T'ai Chi is actually a shortend form of the full name T'ai Chi Ch'Uan.
The Tai Chi that Americans are familiar with is the Yang style twenty-four
posture short form that was founded by Yang, Lu-Ch'an (1799 - 1872). The
forms mentioned in the other writeups are not unique to Tai Chi by any stretch
of the imagination. In fact, most martial arts teach movements in this
manner.
T'ai Chi Ch'Uan is generally taught in 24, 48, 72, 88 (rare), and 108
posture forms. The 24 posture form is also refereed to as the short, or
simplified, form, the 48 as the simplified, and the 108 as the long form.
There is also T'ai Chi Push Hands (sometimes refered to as "pushing
hands"), T'ai Chi Palm, T'ai Chi Chin Na, Bagua T'ai Chi, Mu Lan Ch'Uan
(a combination of T'ai Chi Ch'Uan and Chi Kung). There are also spefic weapons
forms like T'ai Chi Saber (a completely different weapon from the european
saber, it is more closely related to a scimitar), T'ai Chi Sword ( a
stright medium width broadsword), T'ai Chi Staff, T'ai Chi Ball, T'ai
Chi Fan (single and double), T'ai Chi short staff (jo)
T'ai Chi Lessons are frequently preceded by Chi Kung (energy training)
temple exercise to get chi flowing. The art itself in very fluid but
when compared to arts like Aikido not very circular. Many of the hand
movements do, however, move as if you were colding a large ball in front
of your hara. The path of the 24 posture form, which contains the essential
elements of the 108 posture form but leaves out many of it's nuances
and some of it's moves completely, describes a straight line with the exclusion
of 2 movements which are each repeated towards the end of the form at 45
degree angles to the line. The form however, does not continue off on an
angle at any point. The movements in the 24 posture form are concerned
with attacking, or being attacked by, people in front of you or to your
sides. It is extremely well suited to a small number of attackers but
does not hold up as well as some other arts in situatioins with large numbers
of simultaneous attackers from all directions, unless you are extremely
advanced in its techniques.
I would argue that the central focus of T'ai Chi is not to get
your opponent to the ground because T'ai Chi is not a grappling
art. This means that there are no hard holds (you never try to grab on and
not let go) or immobilization techniques for dealing with someone once
you get them on the ground. This also means that its effectiveness begins
to break down when you find yourself laying on the ground. Instead, I would
argue that the main focus of T'ai Chi is to redirect your opponents chi
and use it against them. Many of the the moves use this in combination
with your own chi for attacks with dramatically powerful results.
The theory that someone on their knees is easier to disable only applies
to untrained opponents. An Aikido practitioner on their knees can be at
least as hard to disable as one standing. Many Aikido dojos make sure
their students are comfortable performing a move from a kneeling position
before they ever attempting it standing. A ju-jitsu or judo practitioner
would also have the advantage, be they on their knees or flat on the ground,
if the T'ai Chi practitioner who threw them did not use the time to distance
themselves.