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.


CONTENTS


        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