;;; --------------------------------------------------------------------------- ;;; CamProfile.lsp ;;; code compiled by YZ August 2026 ;;; --------------------------------------------------------------------------- ;;; PLATE CAM PROFILE FROM A MOTION LAW ;;; ;;; PURPOSE ;;; Draws the working face of a plate cam - the shape that has to be cut so a ;;; roller follower rises by a given amount over a given angle, in a given ;;; way. ;;; ;;; THE THREE MOTIONS ;;; Constant velocity The follower rises at a steady rate. Simple, and ;;; violent: the acceleration is infinite at each end, so ;;; it hammers. Use only at low speed. ;;; Harmonic Follows a cosine. Smooth in the middle, but the ;;; acceleration jumps at the ends, which rings. ;;; Cycloidal Acceleration starts and finishes at zero, so nothing ;;; jerks. The one to use at speed, and the default. ;;; ;;; Written as a fraction f of the way through the rise, with h the lift: ;;; ;;; constant s = h f ;;; harmonic s = h (1 - cos(pi f)) / 2 ;;; cycloidal s = h (f - sin(2 pi f) / (2 pi)) ;;; ;;; PITCH CURVE AND CAM FACE ;;; The follower's CENTRE traces the pitch curve - base radius plus follower ;;; radius plus the lift. The cam FACE is that curve pulled in by the follower ;;; radius, along the normal at each point. Cutting to the pitch curve rather ;;; than the face is the classic mistake, so both are drawn, on separate ;;; layers, and which is which is said plainly. ;;; ;;; WHAT WAS FIXED ;;; - The cam face was drawn by starting a LINE command and feeding it the ;;; word "TAN" followed by a coordinate, over and over. TAN is an object ;;; snap: it needs an object picked near a point, not a point. Nothing ;;; usable came out. ;;; - Both motion laws were written as decimal constants - 0.43990, 0.035010, ;;; 0.280050, 0.315050 - with no indication of where they came from. They ;;; are a cycloidal rise scaled to an odd fraction of the period, and the ;;; second one is the first with an offset bolted on. Both are written as ;;; the standard forms above. ;;; - Fifteen variables were global. ;;; - It finished by printing a company's telephone number to the command line. ;;; ;;; CAM - draw a plate cam profile ;;; --------------------------------------------------------------------------- (setq *Cam:Base* nil *Cam:Roller* nil *Cam:Lift* nil) (defun Cam:Layer ( name colour ) (if (not (tblsearch "LAYER" name)) (entmake (list '(0 . "LAYER") '(100 . "AcDbSymbolTableRecord") '(100 . "AcDbLayerTableRecord") (cons 2 name) '(70 . 0) (cons 62 colour) '(6 . "Continuous")))) name ) (defun Cam:Poly ( pts layer closed ) (entmake (append (list '(0 . "LWPOLYLINE") '(100 . "AcDbEntity") (cons 8 layer) '(100 . "AcDbPolyline") (cons 90 (length pts)) (cons 70 (if closed 1 0))) (mapcar '(lambda ( p ) (cons 10 (list (car p) (cadr p)))) pts))) ) ;;; Lift at fraction F of the way through a rise of H. (defun Cam:Lift ( f h law ) (cond ((= law "Constant") (* h f)) ((= law "Harmonic") (* h (/ (- 1.0 (cos (* pi f))) 2.0))) (t (* h (- f (/ (sin (* 2.0 pi f)) (* 2.0 pi)))))) ) (defun c:CAM ( / *error* vars vals cen base roller lift period offset law steps i f ang r pitch face lay1 lay2 v n p prev nxt norm ) (setq vars '("CMDECHO" "BLIPMODE" "OSMODE" "CLAYER") vals (mapcar 'getvar vars)) (defun Cam:Restore ( ) (mapcar 'setvar vars vals) (while (= 8 (logand 8 (getvar 'undoctl))) (command "_.UNDO" "_End")) (vl-catch-all-apply '(lambda ( ) (*pop-error-mode*)) '()) (princ) ) (defun *error* ( msg ) (Cam:Restore) (if (and msg (not (wcmatch (strcase msg t) "*break*,*cancel*,*exit*"))) (princ (strcat "\n** CAM error: " msg " **"))) (princ) ) (setvar "CMDECHO" 0) (setvar "BLIPMODE" 0) ;; AutoCAD 2015 and later refuse (command) inside an *error* handler unless ;; the routine says up front that it will use one. (vl-catch-all-apply '(lambda ( ) (*push-error-using-command*)) '()) (command "_.UNDO" "_Begin") (setq cen (getpoint "\nCentre of the cam: ")) (if (null cen) (princ "\nCancelled.") (progn (setvar "OSMODE" 0) (setq cen (list (car cen) (cadr cen) 0.0)) (initget 6) (setq base (getdist cen (strcat "\nBase circle radius" (if *Cam:Base* (strcat " <" (rtos *Cam:Base* 2 3) ">") "") ": "))) (if (null base) (setq base *Cam:Base*)) (initget 6) (setq roller (getdist (strcat "\nRoller follower radius" (if *Cam:Roller* (strcat " <" (rtos *Cam:Roller* 2 3) ">") "") ": "))) (if (null roller) (setq roller *Cam:Roller*)) (initget 6) (setq lift (getdist (strcat "\nTotal lift" (if *Cam:Lift* (strcat " <" (rtos *Cam:Lift* 2 3) ">") "") ": "))) (if (null lift) (setq lift *Cam:Lift*)) (if (not (and base roller lift)) (princ "\nNot enough given to draw a cam.") (progn (setq *Cam:Base* base *Cam:Roller* roller *Cam:Lift* lift) (initget 6) (setq period (getreal "\nRise over how many degrees <180>: ")) (if (null period) (setq period 180.0)) (if (> period 360.0) (setq period 360.0)) (initget 4) (setq offset (getreal "\nRise starts at what angle <0>: ")) (if (null offset) (setq offset 0.0)) (initget "Cycloidal Harmonic Constant") (setq law (getkword "\nMotion [Cycloidal/Harmonic/Constant] : ")) (if (null law) (setq law "Cycloidal")) (initget 6) (setq steps (getint "\nPoints per degree <2>: ")) (if (null steps) (setq steps 2)) ;; --- the pitch curve, all the way round ------------------ ;; Outside the rise the follower sits on the base circle; ;; inside it, it climbs by the motion law. (setq pitch nil i 0 n (* 360 steps)) (while (<= i n) (setq ang (/ (* 2.0 pi i) n) f (/ (- (/ (* 180.0 ang) pi) offset) period) r (+ base roller (cond ((< f 0.0) 0.0) ((> f 1.0) lift) (t (Cam:Lift f lift law)))) pitch (cons (polar cen ang r) pitch) i (1+ i))) (setq pitch (reverse pitch)) ;; --- the cam face --------------------------------------- ;; Each face point is its pitch point pulled in by the ;; roller radius, along the normal to the pitch curve at ;; that point - NOT straight toward the centre, which is ;; only the same thing where the curve is flat. (setq face nil i 0 v (length pitch)) (while (< i v) (setq p (nth i pitch) prev (nth (rem (+ (1- i) v) v) pitch) nxt (nth (rem (1+ i) v) pitch) ;; Normal is the tangent turned a quarter turn. norm (+ (angle prev nxt) (/ pi 2.0)) face (cons (polar p norm roller) face) i (1+ i))) (setq face (reverse face)) (setq lay1 (Cam:Layer "Cam-Face" 7) lay2 (Cam:Layer "Cam-Pitch" 8)) (Cam:Poly face lay1 t) (Cam:Poly pitch lay2 t) ;; Base circle and centre, for setting out. (entmake (list '(0 . "CIRCLE") (cons 8 lay2) (cons 10 cen) (cons 40 base))) (entmake (list '(0 . "POINT") (cons 8 lay2) (cons 10 cen))) (princ (strcat "\n" law " rise of " (rtos lift 2 3) " over " (rtos period 2 1) " degrees." "\n Cut to the CAM-FACE outline." "\n CAM-PITCH is the follower centre path -" " do not cut to it." "\n Least radius on the face " (rtos base 2 3) ", greatest " (rtos (+ base lift) 2 3) "."))))) ) (Cam:Restore) (princ) ) (princ)