Chapter 40: Adding Inverse Kinematics

Kinematics is a branch of mechanics that deals with the motions of a system of objects, so inverse kinematics would be its evil twin brother that deals with the non-motion of a system of objects. Well, not exactly.

In Max, a system of objects is a bunch of objects that are linked together. After a system is built and the parameters of the links are defined, the motions of all the pieces below the parent object can be determined as the parent moves using kinematics formulas.

Inverse kinematics (IK) is similar, except that it determines all the motions of objects in a system when the last object in the hierarchy chain is moved. The position of the last object, such as a finger or a foot, is typically the one you're concerned with. Using IK, you can then use these solutions to animate the system of objects by moving the last object in the system.

Forward Kinematics versus Inverse Kinematics

Before you can understand inverse kinematics (IK), you need to realize that another type of kinematics exists-forward kinematics. Kinematics solutions work only on a kinematics chain, which you can create by linking children objects to their parents.

CROSS-REF 

Chapter 10, "Grouping and Linking Objects," covers linking objects and creating kinematics chains.

Forward kinematics causes objects at the bottom of a linked structure to move along with their parents. For example, consider the linked structure of an arm, where the upper arm is connected to a forearm, which is connected to a hand, and finally to some fingers. Using forward kinematics, the lower arm, hand, and fingers all move when the upper arm is moved.

Having the linked children move with their parent is what you would expect and want, but suppose the actual object that you wanted to place is the hand. Inverse kinematics (IK) enables child objects to control their parent objects. So, using inverse kinematics, you can drag the hand to the exact position you want, and all other parts in the system follow.

Forward kinematics in Max involves simply transforming linked hierarchies. Any time you move, rotate, or scale a linked hierarchy, the children move with the parent, but the child object can also be transformed independent of its parent.