## APPENDIX A

## SUMMARY OF PARAMETRIC GEOMETRY DEFINITIONS

## AND REGIONAL MILLING COMMANDS

## A.1 PARAMETRIC GEOMETRY DEFINITIONS

## A.1.1 Parametric curve definitions

Conic arc:(Section 2.1) SCURV/CURSEG,Point 1,›TANSPL,Vector,!›NORMAL,Vector,! $ ›CRSSPL,Vector,!Point 2, ... For a CURSEG definition a maximum of 5 points and/or vector constraints can be included.Simple spline curve:(Section 2.2.2) SCURV/SPLINE,Point 1,›TANSPL,Vector,!›NORMAL,Vector,! $ ›CRSSPL,Vector,!Point 2, ... For a spline definition a maximum of 30 points can be included.Smoothed spline curve:(Section 3.1) SCURV/SPLINE,›WEIGHT,Global weight value,! $ ›LIMIT,GLOBAL limit,! $ Point 1,›TANSPL,Vector,!›NORMAL,Vector,!›CRSSPL,Vector,! $ - ›WEIGHT,Value,!›LIMIT,Value,! $ Point 2, ...Combination of previously defined curves:(Section 2.3) SCURV/COMBIN,Curve 1›,Curve 2!›,Curve 3! ... 356

Adding flow and segment data to a curve definition:(Section 3.2, 3.3) Curve Definition, $ ARC FLOW,PARAM,N1,N2,›Tolerance,! $ ANGLE Point,›Vector,! CHORD ›Point1,Point2,›Vector,!! ARC ›PARAM,N2,N3,›Tolerance,! ..... $ ANGLE CHORD SEG,LENGTH,M1,M2 ›,LENGTH,M2,M3! ..... PARAM PARAM Note: in this definition N1,N2, ..., M1,M2, ... are positive integers identifying points at ends of arcs of the curves with N1 = M1 = 0. All arcs should be included.## A.1.2 Parametric Surface Definitions:

Ruled cylindrical surface:(Section 4.1) SSURF/RULED,Curve,AXIS,Point1 ,Point2 VectorSurface of Revolution:(Section 4.2) SSURF/REVOLV,Curve,AXIS,Point ,Vector , CLW , $ Point1 Point2 CCLW Start angle, Finish angle In this definition the angles are specified in degrees.Ruled Surfaces:(Sections 5.1.1, 5.1.2) SSURF/GENCUR,Curve 1,Curve 2 XYZ SSURF/SMESH,XYPLAN,SPLINE,P1,›TANSPL,Vector,! $ YZPLAN ZXPLAN P2,›TANSPL,Vector,!... PN,›TANSPL,Vector,! $ SPLINE,Q1,›TANSPL,Vector,!,...QN ›,TANSPL,Vector! 357

In the above definitions Curve 1 and Curve 2 are flow curves with the same number of segments, P1,...,PN and Q1,...,Qn are points.Cross product surfaces:(Sections 5.2, 5.3, 5.4) XYROT SSURF/YZROT,Curve 1,CROSS,Curve 2 ZXROT SSURF/TRANSL,Curve 1,CROSS,Curve 2 SSURF/SCALE, Curve 1,CROSS,Curve 2 Note: in the above definitions Curve 1 and Curve 2 are simple SCURVs without a flow structure.Single patch surfaces:(Sections 6.1.1, 6.1.2, 6.1.3) SSURF,PATCH,PNTVEC,PLUS ,PT00,PT10,TN00,TN10,PT01,PT11, $ MINUS TN01,TN11,CR00,CR10,TW00,TW10,CR01,CR11,TW01,TW11 In this definition PT00,PT10,PT01,PT11 are points all other symbols represent vectors. SSURF,PATCH,PNTSON,PLUS ,Point 1,Point 2,...,Point 16 MINUS SSURF,PATCH,POLYGN,PLUS ,Point 1,Point 2,...,Point 16 MINUSMesh surfaces:(Sections 6.2.1, 6.2.2) XYZ SSURF/SMESH,XYPLAN, $ YZPLAN ZXPLAN SPLINE,P1,P2,.....,Pn, $ SPLINE,Q1,Q2,.....,Qn, $ SPLINE,....... All the specified spline curves must be defined in terms of the same number of points. Points may optionally have TANSPL, CRSSPL, NORMAL, WEIGHT or LIMIT constraints attached, as in the basic SPLINE definition. Note that there is no mechanism for surface smoothing except in the major spline direction. The modifier XYZ indicates that the surface is a general 3D parametric surface. XYPLAN, YZPLAN and ZXPLAN 358

