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Kinematics Intro

Animation. 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). ScriptingKinematics (specify poses without regard to forces). .

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Kinematics Intro

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

    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

    5. Hierarchical Kinematic Modeling Closely related to robotics

    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 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:

    11. Joint Parameters Joint angle ?i: 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

    12. Non-Planar Joints

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