All of us began our mobility as infants crawling around on the floor on our hands and knees (four-legged movement?) and then finally standing up. From the time that we could stand up, we have grown-up trying to perfect two-legged balance (walking, running, dancing, skiing, mountain climbing, ice skating, bicycling, etc., etc.). It seems ironic that we have gone full circle and are now trying to figure out how to perfect four-legged balance.
The goal of Ballroom Dancing is to take two individuals and combine them into a single entity, a Singularity (a four-legged entity). At the lower levels of Ballroom Dancing, the two partners dance as individuals that just happen to be in a partnership. I call these types of dancers "Pattern Dancers". Each dancer dances their part of the pattern as a two-legged entity. Their balance and movement is based on the two-legged balance they have developed and have always known. At the higher levels of Ballroom Dancing, the two dancers evolve from two-legged dancers into one four-legged Singularity.
Balance is accomplished differently when the dance entity is four-legged. The centers of gravity that used to be in each of the two individuals are now a single center of gravity within the Singularity. It becomes more and more important to be connected to the partner and feel what is going on instead of dancing your own two-legged part. Balance and movement becomes a single four-legged action.
The dance frame is a key connection mechanism between the two dance entities. There must be a constant forward connection between the partners to maintain the feeling of a Singularity. Even though the frame connection is physically at the shoulder level between the partners, the actual connection is logically at the center of gravity of the Singularity. No matter what dance action is being performed, that center connection must be maintained at all costs.
In Smooth and Standard style dancing, the partnership counter balance is at the core connection (center of balance). There is a physical connection at this point. Generally speaking the lady is shorter and lighter than the man. This means that the lady has more of a backward body attitude than the man in order to counter balance the man. The tendency is for the lady to lean back from her shoulders to counter balance the man. If she does this, all of her body weight is in the man's right arm of the frame and there is no forward connection between the partners. If instead, the lady would push her center against the man's center allowing her shoulders to move backwards, she would have a forward connection and at the same time counter balance the man. As the Singularity moves, there is the possibility that the physical connection will be broken. The connection is still maintained, except through a logical connection instead of a physical connection.
In Latin and Rhythm style dancing, there is more of a logical connection to the common center instead of a physical connection. This seems more complex because the common center is basically a moving target. In fact, the common logical center seems to be easier to maintain because there is no physical reference to try to adjust to. The connection seems to be more flexible and adjusts automatically.
There are transitions in both styles of dancing where the center moves between physical and logical connections. Usually this is not a problem because there is only a slight or momentary change. There is a little bit more of a problem when the dancers perform solo turns and other solo type movements. If the dancers realize that the common center remains the same whether the other partner is facing you or has his or her back to you, the transition connection is not a problem.
There is a third part to four-legged movement and that is rotational balance. There are turns when both dancers turn at the same time and others times when only one dancer turns. In pivot type rotations, it is important that the physical connection has a forward "through" the core feeling by both partners. This keeps the Singularity together by neutralizing the centrifugal force created by the rotation. In powered single turns (example: Inside Turns), the connection travels vertically from the power from above down to the center of the turning dancer and vertically upwards from the center of the turning dancer to the power above.
The primary goal of four-legged balance is to simply be aware of your four-leggedness and most of the time it just happens. Be aware there is a whole other entity that is now part of you. Acknowledge your four-leggedness and embrace it.