James Curry may know something about Physics, but he has a lot to learn about Marketing.

The technique you have laid out here has some nice applications in constructing polynomials that are constrained to have certain properties. For instance, you could use this technique to construct strictly positive polynomial by making sure that the polynomial has no real roots (the all appear in conjugate pairs). This polynomial can be integrated to make a polynomial that is guaranteed to be monotonic. And so on.

Very nice post. Thanks!

Wonder if this could be combined with the maths of Strange Attractors?
I remember seeing some fantastic images that came out of those.

Cheers
Lee

I have very little experience with 3D models, Computational Geometry, and the like… so I need to study a lot before I can even try to take a shot at this problem. If you ever get to attack the problem and happen to make some progress, please let me know. I would love to hear about it.

well, some modelling package creates the model using boolean ops which can be translated to machining sequences. but if you’re asking about b-rep to cnc seqs. that would be interesting problem to face.

IMHO, the initial solution to this problem would be just as you wrote. it would combine the knowledge of computational geometry tools driven by rule-based expert system. since the machining operation is subtractive that would be analogous to combinatorial search problem.

1 start with initial volume of material
2 use set difference morphology to achieve which material to be removed (R)
3 reduce the detail (holes, teeth) for later processing (using morphological operators)
4. segment the volume mesh.
5. approximate each segmented mesh with geometries associated with each machining tool (knapsack-like problem)

it seems that it is enough to arrange the rule heuristically or trying combinaton of sequences using genetic programming since it’s solution is so alike with CSG modeling (tree).

Very impressive, indeed!

I believe it would be hard to teach a computer how to switch from one machining operation to another in an optimal way. We, humans, can do it easily. But endowing a machine with imagination is very hard!

It looks to me like most of this part would be cast. It certainly looks like the spaces between the 6 holes was cast (because of the rounded corners).

I entirely agree. Note, however, that I needed a 3D model to serve as an example of a machining sequence, and I liked the shape of this mechanical part in particular ;-) After all, I suppose that the average reader of this blog lacks experience in the machine shop, and examples convey ideas in a more efficient manner.

Indeed, it would make a lot more sense to fabricate the part via casting. But one would need a mold, and to obtain a mold, one would need a prototype, right? Hence, wouldn’t it make sense to machine a block of metal to obtain the desired mechanical part? Once one had a prototype, one could make a mold, and fabricate many other parts via casting.

What would be the point of milling away the material there? It wouldn’t affect the functionality of the part (except to reduce weight slightly). You would save a little money in the cost of materials (with the metal recovered from milling between the holes), but adding another pass with another tool would probably offset that cost savings.

Once again, that’s a very good point. It would only make sense to use milling if one wanted a prototype. For mass production, it would be really, really dumb to use milling.

It looks like the ‘precision’ parts are the toothed hole, the 6 bolt holes, and the flat bottom mating surface.

Agreed. I guess the best solution would be to use casting to obtain a rough model of the desired object, and then machine the parts that you mentioned. I have no idea what is the use of this mechanical part, so it’s hard to guess what should be and what should not be machined. I am pretty sure the toothed hole needs to be machined, though.

It looks to me like most of this part would be cast. It certainly looks like the spaces between the 6 holes was cast (because of the rounded corners).

What would be the point of milling away the material there? It wouldn’t affect the functionality of the part (except to reduce weight slightly). You would save a little money in the cost of materials (with the metal recovered from milling between the holes), but adding another pass with another tool would probably offset that cost savings.

I don’t know what a “carter” is or how it’s used, but it looks like the ‘precision’ parts are the toothed hole, the 6 bolt holes, and the flat bottom mating surface.

admittedly vague

… nevertheless exciting and interesting. One of the problems that I really wanna try my hand at. Will do as soon as I get some free time…

Have you seen the futurama episode where in a horse race, one of the racers won by quantum scale. and the professor said “No fair, you changed the outcome by measuring it!!”

if you don’t get it watch the last 15 sec on this video.