The law of automatic unripe set prescription of curve of the tooth back that shovel tine
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- source:WINNERS CNC Machining
1 arc is begged hand in algorithm foregone and linear O of P1 of two end points, P2, the centre of a circle and R of circular arc radius, the nodical coordinate that begs linear P1P2 and this circular arc (dot I is curve node, the midpoint that nods M to be linear P1P2) the basis is each bits more foregone coordinate, use midpoint iteration to approach a law to be able to beg a curve node simply quickly, its algorithm flow. According to algorithmic flow, the figure that uses Visal Lisp handles function function, design following arc to beg hand in subprogram INTERAL: ? NTERAL of Zuo of Hai Haihan is beg circular arc and linear node (Defun Interal(r O I H / Xo Yo X1 X2 Y1 Y2 X3 Y3 Loop Rr D Delt)(setq Xo(car O) Yo(cadr O) X1(car I) Y1(cadr I) X2(carh) Y2(cadr H))(setq Loop T)(setq Ee 1e-6)(WHILE Loop(SETQ X3(/(+ X1 X2)2.
0)y3(/(+ Y1 Y2)2.
0))(SETQ D(distance O(list X3 Y3)))(setq Delt(-d R))(cond((<=(abs Delt)ee)(setq Loop Nil))((<Delt 0.
0)(setq X2 X3 Y2 Y3))(T(setq X1 X3 Y1 Y3))) : Cond) : While(list X3 Y3))2.
2 arc arc is begged hand in R2 of radius of R1 of radius of O1 of coordinate of algorithmic and foregone the centre of a circle, circular arc and O2 of coordinate of the centre of a circle, circular arc, beg the coordinate of nodical I. The triangular Δ IO1O2 that forms by O11 of two the centre of a circle, O2 and nodical I, can build the following algorithm: IO1=R1IO2=R2D=O1O2=Ditance(O1, o2)Ang2= Angle(O1, o2)Ang1=arccos(R12+D2-R22)2R1*DIX=O1X+R1*COS(Ang1-Ang2)IY=O1X+R1*SIN(Ang1-Ang2) calculates according to above law, use Visal Lisp graph to handle function function, design following arc arc to beg hand in subprogram INTERAA. : : : Function INTERAA is the node that begs two circular arc (Defun Interaa(r1 O1 R2 O2 / D A-o1o2 Cosa Sina A-r1o1o2 X Y)(setq D(abs (distance O1 O2))) : : Of O1o2 line segment from (Setq A-o1o2(angle O1 O2)) : : O1o2 is spent (Setq Cosa((/ +(* R1 R1)(* D D)(-(* R2 R2)))(* 2.
0 R1 D)))(setq Sina(sqrt(- 1.
Example of application of 0(* Cosa Cosa))))(setq A-r1o1o2(atan Sina Cosa))(setq X(+(car O1)(* R1(cos(+ A-o1o2 A-r1o1o2)))))(setq Y(+(cadr O1)(* R1(sin(+ A-o1o2 A-r1o1o2)))))(list X Y))3 uses what industrial and commercial university develops Chongqing " CAD of typical and complex cutting tool " the takes hob of the key inside Kong Shi end panel tooth form of software design scale pursues: The following place gives a program detailed account is scale the program of partial Visual Lisp that tooth form of this end panel pursues. The Visual Lisp program that tooth form of end panel of function Sidtee scale pursues: (Defun Sidtee(ra0 Zk Hk Rk Thi K K1 H0 Rh P0 / Angcxj B1 J0 J1 B0 E A0 A1 G0 G1 O-r H I I0 A1b1o A-a1b1o1 O1 O1-1 R-ka1 R-kg1)(setq Angcxj(/(* Pi 2.
0)zk)) : : Tooth form horn (Setq J1(polar P0(/ Pi 2.
0)ra0)) : : J1 dot: : The following program begs B1, J0, B0, E, A0, A1, G0, G1, H, I, I0 to nod with POLAR function... (Setq I0(polar I(+ TH(I / Pi 2.
0))(/(- K1 K)5.
0))) : : I0 dot: : Of A1B1 line segment in hang down dot (Setq A1b1O(LIST(/(+ (CAR A1)(CAR B1))2.
0)(/(+(CADR A1)(CADR B1))2.
0))) : : The perpendicular bisector angle of B1A1 line (Setq A-a1b1o1(+(angle B1 A1)(/ Pi 2.
0)))(setq O1(polar A1B1O A-a1b1o1(/(* 3 Ra0)2.
0))) : : O1 consults the centre of a circle nods: : Of A0B0 line segment in hang down dot (Setq A0b0O(LIST(/(+ (CAR A0)(CAR B0))2.
0)(/(+(CADR A0)(CADR B0))2.
0)))(setq O0(polar A0B0O A-a0b0o0(/(* 3 Ra0)2.
0))) : : Heart of O0 circle of reference nods (Setq O0(inters A0b0o O0 A0 O0-1 Nil)) : : Heart of O0 circle of reference nods (Setq F0(interaa R-k1a0 O0 R-ka1 O1)) : : The node that begs A0B0 arc and A1B1 arc (Setq F1(interaa R-k1g0 O0 R-kg1 O1)) : : The node that begs G0C0 arc and G1C1 arc (Setq D0(interaL R-k1a0 O0 I H)) : : The node that begs A0B0 arc and linear HI (Setq D1(interal R-k1g0 O0 I H1)) : : Beg the node of G0C0 arc and linear HI: : : The end panel tooth form that the following program seeks the job of each bits of scale that give to pursue medium according to above program (Command " Pline " A1 " W " 0.
4 " " G1 " " ) (Command " Arc " " Ce " when P0 J1 A1)) uses plot of software of CAD of complex cutting tool before, the method that should rely on an user to be caught with the object obtains the curve node that generates tooth back curve and arc arc node. And in Chongqing industrial and commercial university develops " CAD of typical and complex cutting tool " in software, when designing hob of milling cutter of the figuration that shovel tine, gear, worm wheel hob, the arc that uses the article to put forward is begged hand in algorithm and arc arc to beg hand in algorithm, successfully automatic scale gives picture of tooth form of cutting tool end panel, raised the automation rate of whole CAD system from this. CNC Milling