Here's how
The thumping is likely the shaft hitting the shaft log. A cutlass would make that type of noise is if it was severely worn with the shaft spinning dead center in the cutlass but off center it may not. Depending upon zinc location they can wear away unevenly and induce shaft whip other wise it is usually caused by misalignment. The other causes could be a bent shaft, unbalanced prop or a bad motor mount allowing the engine to hop slightly.
Here's the method I use when installing an engine or after having replaced mounts.
1) While on the hard remove or slide the stuffing box forward off the shaft log so you can see the shaft coming through the log.
2) With the coupling attached to the transmission and the bolts only finger tight adjust the engine until you get the shaft centered top to bottom and left to right. Do left to right first, as this is the trickiest, then the up/down. The suggestion Ross made can be used to check centering once you have it visually close. I personally find it much easier to align the shaft to the cutlass & shaft log with it attached to the engine rather than supporting the shaft somehow then aligning the engine to it.
3) While adjusting the up/down & side to side be aware of your gaps between coupling and tranny and use feeler gauges to get it as close as you can during the shaft centering. Heck, it's very easy to center the shaft but then you if you don't pay attention while doing so you could wind up with a 1/8" gap between couplings. Adjusting both at the same time, within reason, you don't need to be exact here, will make finally alignment that much easier. Doing this will ensure that when you do the final alignment you won't knock the centering off much.
Remember this entire procedure is predicated on the premise that the factory built your boat so the shaft log center lines up with the cutlass bearing center. If you are skeptical of this you'll need to confirm these two line up BEFORE doing anything. The shaft log may NOT line up with the cutlass and in this case you want to align the shaft to the cutlass so it rotates perfectly centered in the cutlass and preferably with a new cutlass bearing or only slightly worn. On many boats this means the shaft does not or can not pass through the center of the shaft log without major surgery. This can lead to other issues with stuffing boxes etc.. The engine should be aligned to the cutlass bearing firstly then the shaft log secondly but both are important as you don't want an off center stuffing box wearing the shaft either. On our boat the shaft log and cutlass bearing line up almost perfectly but this is not all that common.
4) With the shaft centered in the cutlass & shaft log begin the fine tuning. I find it best to manually seat the engine after each motor mount adjustment by grabbing the valve cover and wiggling it side to side and back and forth as much as possible. Then re-check with feeler gauges. It will take a while but eventually you will get the coupling to mate to the tranny at .003" or less for a 3- 4" coupling.
5) Re-install the packing box to the stern tube being sure it is in a relaxed position against the shaft and not pressing in one direction or the other. You want it to rest centered over the shaft so the packing nut is not going to rest on the spinning shaft and score it.
6) Once back in the water, with a tuned rig, sail and run the boat for a few hours then re-check the alignment. If it is way off adjust it as close as you can to .004"-.003". With most boats you will find the alignment is off slightly if it is less than .004" perhaps even .005" leave it and continue to use the boat for a few weeks. The boat can take a set and with some this can take a few weeks so it is good to re-check every once in a while. After a few weeks make a final alignment adjustment to .003" or better. As others have said engines move slightly under load, Yamnar more so than others, so starting with a good alignment is a big plus. I have virtually zero vibration on our boat, and also don't have a flexible coupling, but I got my alignment to .002".
When checking alignment do not remove the coupling bolts all the way just loosen them slightly then as you spin the shaft by hand apply a slight hand pressure to the coupling, towards the tranny, if you have a PSS it will do this for you, and check with a .003" feeler gauge in a 360 degree manner. If you're off at say 6:00 to 3:00 on every rotation adjust for that. If your 6:00 to 3:00 alignment moves, say 180 degrees, there is a high likely hood your shaft is bent..
Note: With a new engine or with new mounts you'll want to re-check the cutlass & tube centering after the first few hundred hours as the mounts may settle some. This may or may not show up in a drastic coupling measurement if the mounts settle evenly. Yanmar mounts especially, and the Universal & Westerbeke mounts a little less so, are all prone to this. Repeat the above procedure then you should be good for a long while.
Not Centered Yet: (the white tape is how deep to re-install my PSS bellows)
P.S. I'm sure I forgot something and will re-read after my meeting..