zorn@trwrba.UUCP (Marc E. Zorn) (04/05/85)
When I read the article about the Reuleaux (sp?) drill bit, to me,
intrisically, it didn't look Kosher. I couldn't see how this semi-rounded bit
could make a square hole. So I asked a friend here at TRW, and we talked about
it for a while (he did the work 'cause I wasn't interested enough to do the
Trig :-) ). Here were our thoughts:
1) What does this drill bit look like?
Having never seen one, I can only go by the model which has been
described.
2) With 3 corners meeting at 120 degree angles, how can it make a 90
degree corner?
It can't. The square hole must have rounded corners.
3) Are the corners really really round, or just kind of round? (How
round is this Square Hole?)
Whip out the graph paper, or envelope, or whatever, and draw a 2-D coordinate
system. This will represent one corner of a perfect square hole. Now draw
this Reuleaux thing, with a breadth of one, such that two of the sides are
touching the two axises, and one corner is very close to the origin (i.e., the
Reuleaux will be rotated 15 degrees). A draftsman could measure the result,
but to people of lesser skills (myself included), should use trig to findout
how close the bit can cut the ideal square. We need to draw a dotted line
parallel to each axis which intersect the two far corners. We've just made a
90-45-45 triangle with a hypotenous of 1. Now, we know the far corners are 1
unit away from the far axis, so the vertex of the 90 angle is at coordinates (
1 - 1/sqrt(2), 1 - 1/sqrt(2) ) or roughly (.0345, .0345) (fairly close to the
ideal corner). The blade will deviate from the ideal square hole when the
cutting edge is pushed away from the side by the rounded side of the bit. By
drawing a 30-60-90 triangle, and rotating the bit some, we can see that the
blade will leave the ideal square only .134 away from the corner. So the
"Square Hole which has sides of length 1" is cut with straight sides of length
.832 and miss the exact corner by a distance of .0488.
4) Does it "Really" cut a "square" hole, or is this something that looks
good on paper, but can't be built, or done?
Once again, I have never seen one, so I haven't used one. But, I can see that
if the user had a stiff and steady hand with a drill, the straight sides will
start to deform until it becomes a circle. The only way to avoid this would
be to introduce some mechanism which would change the location of the rotating
axis automatically. By this time, a machinest might as well have used the
alternate methods described in previous letters.
Tye Cowan and...
--
"Member FDIC" {decvax,ihnp4,ucbvax}!trwrb!trwrba!zorn
"Your mileage may vary." Marc Zorn
"Void where prohibited by law." TRW E&DS
"The public was never in danger at any time." Redondo Beach, CAee163acp@sdcc13.UUCP (DARIN JOHNSON) (04/08/85)
> 1) What does this drill bit look like? > It look like an equilateral triangle with rounded sides. To be more exact, these sides have their radii (sp?) at the oppsite vertex. > > 3) Are the corners really really round, or just kind of round? (How > round is this Square Hole?) > > 4) Does it "Really" cut a "square" hole, or is this something that looks > good on paper, but can't be built, or done? > Yes it is square and it has been built. The drill bit allows the triangle to float freely. To actually drill the hole, one has to put a square template so that the bit stays where it is supposed to go. Without this, the drill will spin around off center and drill a funny hole if you can manage to hang on to the thing. It does exist since I have seen a picture of it and the hole it did somewhere (Scientific American?). Darin Johnson