotting 338
13.1.2 Output of a surface GRID 339
13.2 THE GOLOFT STATEMENT 340
13.3 THE REGION STATEMENT 342
13.4 THE GCLEAR STATEMENT 343
CHAPTER 14 PARAMETRIC INTERSECTION OF SURFACES 344
14.1 THE INTERSECTION BETWEEN A PLANE 344
AND SURFACES
14.2 THE INTERSECTION BETWEEN SURFACE 345
CHAPTER 15 INTERFERENCE CHECKING 346
15.1 SELECTING AND CANCELLING INTERFERENCE 346
CHECKING
15.2 DEFINITION OF AVOIDANCE STRATEGIES 349
15.3 OPTIONAL LOGGING OF AVOIDANCE ACTION 350
15.4 EXAMPLE DEMONSTRATING INTERFERENCE 351
CHECKING
15.5 APT 7 SEGMENT CUTTER IN REGIONAL 352
MILLING
15.6 ADDITIONAL TOOL AXIS CONTROL IN 353
REGIONAL MILLING
15.7 GOUGCK FACILITY IN REGIONAL MILLING 355
APPENDIX A SUMMARY OF PARAMETRIC GEOMETRY 356
DEFINITIONS AND REGIONAL MILLING
COMMANDS
A.1 PARAMETRIC GEOMETRY DEFINITIONS 356
A.1.1 Parametric Curve Definitions 356
A.1.2 Parametric Surface Definitions 357
A.2 REGIONAL MILLING COMMANDS 360
A.2.1 SCON Commands 360
A.2.2 SMIL Commands 365
APPENDIX B ERROR MESSAGES 368
B.1 TRANSLATOR ERRORS 368
B.2 EXECUTION ERRORS 375
B.3 CLEDITOR ERRORS 393
INDEX 395