1. Kinematics Intro
:a branch of dynamics that deals with aspects of motion apart from considerations of mass and force Merriam-Webster

2. Animation Scripting Procedural
Kinematics (specify poses without regard to forces)
Procedural
Particle Systems (Reeves ‘83)
Behavioral Animation (Reynolds ‘87)
Intelligent Systems (game/strategy/AI)
Physically Based Modeling (water, gravity)
Input Driven (face animation)
Algorithmic (e.g. Plant growth)

3. Labanotation
(from dance); similar to Jack’s talk about motion indexing -
where are body parts relative to each other?
put together in a series of key frames

4. Two Ways
Forward Kinematics: apply transformation to each node to determine pose.
Reverse Kinematics: given desired position of effectors, find necessary joint angles to achieve pose.
Specify pose by moving limbs, then calculate transformations
Which is associated with motion capture?

5. Hierarchical Kinematic Modeling
Closely related to robotics
Left Arm
Right Arm
L. Elbow
R. Elbow
L. Leg
R. Leg
R. Knee
L. Knee
L. Ankle
R. Ankle
R. Wrist
L. Wrist
R. fingers
L. fingers

6. Using the Hierarchical Model
Node x has matrix for transformation
Used by all nodes in the tree
Recursively walk tree: matrix for node applied to everything in subtree (depth first or breadth first?)
Joints may have one or more degrees of freedom
Rotate about i,j,k, translate

7. Small Example L0 L2 L2 L1 L0 L1 To T1 T2 Lo L1 L1 T0 T2 T1
Each transformation is relative to member above it in hierarchy
1st matrix: T0, Vertex V0 in L0 is moved V0’ = T0V0
2nd Matrix: T0 T1
3rd Matrix: T0 T1 T2
What if there was rotations? Be careful of order!!

8. Joints Revolute joints - allow you to rotate
Prismatic joints (pistons)

9. Who (in the &!*~^) is Denavit-Hartenberg
We like to define points in a local coordinate frame
Need a deterministic method for converting from coordinates in one frame to another
Especially, parent to child in a hierarchy

10. Denavit-Hartenberg Notation
For 1 axis of rotation
Link length: distance down the x axis from one joint to the next
Joint angle:
Xi+1
Zi+1 Zi
Linki
Өi+1 Xi

11. Here, d is zero, and alpha is zero
Joint Parameters
Joint angle Өi: angle between xi-1 and xi about zi
Link length ai: distance from zi to zI+1 along xi
Link offset di : distance from xi-1 to xi along z
Link twist i: angle between zi and zI+1 about xi
Here, d is zero, and alpha is zero
Xi+1
Zi+1 Zi ai
Өi+1 Xi

12. Non-Planar Joints Zi
Zi+1 Zi
dI+1
Өi+1