indicate that the surface is based on a regular grid in the xy-, yz- or zx-plane respectively. GENCUR surfaces: (Sections 6.3.1, 6.3.2) Spline-constrained case - SSURF/GENCUR,C1,C2,...,CN Cross-constrained case - SSURF/GENCUR,C1,...,CN,CROSS,D1,...,DM The curves C1,C2,... and D1,D2,... must be previously defined flow curves; all members of either family must have the same number of flow segments. In the cross-constrained case, each cell of the curve mesh must be bounded by four flow segments.Combination Surfaces:(Section 6.4) SSURF/COMBIN,S1,S2,...,Sn Here S1,S2,... are previously defined surfaces. The system checks that adjoining surface boundaries are coincident, but cross-boundary slope continuity is the user's responsibility. 359

## A.2 REGIONAL MILLING COMMANDS

## A.2.1 SCON Command: (Section 8.6)

Specification of the Part Surface parameters:(Section 8.6.1) SCON/PS,TO,surface,PLUS ,thick ON MINUS where PS indicates part surface parameters TO specifies that the tool is to be offset from the part surface, in the same sense as for conventional APT (TLOFPS). ON specifies that the tool tip must be ON the part surface like TLONPS in conventional APT. NOTE: This may cause gouging. surface is the symbolic name of the part surface, which must be previously defined. PLUS indicates that the tool side of the surface is determined by the cross product, SN, of the TANSPL vector with the CRSSPL vector. MINUS indicates that the tool is on the opposite side of the surface. thick is a scalar quantity representing the thickness of material to be left on or removed from the surface. A positive quantity will be left on and a negative quantity removed. 360

Drive Control by a Synthetic Curve:(Section 8.6.2) SCON/DS,curve,PARAM,ulow,uhigh,AT,vector ON CRSSPL where DS indicates drive control parameters. curve symbolic name of a previously defined synthetic curve. PARAM indicates drive control parametric limits follow, i.e. bounds of drive geometry. ulow lower extent of drive curve. uhigh upper extent of drive curve. AT Type of drive control . ON 'AT' - tool contacts part surface at the point where tool projection vector from control point pierces the surface. 'ON' - tool tip is constrained to be on the tool projection vector from the control point. vector symbolic name of a fixed tool projection vector from curve to part surface. CRSSPL indicates that the fence of CRSSPL vectors attached to the synthetic curve are to be used as variable tool projection vectors. 361

Drive Control by a Mesh Structured Sculptured Surface:(section 8.6.2) SCON/DS,surface,PARAM,ulow,uhigh,vlow,vhigh,AT,vector ON NORMAL where DS indicates drive control parameters. surface symbolic name of a previously defined mesh structured sculptured surface. PARAM indicates drive control parametric limits follow, i.e. bounds of drive surface. ulow lower extent in TANSPL direction. uhigh upper extent in TANSPL direction. vlow lower extent in CRSSPL direction. vhigh upper extent in CRSSPL direction. AT Type of drive control. ON vector symbolic name of fixed tool projection vector. NORMAL the surface normal at a point on the DRIVE surface will be used as the tool projection vector. 362

Tool Axis Specification:(Section 8.6.3) Fixed Tool Axis: SCON/AXIS,vector where vector symbolic name of fixed tool axis vector. Variable Tool axis: SCON/AXIS,NORMDS,PLUS MINUS For synthetic curve drive control the attached fence of CRSSPL vectors is used for tool axis orientation; for sculptured surface drive control the surface normal is used. PLUS tool axis vector the same direction as the variable vector. MINUS tool axis vector reversed.Feedrate Specification:(Section 8.6.4) SCON/FEED,f1,f2,f3,f4 where f1 feedrate for passes in major direction while regional milling. f2 feedrate for side stepping between major passes. f3 feedrate for plunging into material, when this is required. f4 feedrate for rapid withdrawal to and traverse across a clearance plane. Note: All four values must be input, but a zero value will be ignored during regional clearance processing. 363

