Here's a long posting on a complex topic recently raised on this list.
I'd never experienced shimmy until I had my Proteus Pro-Tourist 'fixed' by a well-known bike shop a few years ago. After repairing a broken braze joint on the rear brake bridge, they realigned the frame to correct some things they said were obviously wrong. Ever since, I've experienced VERY SERIOUS shimmying when I've got my large Beckman panniers mounted. The bike is almost unrideable when the panniers are fully loaded but is fine with lighter panniers and lighter loads. If the rear wheel bearing is the slightest bit loose, things get noticeably worse but I think everything on the bike is pretty well perfectly adjusted now. According to the article I've copied below, the problem may be that the bike is now just too perfect (which I find hard to believe.) The author is Jobst Brandt, who wrote The Bicycle Wheel. The moral of this article is that if your bike shimmies, try bending one of the tubes, riding without a saddle or letting your leg (or beer belly) rest against the top tube. I do believe at least some of the points made in this article (but not the bearing issue; also, the weight of panniers is important.)
I'm teaching Classical Mechanics to junior-level physics majors this semester and am tempted to make this one of the problems that they are asked to solve with a numerical simulation; but it's probably too difficult for homework. It might make a good senior project; perhaps I should collect a list of bicycle/physics issues like this that a senior physics major could examine with both calculation and experiment. Are there any other unresolved issues out there? I know that much has been written about some aspects of bicycle construction and I have an interesting book 'Bicycling Science' by Whitt and Wilson, 1974, MIT. It has a very brief discussion of stability (wheelbase, fork angles et al) and damped oscillatory behavior at low speeds, but doesn't discuss anything resembling shimmy.
The following article was found on the web site:
http://www.faqs.org/
Subject: 8h.5 Shimmy or Speed Wobble From: Jobst Brandt <jobst.brandt@stanfordalumni.org>
Shimmy is not related to frame alignment or loose bearings as is often suggested. Shimmy arises from the dynamics of forward motion and the elasticity of the frame, fork, and wheels, and the saddle position. Both perfectly aligned bicycles and ones with wheels out of plane to one another shimmy nearly equally well. The same is true for bearing adjustment. In fact shimmy is more likely with properly adjusted bearings than loose ones. The bearing or alignment concept is usually offered as a cause of shimmy and each airing perpetuates the idea.
Shimmy, the lateral oscillation at the head tube, depends primarily on the frame and its geometry. The inflation of the tire and the gyroscopic effects of the front wheel make it largely speed dependent. It cannot be fixed by adjustments because it is inherent to the geometry and elasticity of the components. The longer the frame and the higher the saddle, the greater the tendency to shimmy, other things being equal. Weight distribution also has no effect on shimmy although where that weight contacts the frame does.
In contrast to common knowledge, a well aligned frame shimmies more easily than a crooked one because it rides straight and without bias. The bias force of a crooked frame impedes shimmy slightly. Because many riders never ride no-hands downhill, or at least not in the critical speed range, they seldom encounter shimmy. When it occurs with the hands on the bars it is unusual and especially disconcerting. There is a preferred speed at which shimmy initiates when coasting no-hands on a smooth road and it should occur every time when in that critical speed range. Although it usually does not initiate at higher speed, it can.
Pedaling or rough road interferes with shimmy on a bicycle that isn't highly susceptible. When coasting, laying one leg against the top tube is the most common way to inhibit it. Interestingly, compliant tread of knobby tires give such high lateral damping that most bicycles equipped with knobbies do not shimmy.
Shimmy is caused by the gyroscopic force of the front wheel that acts at 90 degrees to the axis of the steering motion. The wheel steers to the left about a vertical axis when it is leaned to the left about a horizontal axis. When the wheel leans to the one side, gyroscopic force steers it toward that side, however, the steering action immediately reverses the lean of the wheel as the tire contact point acts on the trail of the fork caster to reverse the steering motion.
The shimmy oscillates at a rate that the rider's mass on the saddle cannot follow, causing the top and down tubes to act as springs that store the energy that initiates the return swing. The shimmy will stop if the rider unloads the saddle, because the mass of the rider is the anchor about which the oscillation operates. Without this anchor no energy is stored. The fork and wheels may store some energy, although it appears the frame acts as the principal spring.
Shimmy can also be initiated with the hands firmly on the bars by shivering, typically in cold weather. The frequency of human shivering is about the same as that of a typical bicycle frame.