First thing I did was to pry off the two plastic covers over the swingarm nuts (pink arrow, photo left).  I wanted to make sure that the 27mm socket I owned would fit in between the nut and the frame before I started the job, otherwise it would mean a trip over to Sears to see if I could find the correct socket.  

Fortunately, the 1/2" drive 27mm socket I have worked fine without any modifications on both the '86 and '84, although it just barely fit the '84.  Apparently, some BMW's were not machined concentrically in this area, and the 27mm socket may have to be machined or ground to fit.  Bob Fleischer goes into this in detail in his article listed above.

By the way, a 1-1/16" socket will also work, because 27mm is almost exactly 1.062. 

Some sockets may have too large a radius at their open edge, which may prevent enough of the socket's "teeth" from grabbing the very thin swingarm nut.  You may have to grind or machine off the end of your socket to fit.  Craftsman sockets have a (bad) reputation for having too large a radius, which helps them slip easier over a nut, but can also make them slip off just as easy in tight spots such as this.  Although most of my tools are Craftsman, and I've never really found this to be a problem.

I thought perhaps I could get away without taking off the fuel tank, but that dream quickly ended.  It's much easier to remove the airbox and to gain access to the area you'll be focused on if you remove the tank. This goes for both model years. 

Fortunately, removing the tank on most Airheads is pretty simple; on the '86, pull off the C-shaped circlips underneath at the back of the tank, which are accessible after lifting or removing the seat.  The '84 has a couple of thumbscrews that hold the tank on to two threaded bosses.

Disconnect the fuel lines (making sure the petcocks are off!) and the fuel overflow line from under the tank, and all you have to do is lift up the tank, one hand on the back and one on the front.  Be careful you don't scratch the tank on either the handlebar assembly or the open seat (on the '84).  If the tank hasn't been off in a while, it may stick to the rubber bumpers up under the front of the tank and all of a sudden pop off and the momentum may bang the top of the tank up under the handlebars.

Next, remove the airbox assembly (pink/white arrow) and remove the air filter.

By the way, the yellow arrow points to the spark coil on the '86.  This is the original coil, and I didn't notice at this time that the coil had the typical crack right down the center.  

The bike became very hard to start and later on I replaced it with the newer BMW design coil and the bike starts fine now.

On the '86, remove the wing nut from the rear brake adjustment rod and slide the rod out from the adjuster arm.  This will allow you to slide the swingarm assembly back.  

This step is necessary on this bike, a 1986 R65, which has the single-sided "mono-shock" swingarm.  I didn't have to mess with this on my '84 RS, because it has a rear disk brake.

Remove the 27mm nuts from the swingarm pivot, then remove the swingarm pivot pins with a 6mm Allen wrench. 

Lift the swingarm slightly to take the pressure off the pivot pins and they should slide right out towards the back of the bike.  

Be careful at this point, as the swingarm is loose.

Photo of the swingarm pivot pin and 27mm nut after removal.

There are four bolts that hold the transmission and engine case together, two on each side, upper and lower.  The upper bolts are 13mm hex bolts and are located inside the airbox.  The lower bolts are 6mm Allen; the left side bolts to a threaded hole in the engine case and the right side goes through the engine case and is held by a hex nut and washer.

The yellow arrow in this photo points to the 13mm bolt on the right top, in the airbox (right side in this photo, yellow arrow) the lower 6mm Allen is shown in the next photo.

There's also a 13mm hex bolt in the center of airbox that must be removed; this bolt holds airbox on to the top of transmission. You'll have to disconnect some of the tubing (turquoise and pink arrows) to get to the bolts.  Note that this bike is shown with the "pulse-air" injection system and airbox valve removed; see the wBW article on how to remove the pulse-air injection system for maintenance.  By the way, the Wiha long ball-end hex wrenches (wBW review) and the 13mm Gearwrench (wBW review) box end wrench really helped access the nuts and bolts for the spline lube.  I have no connection with Wiha other than as a satisfied customer, but you should check out their tools.

