This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
From: Jobst Brandt <email@example.com>
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.