When a joint chain is first created, the individual joints make up a simple hierarchy. Each subsequent joint in the chain is a child of the joint before it. When you build a joint chain in a straight line (by snapping to the grid), it is clear that the only attribute with non-zero values is the x translation. This value represents the distance from a joint’s pivot to its parent’s pivot. The rotation value for the joint has a similar relationship to a parent, but there is another transformation stuck between the joint and its parent, and it can alter the relationship. This transformation is a rotation axis known as the joint orient. For now, think of it as an offset between the parent and child. By default, the joint orient attribute is not shown in the Channel box when you first create a joint chain. In the next section, you will explore the joint orient further.

[Figure 12] The Channel Control information.

This method of positioning joints after initial creation is the safest method to ensure that the local rotation axes of the joints are preserved and that no unnecessary transform values are placed on any of the attributes. Later in the book you will be building a character rig (Chapter 13), and you will use this method to position the arm joint chains.

Setting Joint Limits
With your joint chain built, zeroed out, and the LRA placed properly, you may want to set some limits on how far the joint can rotate or translate. Most of the time, you do not want a joint to translate. Moving a joint can cause some really strange deformations to the geometry skinned to your joints. Locking off the translation channels of a joint is a usually a good idea.

Setting rotation limits is also great for controlling rotations on characters. Depending on the character’s expected performance, setting up joint limits can help define a range of motion that the character’s geometry will work within. Some animators may be opposed to joint limits, though, because they restrict what they are able to do with a character. If the character has no limits, then the animator can define the range of motion that is appropriate, given a particular scene or action. This makes a lot of sense from the animator’s point of view, as it allows him to push the character into poses that might work for the performance, but it makes the job of the character TD more difficult, because it means that the skin must be able to perform over a very wide range of motion, and sometimes past that point.

[Figure 13] The Attribute Editor limit information.

The joint limit information can be entered in several different ways. If you want to completely lock off any rotation or translation values for an attribute, you can do so in the Channel box by highlighting the text for the selected attribute(s), right-clicking, and then choosing Lock Selected from the menu that appears. This can also be done in the Channel Control window (see Figure 12).

Kinematics — Skeletal Systems
In simple terms, kinematics is the math behind movement in a system. Character TDs rely on the theories of kinematics to create skeletal systems that speed up animation interactivity and add realistic movements to characters that benefit from articulated joints. There are two widely used techniques for controlling a character’s skeletal systems: Forward Kinematics (FK) and Inverse Kinematics (IK). Let’s take a closer look at these two systems.

Forward Kinematics (FK)
Forward kinematics is based on simple relationships in a hierarchy of joints, much like what we find in our own bodies. For example, if you move your shoulder joint, the rest of the arm joints below the shoulder will follow. Imagine a jointed action figure like GI Joe. You rotate the arm at the shoulder, then you rotate the forearm that has followed the shoulder to get the arm in the position you want. Many animators prefer this type of interaction with their characters, as they like the intuitive method of posing a character with rotations.