The drawbar on my Torus has a square head. Rather than making a completely new drawbar (thanks LeeWay for the detailed description) or using 8-point sockets, I decided to try a third way and machine a hex head out of the square head. The square head of my drawbar measured 0.650"
I decided to use a 5C six-sided collet block and do the machining on a manual Bridgeport mill in my community college machining class. The instructor said the best way to do this was to have one of the corners of the square head pointing at 12 O'Clock and then machine one of the hex flats at that position.
I had two problems staring me in the face while standing at the Bridgeport:
1. Was the orientation that the instructor suggested correct? If yes, why?
2. Assuming that the suggested orientation was correct, what was the maximum sized hex head that could be machined out of the 0.650" square head?
Doing some quick searches on my smart phone (not a real smart use of scarce machining time) I found the two websites listed below and determined that the instructors suggested orientation was spot on.
Square in a Hexagon etc
geometry - Smallest square that can be fitted outside the regular hexagon - Mathematics Stack Exchange
I still had no idea of what the largest size hex head could be machined out of the square head. Both of the websites above, and others that I found, always gave the size of the hex vertex when given the square side dimension. I, of course, wanted the hex head flat-to-flat dimension given the square side dimension. Surprisingly, I could not find such a relationship in any of my Internet searches.
Using the two website above, and a bunch of work, I came up with the following formula.
F = S
√3 (√6 - √2) ; where S is the square side dimension and F is the maximum hex flat-to-flat dimension
2
Or F = .8965754722 S
So, plugging in my square head drawbar size of 0.650" gives a maximum hex head flat-to-flat dimension of .5828". I actually went a little larger than the "maximum" size calculated by the formula and made a 15 mm (.5906") hex head. I decided that I didn't care if a couple of the hex corners were rounded a little bit by going over the "maximum".
Almost done machining the hex head on the Bridgeport using the 5C collet block
Set up at home on my G0602 10x22 lathe and ready to face the end and cut a chamfer
Finished hex head drawbar. I didn't take a lot of material off the end of the drawbar, but you can see some voids that were uncovered during the lathe facing operation. I finished the hex head by deburring with an 3M EXL grinding wheel and then "polishing" with a 3M scotchbrite wheel.
Titaniumboy