The left side of the airbox also has a 13mm bolt and a 6mm Allen as its lower engine bolt.

Remove this 6mm Allen bolt; this is the bottom right lower side.  Note the cutaway on the cooling fin.  

This bolt goes through the engine case and has a 13mm nut on the opposite end of the bolt.

This is the left side, lower 6mm Allen bolt.  The hole is threaded, so this bolt connects directly to the engine case. 

Some Airhead models (like my '84 RS) may require that you remove the bolt holding the foot rest on this side so that the shift linkage doesn't prevent you from being able to slide the transmission back. 

This photo shows the airbox removed.  It comes out easily after the center bolt and the two top 13mm hex head bolts are removed.  The yellow arrow points to a crankcase breather hose.  This hose was cracked from age, but they wanted a fortune for a new one at the BMW dealer, so I coated the old one with black silicone RTV sealant.  It has a strange bend in it and I couldn't find a cheap replacement.  Not sure if it will hold up over time, but we'll see...

I didn't have to remove the battery.  Removing the airbox, which is much easier, gave me all the room I needed to work.

Pivot pin removed from left side of bike.  Transmission to engine case bolts removed also, so the transmission is ready to slide back away from the engine case.

I had to remove the left footpeg also (8mm Allen bolt, 17mm nut) to pull the transmission back.  The shift linkage also had to be removed.

The monoshock on the '86 was in the way of removing the transmission, so I had to remove the upper bolt from the shock tower and slide the shock out of the way.

To slide the transmission back, pull in the clutch.  The action of the clutch should move the transmission away from the engine case.  Carefully slide the transmission back; you may have to pull on the swingarm a bit.  Be careful -- there is an electrical sending unit under the transmission and you could damage it when it slides back.  Don't put any weight on it either.
 

I had to remove the clutch actuator rod on the '84 to have enough room to slide the transmission back.  This is easy to do: slide the clutch cable off the bottom (you can just see it below the yellow arrow in about the center of the frame).  

Take off the bolt and washer and slide out the bolt, and the actuator comes right off.  This gives you some room to clean everything up in back of the transmission while you have the actuator off.  I put a dab of moly lube on the bolt before I re-installed the actuator rod.

Here's a photo of the spline.  Use an old toothbrush to clean it off with some contact cleaner, brake cleaner or other quick evaporating spray cleaner.  Be careful not to get the old dirt and goo sprayed all over the clutch and other areas; you may want to put a couple of rags in there to protect the clutch.

Take a tiny bit of moly grease and coat this spline with an old toothbrush or cut off paint brush.  I used Honda's Moly 60 paste (here's a source where you can purchase a 3 oz. tube for about 8 bucks), but there are plenty of good ones on the market.  I wouldn't get too uptight about what type to use; unlike a K-bike, this job is easy enough and only takes a couple of hours at most, so you can get in there much more often than on a K to check the wear and lube it properly.

I was only able to pull the transmission back from the engine case about 20mm on either bike (about 3/4"), but that gave me enough room to do the job.

Installation is reverse of this procedure.  Squeeze the clutch back and forth as you're sliding the transmission back on over the spline; this will help to ensure everything is lined up.  

You'll need to "balance" the swingarm between both sides of the frame.  The procedure for this is fairly well described in the Clymer Airhead manual, but basically the swingarm has to be centered between each side of the frame.  I used a Vernier calipers to measure this.  It's a procedure that calls for patience.  As you tighten one side's swingarm pivot pin, the swingarm moves the other side.  

You have to go back and forth until you get the correct distance, but remember that when you torque the pivot pin and put on the 27mm Allen nut, you may throw things out of whack.  I never was 100% sure I got this right, but the bike doesn't seem to mind.  Make sure you re-torque the swingarm locknuts to the correct torque -- I forgot to do this on one side and had the nut back all the way off while riding, not a pleasant experience!

Lubing the splines on the '86 has made a big difference in the way it shifts -- it really shifts beautifully and the transmission seems like it "snicks" right into gear.  The '84 must have had a spline lube done by the previous owner, because I could still see the lube on the splines.