The concept of balance in Ballroom dancing is complicated because the partnership and individual partners go in and out of so many different balance variations. There is "Two-legged" balance (a dancer's personal balance in solo movements), "Three-legged" balance (connected to the partner with just one hand) and "Four-legged" balance (a full partnership connection). Add to each one of these variations the elements of horizontal movement, vertical movement and rotational movement. Understanding balance in all its forms is essential to becoming a proficient and competent Ballroom Dancer.
Let's start with "Two-legged" balance. The goal is to have the individual dancer balanced at all times (when stationary and in motion). A couple of examples are the "Walk-Around Turn" in Latin/Rhythm dancing and the "Open Side Locks" solo turn in Smooth dancing. The personal balance in a stationary male is different than the personal balance in a stationary female. The male dancer's body is essentially straight up and down and can be balanced simply by lifting his head so that it is balanced over his body (like a solder standing at attention). The male's balance point is just above his fore head (not in the center of the top of his head). The female dancer is different because of the weight of her breasts on the front of her body. Her balance point is the top of her sternum. Her head (behind the top of her sternum) counter-balances her breasts (in front of her sternum). The lady has a curved slightly backward feeling when she is in a balanced position.
Examples of "Three-legged" balance in Standard/Smooth dancing would be a "Syncopated Underarm Turn", an "Open Chair", "Continuous Hovers", etc. Examples in Latin/Rhythm dancing would be "Open and Crossover Breaks", "Underarm Turns", etc. The individual dancer's personal balance is slightly different when "Three-legged" because of the addition of the single hand connection. The hand connection is generally used for power and control in these types of movements.
"Four-legged" balance is the full partnership connection in both Standard/Smooth and Latin/Rhythm. This could be "Closed Dance Position", "Promenade Dance position", or "Outside Partner Dance Position". The goal here is to balance the partnership not each individual dancer. Each partner has a center of gravity (which is used intuitively) but the partnership has a unique center of gravity that is not intuitive. This has to be learned. The man is usually bigger than the lady and along with the offset dance position; the partnership is not perfectly symmetrical. The balance of each individual dancer must be adjusted to balance the partnership (the two-headed four-legged animal). Ideally the partnership moves, not the individual dancers.
I like to compare the partnership balance to riding a "Teeter Totter". The man (because he is usually bigger) has to move forward on the board (or the lady move backward) in order to become balanced. Usually each will adjust until the balance is achieved. As the "Teeter Totter" moves up and down, each side is also adjusting the individual balance so as not to fall off to either side of the board. Let's now rotate the "Teeter Totter". Now each individual is adjusting their balance to compensate for centrifugal force of the partnership. Add to this horizontal movement and you essentially have partnership dancing.
As you can see from the above, there is "Two", "Three" and "Four" legged balance. There is also "vertical balance", "horizontal balance", "rotational balance", "change of direction balance", "powered and un-powered turn balance", etc. This seems very complicated, but once you understand how it works, it will eventually become second nature.
In order to balance the partnership, each dancer must feel their other half in order to know (feel) what is required to balance the partnership. This is accomplished by having a forward feeling through the frame connection. The "four-legged animal" is solidified by this forward feeling connection. The biggest problem dancers have is not maintaining this connection all of the time. The connection must be there all of the time. If it is not, the action required to balance the partnership will be too late. When the connection is there all of the time, balance will be based on feeling not thinking. This frame connection must be a normal part of the partnership feeling.
The partnership (four-legged animal) must have a solid base to support all of these different types of movements and still be balanced. The partnership always has four feet on the floor. The "supporting foot" has 98 percent of the bodies' weight, and the "free foot" still retains 2 percent of the bodies' weight. This creates a sliding action of the feet on the floor in both Standard/Smooth and Latin/Rhythm dancing. The only exception to this is if the dancers are performing "kicks" or some other non-standard action. Having four on the floor improves the partnerships' balance dramatically.
I have had several dancers come to me complaining about balance problems due to what they perceived as "vertigo". I discovered that all of them tended to dance with their heads in a down position. Once I got their heads up in the correct position, developed a partnership connection and got all four feet on the floor, the partnership balance problem was solved.
Pattern dancers (dancers that walk through patterns in front of each other) dance as two individual dancers not as a single partnership regardless of whether they are "Two", "Three" or "Four legged".
Partnership balance is rooted in each partners' ability to feel each other. Once the feeling of the partnership is developed, all the aspects of balance start to become intuitive.