Unbalanced bike

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ttcycle

Cycling Excusiast
If you've checked all the above then there could be a frame misalignment. Sheldon Brown shows you how to tie a piece of string from the headset to the two drop outs and measure each side. If it's steel it can be fixed if it's not massively out
 

dddd

Regular
Usually, once (as has been mentioned) the cables and headset have been ruled out, I will check to see how the front rim centers under the fork crown, then "flip" the front wheel to see if this changes. If it changes, the wheel dish needs to be addressed, either by correcting the axle spacing or by tensioning spokes to one side.

If the bike pulls toward the RIGHT, then the tyre's contact patch on the ground needs to be moved toward the right, perhaps just a few millimeters to achieve full correction.
With the wheel tilted whilst the axle is loosened on the fork, first check to see if manually centering the rim under the fork crown will perhaps move the road contact patch toward the right, which might by itself effect an improvement in the steering. If so, then the dropout axle slot on the right side could be deepened using a round file to preserve this centering every time that the front wheel is installed.

If tilting the wheel in the fork doesn't work out using a known-symmetric front wheel, then the fork legs may then need to be moved (bent) toward the right side.
Bending the fork legs is simple, but one should first have some experience bending metal tubing! You don't want the tubing to collapse in and buckle, which it tends to do.
I usually bend the fork legs one at a time, and use the fork end axle spacing dimension as a reference for how far that each leg is being bent. You need to end up with the correct axle spacing distance after the fork legs have been corrected.

Hopefully, after the fork correction, the wheel will center between the fork legs under the fork crown, but this needs to be considered before one begins bending the fork legs!

An alternative is to bend the lower fork ends toward the right with the rim still installed with tightened axle. This is the better way when bending the fork legs one-at-a-time would not allow the rim to center under the fork crown, since with this alternative method the bending stress will be moved up into the fork steerer tube inside of the frame.

I've restored many bike's steering centering by applying force to fork ends or axle using my foot, with bike laying on it's side. It takes care, but can be done without tools (other than a measuring rule). In the field, I have used the bike's wheel/axle to measure the fork end spacing and to measure my bending progress.
I usually keep my left hand on the left handlebar end to stabilize the steering and use my right hand or foot to push the saddle post toward the ground while using my left foot to apply downward force at the fork ends. A block of wood here and there, such as under the crank arm or rear axle, will help level and stabilize the bike while you are "jumping" on it. Some frames require a lot more or less force to correct than will other frames.

All of these left and right side instructions would of course have to be reversed if the bike happened to be pulling toward the left whilst riding.
Similar methods can be used to correct mis-centered rear dropouts, to bend the chainstays back into center with the main frame and bottom bracket or to increase the rear frame spacing to accept a wider wheel.
Be patient, and if it takes several tries to get things in line just consider it good exercise. This can be quite physical work for those who are not very heavy and/or strong, and of course one must keep their balance while working over the bike.

This bending of the frame and fork is known as cold-setting, and most steel frames are able to withstand multiple corrections without appreciable weakening. Even good-quality new frames and forks are bent into straightness after bronze-welding (brazing) or welding, while some cheaper models skip this necessary step, leaving it up to the owner.
 
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