not much of a ball left after your 1/8th hole in a 1/4in ball. Why not start with a piece of rod, drill 1/8th turn a 1/4in radius on the rod part off.? Depends on the material you want the ball made of. tap before you turn the rod to desired radius. hope this helps.
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Use cushioned jaws (aluminum, fibre, whatever...). Chuck it in the lathe. Face off the end to about 3/32" (smaller than your hole) and use a center drill to pilot the hole. Then drill, tap, and be happy.
Don't be amazed, if this is a ball bearing, if it's brutally hard and unpleasant to drill and tap. Sharp, fresh tools all-round, cutting fluid, and never dwell in the hole.
Roughly: take 2 pieces of 1/4 in steel plate, clamp one on a drill press and clamp another on top. Drill 1/8 in. hole trough both; counter sink the top of the bottom piece & the bottom of the top piece so the ball contacts the plates at a greater than 1/8 diameter, ie grip the ball away from the hole. Now insert ball in countersink of bottom plate, clamp top piece on top and drill. Worked well.
Best anneal the ball if you intend to tap the hole. Just put it on a piece of steel acting as a muffle, heat both to red-orange by directing flame at the muffle rather than the ball. Dump the hot ball into some vermiculite and cover so it will cool very slowly. It will then be easy enough to drill and tap in the lathe, using a collet to grab it. I've done this a number of times.
A 3/4" steel ball with a hole thru it is a useful tool for cutting high branches in a tree.
Run spectra musky line thru hole and tie. Shoot ball over high branch with slingshot. Pull heavier line over branch using the musky line as puller.
Now pull up your person-powered chainsaw-in-a-can:
Working with a cooperative partner, play seesaw until branch falls. Said partner can be a woman in that it is not hard work at all, if said woman can indeed be a cooperative partner and be able to either lead or follow and not need to discuss the living shit out of every freakin' pull of either rope.
It's quite amazing how easy this is to do with the right partner, and how well it works.
Don't have any, don't want to buy a set just for this. I buy too many other tools just for other thises.
I used a string tied to a magnet, through a hole in a 90 degree bit of pvc plumbing on the end of a long enough pipe such that I can put another string tied to a nut over the branch I'm cutting; pull the first string, nut falls on the other side, hoist saw, cut.
I bought HF's version, which works pretty well on smaller branches:
larger branches it takes excessive force to make the teeth dig in and the lower part of the cut can compress and trap the saw when the branch starts to sag. I had planned but forgot to rig a pulley where the helper would stand to angle the ropes out below the branch.
The throw weight is slug of 3/4" CRS rod roughly tapered and cross- drilled on the end. The line is tied to a U of wire with its ends bent into the hole. The wire comes out with a really strong pull, in case it hangs up.
You don't need a collet to hold this, just machine a sleeve from some soft material with a thin wall and an ID the size of the ball or very slightly over, slit the sleeve with a hacksaw or whatever comes to hand and then use the sleeve to hold the ball in a 3 jaw chuck. I've done this many times when I've had to hold items where the finish could be damaged by the chuck jaws and it works very well. If concentricity is really an issue then mark the master jaw location from the sleeve machining and maintain that for the subsequent operations.
Do you have a lathe? If so -- there are *lots* of "thises" for which collets are the right solution. (This is presuming that the lathe is big enough to hold the right size collets. If the lathe will handle
5C collets, you can handle "thises" up to 1-1/8" (short workpiece) or 1" (long stock through the spindle). Smaller lathe spindles will restrict you to smaller sizes. IIRC, 3C collets go up to 1/2".
And further, a couple of collet blocks (hex and square) and an inexpensive spin index (< $50) with a set of 5C's are handy as pockets on a shirt at the mill. I use my 5C's much more at the mill than I do at the lathe. Most of my 5C's are cheap import nearly junk suitable only as holding fixtures, though I do have a few quality collets in often-used sizes, found as lucky scores at surplus: Hardinge, South Bend, etc.
For a one-off expedient solution, I agree with Billington: make a soft cylinder, slit it thrice (using your spin index, a 5C collet and slitting saw at the mill), grab the workpiece in it with the 3J and have at it. That's so easy to do I don't even keep the expedient collets thus made. Or, you could make the three slits with an abrasive wheel in a Dremel. Not as pretty, but who's looking besides you?
Believe it or not, the pocket chainsaw would be considerably faster -- and it would be much less likely to result in a visit from the guy across the lake whose cabin is being rained on by your high-angle .223 fire. He'll likely be packing a .30-06, .308 and/or a 12-gage when he and his brother or son come to return your greeting and punch a few holes in your parade as a gesture of neighborly reciprocity.
Primacord does a superb job of surgically severing small to medium limbs of various descriptions. It and caps were readily available commodities not all that many years ago, not so much now.