Everyone likes to be remembered and so, I assume, the lucky few who get their names associated with an algorithm (eg. Pierre Bézier) or object (eg. Woodruff keyway) must get a warm glow inside and I wonder how hard is it to get a shot at eponymous immortality in CAD/CAM? Do you have to have an enormous brain or simply be in the right place at the right time?
I think it is a bit of both, and last week: I came across a contemporary contender for such geometric namesake fame: the “Sells Hole”. A “Sells hole” is a tear drop shaped hole that in twenty years time could replace large number of traditional “round” holes found in mechanical components. A bold statement, but not crazy when you know the back ground ………..
Some of my students are building an open source, home made, rapid prototyping/manufacturing system called a RepRap machine (http://reprap.org). They have downloaded the design (models, electrical circuits and software) from a group whose aim is to create a machine that can (amongst other things) fabricate duplicates of it own components (excluding electronics, and metal fastening etc). In the picture below you can see one of RepRap machine’s components.
The “Sells holes” (labelled A) are design to be fabricated by a layered manufacturing system without the need for support (e.g. an FDM machine will build a 45 degree overhang with out the need for scaffolding that has to be removed later ). Create by a man called Ed Sells - it's the profile of a horizontal 'cylinder' that doesn't need support and which, in the vast majority of cases, works just as well as a circular cylinder for things like bolt holes.
Currently most rapid prototyping systems produce models of parts that will ultimately be manufactured by other processes such as CNC machining or casting. Because the Reprap is designed to be a functional machine produced by RP it can incorporate features that are easy for the manufacturing process to form (a sort of DFLM: Design for Layered Manufacture). Its a safe bet that eventually, nearly everything will be produced by powder based fabrication (e.g. SLS, DMD etc) and then, perhaps the world will be full of “Sells Holes”.
I can’t end without mentioning my favourite Eponymous shape: The Hannoid.
Sometime around 1994 I was watching the 3 year old daughter (called Hannah) of a friend play with her plastic building blocks when I realised (to my horror) that she had created a physical shape with a hole impossible to identify with automated feature recognition systems.
Most feature recognition systems use inner loops and face/edge curvature to locate depressions such as holes. What is distressing about the Hannoid is that its local geometry gives no hint that there is a through hole.
Does Euler-Poincaré work for Hannoids? A few lines of scheme
(define hannoid (solid:block (position -45 -45 -20) (position 45 45 20)))
(define slot1 (solid:block (position -15 -45 -20) (position 15 45 0)))
(define slot2 (solid:block (position -45 -15 20) (position 45 15 0)))
(solid:subtract hannoid slot1)
(solid:subtract hannoid slot2)
Creates a model which ACIS reports as having:
1 lumps, 1 shells (S), 0 wire, 16 faces (F), 16 loops (L), 88 coedges, 44 edges (E), 28 vertices (V)
Euler-Poincaré formula for objects with holes: V - E + F - (L - F) - 2(S - G) = 0
(where G = the number of through holes = 1). This relationship holds for the Hannoid: 28 -44 + 16 – 0 – 2(1-1) = 0 ……so its a “proper” manifold body with a “real” hole.
Almost 15 years late the Hannoid still gets some hits in Google as an example of difficult problem for applications like automated sketch understanding and feature recognition. Eponymous immortality from plastic building block…there is hope for everyone!
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