A Shop-Made Compact Rotary Broach

I think the dished cutter face is just fine, if not advantageous. The degree of "rock" needed at the cutter face decreases with the number of cutter points, so a square broach needs more freedom than a hex. What is clear to me is that the pivot at the ball needs to allow an angular sweep equal to or greater than the contribution of the shank offset offset. Since it involves faces and offsets, I'd need to draw a sketch or model it to find the exact clearances needed, but the ball pivot needs to cancel the offset and set the point to cut, so the ball needs a little more freedom. The larger the diameter the cutting tool, the more freedom needed- either by increasing the pivot range, or by altering the length of the tool.
 
the ball needs a little more freedom.
Another thing I might have to look at is the clearance between the shank body and broach holder where the ball is. I just might have gone a bit too deep and therefore narrowed the gap between the two bodys and therefore restrict the rocking motion........damn I sound like some kind of professor with all my "Therefores".
 
Another thing I might have to look at is the clearance between the shank body and broach holder where the ball is. I just might have gone a bit too deep and therefore narrowed the gap between the two bodys and therefore restrict the rocking motion........damn I sound like some kind of professor with all my "Therefores".
so the rocking motion is only because it's at an angle and offset at the point it attaches to the tailstock or quill. The holder does not rock, it turns.
and it should not have play.

I think you are thinking that it rocks when it is purely what part is closest and pushing down on the metal. as the holder or piece turns, another area is closer. Many of these rotary broaches have 2 or 3 bearings a thrust bearing and 2 bearings inside the housing to hold the holder in place so they don't rock, they just turn.
 
What makes a broach a broach is it cuts on the infeed axis, so I have been using the term "rocking" to refer to the motion of the tool face as it rotates into and out of the angle created by the shank offset. It's a rotary tool but the cutting is axial to the rotation, especially visible when flattened and viewed from the side. Its not a wallowing action or metal forming, it's a true cut, and to do that, the tool needs at least enough angular displacement at the ball joint to create the axial cutting motion. The rotation of the tool is free and bound by the bore at the start of the cut, it is in and out movement from the angles affecting the cutting edges that does the work.
 
When I use the term "rock" I mean that the broach cutting tip stays on center while the shaft of the broach wobbles in a circle that looks much like a wobbling spinning top.
Here is exactly the motion I am trying to describe:
You can see the need for clearance between the yellow broach and the blue part in the video. The broach does not turn with respect to the work. If you are doing this on the lathe you would put the work in the chuck jaws and rotate the work but the broach would rotate at the same speed as the work. I have used my broach both ways. I think it is easier to conceptualize on the mill.
This video describes the tool on a lathe but the motion is the same with respect to the workpiece:
 
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I finaly got around to this again,so I took a chance and doubled the off center measurements and then finaly I got a square hole. Tried it first with aluminium in the lathe and then on EN8 on the mill. The video is just to show the increased rocking motion.
View attachment 20230808_160354.mp4
Is there a prime rpm to do this? I found that quite a bit of force was needed.
20230808_162402.jpg20230808_160609.jpg
 
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