This is a shamless copy of some I saw on one forum or another, or maybe more than one. I'm not sure who made the first one or I'd give them credit for it right here. The bottom line, it was free because I made it out of metal I had in my "metal archive", and it works essentially perfectly for chambering barrels.
This piece in the tail stock pushes on face of the collar that holds the reamer. That face of the collar that holds the reamer was machined in the same setup where the center hole was bored so the plane of the collar face is dead nuts orthogonal to the bore axis, which means it is also as perfectly orthogonal to the axis of the reamer as I can practically make it. I made a collar instead of a tap holder type because I couldn't see any way to guarantee both faces of the tap holder were in exactly the same plane, which as is discussed below, is key to how a pusher like this functions.
The pusher itself is a piece of mystery metal, from a drop rack in a metal yard far away, machined to have a MT #3 taper on the back end. This was then put in the headstock of my 9" SB, parted, faced and drilled out 29/64". The important point is that the plane of the pushing face is dead nuts orthogonal to the axis of the pusher. As will become evident, this is key to why it works well.
While I've seen the pictures, I've never seen an explanation of why this design works so well, so I thought about it a while before I made this one. I wanted to machine it controlling as exactly as I could what ever the critical parameters were that made it work. I came up with the following hypothesis to explain why I think it works as well as it does.
It, and the Manson my friend the "real" gunsmith with the borescope has, work on pretty much the same principle, and tend to create forces that react against the pilot to drive the back end of the reamer in the direction to correct for parallel axis misalignment between the spindle centerline and the reamer centerline.
My tail stock ram CL is right in line with the lathe spindle front to back as close as I can measure it. It is about 0.002" high with the tail stock clamp torqued down as tight as I can reasonably get it using the handle it came with (I plan to take it apart and weld a square drive socket on it so I can use a torque wrench - but it won't get any closer even with a cheater bar, I tried, but didn't over do it). The important part is that the tail stock spindle axis is "parallel" to the spindle axis, but offset ~0.002" above it. This parallel offset is probably found to one degree or another on most of the lathes used for chambering. That being the case, if the reamer is pushed square to the axis it will self center parallel with the lathe axis.
Why will it self center?
If you had a pencil lying on the desk with a cross stick glued to it, you could push it with two fingers and it would stay pointed in the direction you are pushing. If you push on the eraser with one finger, when the pencil gets a little off line, it will tend to go further off line.
The first case applies to this and the Manson pushers. The pushed surface on the collar is orthogonal to the reamer centerline, and the push surface of the annular ring that does the pushing is orthogonal to the tail stock centerline. If the reamer tries to tilt out of parallel with the centerlines, the ring acts on the side opposite to the direction of tilt and tries to push it back to parallel. This moves the back of the reamer to stay in line with the pilot so it remains parallel to the spindle centerline.
Even though a reamer cuts on the side, it seems to want to be inherently self centering on the bore left to it's own devices. My theory for thi is that for small deviations from parallel with the bore, the reamer presents a greater frontal area off set on the side in which it is out of alignment. This greater frontal area will tend to react against the pilot to push the back end of the reamer back into into alignment with the axis of rotation. This correcting force from the front of the reamer is apparently stronger than the destabilizing force from the offset push at the back, (for small deviations - it isn't for large ones), so within limitations of small deviations it overcomes the inherent instability of the pushing scheme. And that is why I think the Bald Eagle reamer holder works (and I proved to myself that a pusher based on that principle does work just fine) inspite of the inherent instability of it's design.
With the correcting force from the front of the reamer, and the inherent correcting force on the back of the reamer from the annular (or planer in the case of the Manson unit) pusher, the reamer should follow right along a path parallel to the lathe axis if the bore is centered on the lathe axis. This emphasizes why it is so extremely important to have very precise bore alignment with the spindle axis in the area where the chamberi is being cut. This may seem obvious but it is important because it means the floating holder will "not" compensate for the bore being misaligned with the axis, on only compensates for the reamer being misaligned with the bore.
Given the principles involved I could have made the annular pushing surface larger in diameter (keeping the center hole the same size - 29/64" for a 7/16" reamer shank) but it seemed to me the increased surface area might somehow add friction to the system, make it sticky, and impede it's operation, so I didn't do that. As it is, it works just fine.
I've seen no indication that I need to add a second handle on the other side to maybe get a more symmetrical torque reaction, but I could do that if I had to. I didn't use shoulder bolts in the collar and slots in the pusher for torque reaction like the Manson holder has because I think that if the bolts and slots were not precisely aligned on a diameter that would tend to push the reamer off center. I wasn't sure how to do that as precisely as I needed to so I stuck with the handle.
Finally, when I hold the handle my thumb is right over the set screw that is tightened on the reamer, my fingers under the handle to resist torque reastion. This "grip" effectively eliminates side force because it is a torque couple. You can demonstrate this to your self if you use a long extension on a socket wrench. If you just pull on the handle the thing will move sideways. if you put your thumb on the rachet head and counteract the finger pull on the handle you can apply torque to the wrench with no side force. That's how I hold this reamer holder. It works just fine and the torque couple is why.
In know, I know, I'm putting some to sleep, and others think I'm regrinding flour into molecule sized dust particles (the smallest particles that are still flour), but I like to know why things work. I don't seem to be able to resist trying to figure things out. My engineering gene made me do it.
That's my story and I'm sticking to it.
Let me add, I've no indispensible ego attached to any of this, I'm just looking for the truth of it, so if you have a different view of the physics at work, please share it.
Fitch