"Two-headed, four-legged animal", sounds like something out of a horror movie. Any time "man" creates something trying to mimic nature; it seems to come out a little weird. This makes our "man" made four-legged creature much more complex than natures' four-legged creations. This creature was not designed overnight. The current two-headed four-legged animal has evolved over time and is still evolving.
Let's take a look at this "man" made creature compared to natures' four-legged animals. The most obvious is that it has two heads, instead of one, each looking at the other. Then there are the four feet, two of the feet pointing toward the other two. The legs are generally of different lengths as well. There are four arms of different sizes trying to hold the two halves of this creature together. The two halves are usually of different weight and size. Each half has its own control and decision making center (separate brains). Each half learns and thinks differently. The two halves have different levels of strength and coordination. How will this weird two-headed four-legged animal ever survive in the wild jungle: the dance floor?
Somewhere back in time it was decided that the man would be in charge (lead). He became the leader probably because he was bigger, stronger and carried the biggest club. The laws of physics and geometry are used to understand how the rest of this two-headed four legged animal moves and survives on the dance floor.
One of the first problems to solve is the communication between the two halves. The only physical connection between the two, are the arms. The communication link is the "frame". This is how the lady feels what to do and how the leader indicates his intentions. However, the leader does not drive her like he would steer a car. The body moves the frame (arms). The frame does not move by itself. As a trained dancer, the leader also knows that he must move from his supporting leg in order for the lady to be able to feel the movement. The frame has a reaching connection toward each partner. It is firm but not frozen. It is directly connected yet flexible. The frame connection never changes whether you are moving forward, backwards or in any direction.
The partnership has the lady offset to the leader's right side by about half a body. This allows the legs to move in between each other and keeps the knees and toes from bumping. Each partner has a center of gravity and the partnership has its own unique center of gravity. The two-headed four-legged animal movement passes through the common center of the partnership. This common center of gravity is what unites the two halves and allows movement as a single entity. This offset of the partners, dictates that the counter balance of the partnership be on a diagonal from each other.
Even though the frame is physically connected high in the partnership, the power and movement must be lower through the center of the partnership for controlled movement of the two-headed four-legged animal.
The goal of the partnership is to create an entity that moves as one on the dance floor. One what? One two-headed four legged animal, of course. Unfortunately for the lady, she can dance only as well as the man leads. The concept is for the lady to participate in the lead, to add to the lead, to enhance the lead, to add power the lead, etc. This is achieved by the lady feeling what to do and participating in the partnership. This also means that the leader must lead in such a manner to allow the participation of the lady. This is what creates the unique four-legged feeling that can't be generated by a single two-legged animal.
The above is by no means a complete description of what goes on in the internals of the two-headed four-legged animal, but hopefully this will open your thinking on analyzing four-legged movement.