Stepover Control:(Section 8.6.5) SCON/STEPOV,s1,s2,s3,s4 where s1 = 0 fixed parametric step required. > 0 maximum allowable cusp height between consecutive passes. s2 > 0 maximum physical stepover distance. < 0 if s1 = 0 parametric stepover across the drive surface. s1 > 0 maximum parametric step. s3 additional thickness to be added to part surface while stepping over. Equivalent to lift off and plunge between passes. s4 Not used. NOTE: A value must be entered.(e.g.0)Clearance Plane Specification:(Section 8.6.6) SCON/FEED,plane where plane symbolic name of an APT planeCancelling Regional Milling Conditions:(Section 8.6.7) SCON/INIT,ALL PS,DS,... where ALL cancels all regional milling conditions. PS,DS,... permits selective cancellation of groups of conditions. 364

## A.2.2 SMIL Command: (Section 8.7)

Tool Positioning:(Section 8.7.1) scalar SMIL/POSN,DS,PARAM,u,v,INCR,vector plane where u,v are the parameters of the drive control point and tool projection vector, within the range specified for the drive control geometry in the preceding SCON/DS statement, which are to control the tool position. Note: If the drive geometry is a curve,the v parameter must be included but it is ignored. scalar INCR,vector indicates how the tool is to be backed plane off from the part surface. This couplet must be programmed even if no back off is required; in which case INCR,0 should be programmed. scalar causes the final tool postion to be back along the tool projection vector by this scalar amount. vector causes the final tool postion to be the result of moving the tool from the surface contact point in the direction and by the magnitude of the vector. plane causes the tool end to be retracted to the plane by the shortest distance from the surface contact point. 365

Single Tool Path:(Section 8.7.2) SMIL/PATH,DS,PARAM,ust,vst,TANSPL,PLUS ›,1! CRSSPL MINUS where ust,vst are the parameters of the initial point on the drive control surface. If the drive geometry is a synthetic curve, the vst parameter must still be included but is ignored. The point must be within the bounds of the drive geometry region defined by the preceding SCONM/DS statement. TANSPL indicates which curve through the CRSSPL point selected by ust,vst is to be used for tool path control, TANSPL or CRSSPL. NOTE: Only TANSPL has any meaning if the drive control geometry is a synthetic curve. PLUS indicates the direction of traverse MINUS along drive control curve: PLUS in the direction of increasing parameter; MINUS in the direction of decreasing parameter. 1 Optional parameter. If set to 1 will cause the first cut vector of the tool path to be omitted from the cutter location file. If this parameter is omitted or set to zero, then the first cut vector will be produced. 366

Area Clearance:(Sections 8.7.3 and 8.7.4) SMIL/ZIGZAG,DS,PARAM,ust,vst,TANSPL,PLUS ,STEPOV,PLUS ›,1! PICKFD CRSSPL MINUS MINUS where the boundaries of the region to be machined are defined by the preceding SCON/DS statement. The drive geometry mbe a mesh structured sculptured surface. In the case of PICKFD, the clearance plane to which the tool is retracted and across which the tool is traversed between passes, is defined by the preceding SCON/FEED,plane statement. ZIGZAG indicates the type of area clearance PICKFD required. ust,vst are the parameters of the drive control point at which the area clearance tool path is to commence. TANSPL indicates the direction of the major CRSSPL tool path with respect to the drive control surface. PLUS indicates the initial motion direction MINUS in the case of ZIGZAG or the motion direction for all passes in the case of PICKFD. PLUS - increasing parametric value. MINUS - decreasing parametric value. STEPOV,PLUS indicates the direction of step over MINUS in the alternate spline direction to that selected for the machining passes. PLUS - increasing parametric value. MINUS - decreasing parametric value. 1 Optional parameter. If set to 1, then the first cut vector will be omitted; if omitted or set to zero the first cut vector will be produced. 367