I don't see much point in removing the whole tensioner housing, there's not much to see in there. But, you can (and probably should) remove the adjuster screw, plunger, and spring assembly from it, it just screws out. What you'll be looking for is the damper washer, a copper washer placed on the plunger rod to quiet the operation of the unit. Many times they are missing and then the tensioner can make noise, sounding like loose valves .....
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If missing, this will also allow the end of the plunger to come out past the end of the adjuster screw during operation. If you loosen the adjuster so it's flush with the plunger, you will have the chain set too loose.
I find the "book" method for setting the cam chain tension very confusing and easy to screw up. The first time I tried it many years ago, I ended up with the chain way, way too loose. Every time I rotated the engine, the rod would pop out past the adjuster, so I loosened it to make it flush. Another engine revolution would have the same thing happening so I'd loosen the adjuster more, etc., etc. My setting ended up being way too loose. I started the engine and it rattled like the valves were loose. There had to be a better way, and there is - you check and set the tension while the engine sits there idling. I borrowed and adapted this from the cam chain adjustment instructions for Yamaha's big singles .....
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The actual instructions can't be applied. You can't set the motor on the "T" mark. There is no spot during a 650 engine revolution where all the valves are closed and there is no tension on all the rocker arms. It's the note at the bottom that's important. We can do this on our 650, and it's a pretty much foolproof method for checking and setting the chain tension. You want to see a small amount of in-out movement on the plunger, maybe 1 to 2mm. If it moves more, the chain is too loose, if it moves less or not at all, the chain is too tight.
Easiest way to do the adjustment is to tighten the adjuster until the rod almost stops or stops moving, then loosen it back up until you get your 1 to 2mm of in-out movement. Don't worry too much whether the rod is flush with the end of the adjuster screw, that can vary due to worn (or missing) parts.