Here's the simplest test:
Get an EMPTY case, preferably one that's been de-primed, so no ridges or cratering of the primer might give a false reading.
Clean the gun thoroughly, including the chamber and the front face of the frame around the firing pin hole.
Chamber the case and move it into position aligned with the barrel.
Push the cylinder to the REAR, and hold it there FIRMLY.
Insert an ordinary feeler gage into the frame between the case and the frame.
Check different feeler gages until you determine the gap.
Then, push the cylinder FORWARD and hold it there firmly.
Again gage the gap between the case and the frame.
The difference is the amount of end shake, or back and forth movement of the cylinder.
Assuming you have a S&W, the spec is .001 to .006 MAX.
There are two "fixes" for the S&W:
First is the factory approved method in which the shaft of the yoke is stretched by peening.
A hardened insert is inserted into the shaft to support it and the end of the shaft is gently peened with a small hammer to actually stretch the shaft.
A second stretch method uses a modified tubing cutter.
The cutting wheel from a copper tubing cutter is rounded off until the cutting edge of the wheel is a round shape, non-cutting shape.
Again, a hardened steel insert is inserted into the shaft to prevent collapsing it.
The cutter is applied to the middle of the larger diameter rear area of the yoke's shaft and the cutter is rotated and tightened until a shallow groove is pressed into the shaft.
This stretches the shaft.
In either method, a special guided trimmer cutter is used to square-up the end of the shaft, and trim it to the proper length.
The second method of correcting end shake is to use hardened stainless steel washers.
The shaft is again trimmed with the guided cutter tool to square-up the end of the shaft and to insure it's perfectly level with no high spots.
After estimating how thick a washer is needed, the appropriate washer is oiled with a good lube and dropped into the cylinder's central hole.
This washer corrects the excess end shake.
In conjunction with thicker or thinner washers, the shaft is trimmed with the piloted cutter tool to give a final fit of .001 end shake.
The washer method is good, AS LONG as no one disassembles the cylinder and inadvertently looses it, AND as long as it is properly lubed.
Note that these methods DO NOT work on Colt revolvers.
