Arcs don't line up after array

[Crystallize123]

Hello, I am currently writing a Lisp routine to draw a spur gear with root fillets.

After using ARRAY, I realized there is this tiny imperfection between the teeth which makes it impossible to REGION.

I wonder if anyone has any solutions for this.

Here is the code for the fillet arcs. The full program is a research project so I am quite hesitant to share.

  (command "_ARC" "C" (list (- fillet_r) base_r) (list (- fillet_r) root_r) "a" 90)
  (setq fillet (entlast))
  (command "_ROTATE" fillet "" (list 0 0) (rtd half_angle_base))

  (setq cos_fillet_num (+ (expt (- base_r fillet_r) 2) (expt base_r 2) (- (* 2 (expt fillet_r 2)))))
  (setq cos_fillet_dem (* 2 (- base_r fillet_r) base_r))
  (setq fillet_angle (acos (/ cos_fillet_num cos_fillet_dem)))
  (command "_ARC" "C" (list 0 0) (list (- fillet_r) root_r) "A" (rtd (- fillet_half_angle_base fillet_angle)))
  (setq unfilleted_base (entlast))
  (command "_ROTATE" unfilleted_base "" (list 0 0) (rtd half_angle_base))

 

Apologies for not formatting the code. If you need details on the math then just ask me.

Edited 11 hours ago by SLW210
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[SLW210]

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There are several gear LISP around.

 

LISP routine for 2D internal involute gears. - AutoLISP, Visual LISP & DCL - AutoCAD Forums

 

A pretty good thread on drawing gears by hand, it will give steps needed to be accurate. 

 

How to 2D Draw A Tooth of Gear? - AutoCAD Beginners' Area - AutoCAD Forums

 

Though in your case, you might just need a LISP, etc. to Trim and or Join the imperfections, maybe FILLET>R=0.

 

In reality, you have something slightly off with the math and could just be rounding errors and/or just a very slight imperfection somewhere.

 

You might want to post a .dwg and your math.