I assume the photo shows the back of the backplate with the threaded boss that screws onto the spindle, and that the other face has a raised section that lines up with the recess in the back of the chuck. This is the register which provides the correct alignment for the chuck.

Old school method would be to lay a sheet of paper over the back of the chuck and rub over with a charcoal stick or chalk stick or something similar. This will highlight the locations of the mounting holes and the recess for the register. Now lay the piece of paper over the backplate, line up the register recess, and centre pop through the paper for the 3 mounting holes.

A modern alternative would be to lay the chuck backside down on the photocopier and take a copy of the back face, then go to step 2 above.

The bolts are only there to hold the chuck on and stop it spinning, it's the register that provides the precise alignment, so a little inaccuracy in the position of the holes is not a major problem and they can be made oversize if needed.

Much as per Howard, but remember to size the spigot for fitting the chuck quite precisely. Some may say it doesn’t matter if the spigot is undersized – but the spigot is there for a reason! Done correctly, the two will be a very close fit, and re- positioning the chuck, when/if ever removed for cleaning, etc, will be a precise operation.

Size the spigot (last finishing cut(s)) when the backplate is cold – it will become a loose fit if cut even only warm, let alone hot. Undercut the inner corner so that the chuck can seat completely to full depth, unless the chuck already has a chamfer to endure complete seating onto the spigot. Marking the orientation, with a dot punch mark, to make sure the chuck can be replaced in the same position, is also good practice.

Radial runout in a four jaw independent does not matter, you have to compensate for that every time you put work in it. Check the runout of the chuck body face, that is more important, if that is not good, then a dead straight bar set to run perfectly near the jaws will have increased runout further away from the jaws.

Simples, been there, done that, wrote the article.

The article was published in Model Engineers Workshop so should be easy to find using online indexes. However, as I am using an IPad, I can’t read the google pdf index. Perhaps someone can post the article link in this thread?

Basically, clamp the chuck body to an angle plate or drill table by using a centre bolt and washer. Then line one of the chuck retaining holes up with the spindle. I used the plain end of a drill. Clamp the back plate to the back of the chuck and centre drill the hole and drill through.

Use a smaller pilot drill and then carefully drill through clearance for the chuck fixing screw making sure not to drill into the chuck body. Rotate the backplate and inert one of the screws into a spare hole through the backplate into the chuck. Drill the next hole and repeat for any remaining holes.

The chuck will be fired and ready to use. No marking out, no maths, just a simple drilling job.

The article was published in this forum so should be easy to find and link to.

Writer was DC1 and should be easy to find.