Introducing Forward and Inverse Kinematics

Forward and inverse kinematics generally have to do with a system of connected parts, such as a chain or a jointed arm. They have to do with how that system moves, and how each part moves in relation to the other parts and to the whole.

Often, a kinematics system has two ends: the base and the free end. A jointed arm is usually attached to something fixed at one end, and the other end moves around to reach and grab things. A chain might be attached to something on one or both ends, or not at all.

Forward kinematics (FK) deals with motion that originates at the base of the system and moves out to the free end. Inverse kinematics (IK) deals with the opposite : motion originating at, or determined by, the free end and going back to the base, if there is one.

Some examples are in order. In most cases, the limbs of a body in a walk cycle will be done with forward kinematics. The thigh moves, which moves the calf. The calf moves, which moves the foot. The foot moves. In this case, the foot isnt determining anything. It winds up wherever it winds up, based on the positions of all the limbs before it.

An example of inverse kinematics would be pulling someone by the hand. Here, the force applied on the free endthe handcontrols the position and movements of the hand, forearm, upper arm, and eventually the whole body.

Another, more subtle example of inverse kinematics is an arm reaching for something. Again, the hand is what is driving the system. Of course, you can say that, in this example, the upper arm and forearm are moving and they control the position of the hand. That's true, but there is a direct intention to put that hand in a specific place. That is the driving force. In this case, its not a physical force, but an intention . The forearm and upper arm are simply arranging themselves in whatever configuration necessary to position that hand.

The differences will become clearer as you go through the examples in this and the next chapter. But for now, remember that dragging and reaching are generally inverse kinematics, while a repeated cycle of motion, such as walking, is usually forward kinematics, which is the subject of this chapter.