I have a 06 road king that recently developed a bad wobble as soon as I hit 120 kph. If it starts by just going over a bump I have to slow down to 90 or it'll literally knock the bike over. In high speed corners it's exceptionally bad. I replaced the tires thinking that was it, tightened spokes, had the new tires balanced but it's back again. What can I start checking to narrow down the problem?

 

Steering head and swing arm are two places I'd start with. To properly check the swing arm you will need to slacken the drive belt.

 

Check the front motor mount. Its VERY common for 02-06 bikes for them to shear in half like a sliced bagel. New HD replacements are supposed to be made of better material

 

Both previous suggestions are good & worth checking. I always had a high speed handlebar shake between 85 & 90 mph on my 05 RK since it was new. I installed a "True-Track" swing arm anchor in 2005 & my bike is stable up to 120 mph.
About five years ago it developed a low speed shake & I found the steering head nut had loosened up. Tightened to specks shake gone.

 

I had an 07 Road King that developed a wobble and I discovered that my spokes were so loose that the outer rim would move independent of the inner rim. Just something to check.

 

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Been there done that!

Thats generally caused by loose steering head bearings (requiring adj) and or worn out steering head bearings requiring replacement along with loose & or sloppy rear swing arm bearings & or bushings that requiring replacement because as far as i am aware there is no adj to tighten rear swing arm bearings / bushings.

Worn tires along with bad motor mounts ,weak & or mushy front & rear suspension can also add to this problem in which case at very least i rec checking motor mounts & going to SE hvy wt oil in forks & change oil in stock rear airshocks to 10wt suspension /shock fluid (not fork oil !) that will tighten things up a bit too.

Last resort if doing the above doesn't fix it would be to install one of the kits that attach from the frame to trans or the motor that firms things up too.

Scott

 

Swing arm isolaters not mentioned yet , they are due at that age. True track is on my wish list. I've Already done all the other stuff that's been mentioned.

 

Some of my rear spokes are loose. I'm thinking that has to be it, I can grab the rim when lifted off the ground and shake it a bit and it's the rear tire that has a big wobble in it when spinning.

 

Now would be a good time to get that spoke wheel off of your bike and replace it with a good cast wheel.

 

Air pressure