clutch is dragging on 2016 rocket3 roadster

Believe I would try adjusting clutch a final time before taking it apart. Try taking a little of free travel away and see if that doesn't allow clutch to dis-engage. Barnett is a great way to go if you have to replace clutch. Make sure you have new style lifter shaft and bearing.
 
It's not a terribly difficult job, in case you've never done it. The hardest part is removing and draining the radiator.

But, it is a bit time consuming. If it were me, and it does sound like the clutch is worn, I'd order a Barnett Clutch and go ahead and put it in there while you're already in there.

Btw, @warp9.9 gave me the tip on how to avoid also draining the oil- just tip the bike back a bit with jack stands to minimize oil loss- worked great!

Here are the parts for the Roadster you'll need....

Coolant

O Ring T3600910 $1.28
2011 Triumph Rocket III CLASSIC & ROADSTER O ring. System, cooling - T3600910 | HERMYS TRIUMPH eSTORE, Port Clinton PA

Water Pump gasket T3600169 $4.01

Clutch Cover Gasket T1260107 $12
2011 Triumph Rocket III CLASSIC & ROADSTER Gasket, Clutch Cover. Engine, Covers - T1260107 | HERMYS TRIUMPH eSTORE, Port Clinton PA

Barnett Clutch $238
Part# 303-75-20003
Amazon.com: Barnett - 303-75-20003 - Complete Clutch Kit : Automotive
amazon says 303 75 20003 does not fit 2016 roadster
 
amazon says 303 75 20003 does not fit 2016 roadster
I double checked and you're right, according to Amazon. I didn't think there was a change between 2011 and 2016 for the Roadster. It does fit mine. However, I looked it up on the Barnett website and it shows as the correct clutch for your bike. You can double check to confirm, but here it is....
 
I double checked and you're right, according to Amazon. I didn't think there was a change between 2011 and 2016 for the Roadster. It does fit mine. However, I looked it up on the Barnett website and it shows as the correct clutch for your bike. You can double check to confirm, but here it is....
ok thanks
 
Wow, that is some serious oil overkill, though I put the same oil in my touring when my clutch was dragging hoping that it would correct the issue, no luck, no amount of clutch adjustment would fix it, I went in and the steels were warped and burnt, the fibers weren't much better, and the bearing was spinning in the pressure plate, quite the mess, ended up replacing everything, except the clutch basket, and the little arm the cable connects to actuate the clutch, everything else including the clutch lever and cable was changed, should have done the detent spring at the same time, had to go in a 2nd time 5 months later to change that.
I picked up the clutch kit for a 2013 (pretty sure this was the year) Suzuki Hyabusa clutch pack, comes with steels, fibers, springs, and a gasket that I gave away to someone, the whole kit was $140 CAD, and slipped right in, my clutch is nice a smooth, shifts to neutral with no effort, it is great. The clutch was never quite right when I first purchased the bike, so I think the previous owner started to fry it out, and then I finished the job doing a few days of constant slow speed maneuvers during an advanced riding course. in Canada it was the OPP golden helmets course, in the U.S. I think they call it motorcycle rodeo. I haven't known anyone to blow a Busa clutch pack, but I know a few that have destroyed the clutch basket on their Busa
 
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