Wheel alignment

[Moleskins]

This question relates to a Triumph 3TA but I suppose it would be the same for other makes and models. 
I’ve done a complete strip down and rebuild on a 3TA. It’s now coming to the final adjustments and make sure everything is tightened up time before I ride it up the road.
There are no marks on the frame to indicate that the rear wheel is pulled back evenly so how do you do this ?
To my thinking the front wheel and rear wheel should run in line, one behind the other but if I set this up with a piece of string I find that the rear wheel isn’t sitting evenly between the swinging arm. Also it’s not even if you look at the rear adjusters.
So what do you set it up to?

[R]

Its a bit rough and ready, but if you slot a pair of 4x2 timbers either side of the wheels,
you can see how aligned they are, sorta.
This is a bit dependent on the front and rear tyres being the same size (width),
but packing pieces can make up the difference.

Laser alignment is probably the modern way to do it these days, but who has one (two) of those....

[Grunt]

I’d agree the wheels should be in line.

There’s not much you can do about the front wheel other than checking the offset of the rim if you’ve respoked it I’d also check this on the rear wheel. If you look closely at the rear frame loop and swinging arm you will likely find it isn’t on the centre line of the frame and is offset. The quickest way to get a rough idea of whether the rear wheel is true in the swinging arm is to measure from the center of the swinging arm spindle to the centre of the wheel spindle making sure they are the same on both sides. It would be as well to check the engine sprocket is in alignment with the wheel sprocket while your at it just to make sure the spacers have gone back in the right place. If you then check the front and rear wheel alignment with string or timber as R suggests then you’ll have a good idea whether anything’s amiss. I’d ignore the markings on the adjusters and certainly wouldn’t go by the tyre or rim being central in the swinging arm. I’m also assuming the frame or forks aren’t bent.

[Moleskins]

Thank you both, I’ve not respoked wheels so they may be either right or wrong.
I’d not though of measuring from swinging arm spindle to wheel spindle, I’ll add that into the mix.
It makes you wonder how anyone rode and serviced them back in the day but it probably helps to explain why Japanese bikes quickly became popular with simple things like frame markings to help owners.

[iansoady]

Frame markings are wildly inaccurate. The only reliable method is a straightedge (or string as second best). Prop the bile up so that it's reasonably level without using the centre stand. Put your straightedge by the right hand side of the wheels making sure it touches both front and rear of the back tyre. If the wheels are in line it will also touch both sides of the front tyre (if the tyres are the same section - if not you need to measure widths and make appropriate adjustments).

There's no reason the back wheel should be central in the swinging arm. Some are some aren't.

If you have a steering damper you can use this to stop the front wheel flopping about.

If you can't manage this then perhaps old British bikes are not for you.

[TGR90B]

Also make sure the rear sprocket is in line with the chain (as best you can). This will at least tell you if the wheel is correctly located in the frame.

[Rex]

The front rim should be central between the fork legs, and the rear rim should be central to the frame spine. The front is easy to check with a steel rule but the rear would need the mudguard removing. If you have any doubts it would be worth spending some time dismantling to check properly.
Forget frame graduations  as that's those clever Japs, and don't trust frame slot length or S/W clearances either.

As said, string or timber will do the job as will two cheap lasers, but you're going to struggle with an old bike if this sort of task is too taxing? 

[Moleskins]

Thanks for the replies. I’d had the string out with the bike up on a lift so the centre stand wasn’t in the way. As this is fairly important I thought it was best to ask. I’m glad I was on the right track (pun intended).

[iansoady]

Also make sure the rear sprocket is in line with the chain (as best you can). This will at least tell you if the wheel is correctly located in the frame.

I find it harder to do this than line the wheels up as chainguards and bits of frame get in the way......

[Rex]

Good old Mk 1 eyeballs are good for this, and verified with another of those cheap lasers. Just aim the beam from the tips (centre-line)  of the rear sprocket to see if it hits the c/l  of the gearbox sprocket.
Many don't, usually down to people losing axle spacers or not correctly fitting bearings.