Figure 4. Lip Bone Hierarchy

Chain these joints together starting from the bone in the centre and ending at the corner of the lips. This should give you four joint chains, two for the upper lip and two for the lower. Notice that to complete the chains you will need to duplicate both lip corner joints as well as the upper and lower joints at the middle. You'll need these repeated bones to be on top of each other later on during the skinning process.

Orient the bones so that they point along the Y axis and the Z axis is aligned to the world up direction (usually +y). You can orient the axes in any order you like but I prefer the bone running down the Y axis, although that may come from many years of habit and hard drinking. You can use the standard Maya Orient Joint command, but I find it a little unpredictable and prefer custom scripts like Michael Comet's CometOrientJoint.mel or jsOrientJoint.mel by Jason Schleifer.

Change the rotate order of all your bones to yzx so that the axis running down the bone (Y) comes first and the axis aligned with the world up (Z) comes second.

Rename the joint chains to your little hearts desire. I named them LTbone_1 through LTbone_ whatever your end bone number is for the Left Top bone chain. Then RT (Right Top), LB (Left Bottom), RB (Right Bottom) respectively. You can name them after your favourite polka bands if you like, as long as you can keep things organized. We'll be going into the Component Editor later and you’ll need to keep track of which joint is which.

Now you should have four joint chains running down the middle of the lips ready to have animation controls put on them. While we're in skeleton making mode we should make some joints for the jaw and head.

Switch to the side view and add a joint at the jaw, ending at the chin. Rename them jaw and chin.

Make a single joint for the head (it doesn't matter where, because it will just be a placeholder. I like to put it somewhere above the jaw near the back of the head.) Call it head.

Create another single joint somewhere above the joint chains for the top lips and rename it Mouth_Top.

Create another single joint under the bottom lip chains and call it Mouth_Bottom.

Parent the top two lip joint chains to Mouth_Top and the bottom two to Mouth_Bottom.