: "dakeb" wrote : : > "John" wrote : > Thanks for your help Walther. : >
: > It's not a gearbox but similar. It's a bottle cap. Do you have an : > idea what is the proper formula to use for a gearbox? May be I can : > use it to model my cap. : Machinery's Handbook has a couple pages of formulas used in gear design. The approach is fundementally different. Since two gears are being mated, once the diametral pitch (size) of the teeth is decided and the ratio between the gears is determined, the formulas tell the diameter of the gear. Gears don't generally, as in your problem, start with a given diameter then see how many evenly spaced 'teeth' can be placed around it at some spacing.
: This is not for a gear, it's for a straight knurled bottle cap: : : You need a relation something like:- : : p1=floor((d2*pi)/d3) : : where : : p1 = number of instances : d2 = pitch diameter : d3 = width of instance : substitute the actual d and p numbers of your feature from the model into : the formula. : : The floor function rounds P1 down to the nearest lower integer (can't have : real number of instances). : : Then d4=360/p1 will give you the pattern increment angle.
This looks like a good way to get even spacing of an approximate width of triangle. It does have the limitation though of being based on an arc segment whereas what you're trying to fit is the chord of a fixed width. Or at least that was the premise from the original question. Walther's answer had a similar premise: pattern by segmenting a curve. Somehow, when this was first presented, I visualized the curve as a straight line. Offsetting points along it at 1mm intervals turned into saw teeth and made perfect sense ~ until I mentally tried wrapping the curve around a circle and all those teeth got smaller. And the fewer the 'teeth', the more dramatic the effect.
So, while you may be able, with this method, to divide the circumference into pretty even arc segments, the triangle base (chord length) will be less. In the simplest case, where the ratio is the highest, draw a line through the center of a circle: the chord is the diameter, the segment length is half the circumference (pi*D/2) or 1.57 times the chord length.
I tried this problem using the base of the triangle as the chord, bisecting the chord with a line drawn from the center to perpendicular to the chord, drawing a line from the center of the circle to one end of the chord and setting up a classical trig problem (which could likely be worked into a part relation) to find out the center angle, then dividing that into 360 to get the number of pattern instances. The problem with all these scenarios for patterning is they won't come out evenly with both a fixed diameter and a given chord length. The advantage of this way is that you ignore the circumference. It comes closest to the desired length of the base of the triangle.