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Mechanism and Robot Kinematics, Part I:
Algebraic Foundations
C= harles Wampler
General Motors R&D Center
<= /span>
In collaboration with
Andrew Sommese
University of Notre Dame
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Content-Location: file:///C:/4E4BB24E/Wampler_Kinematic_AlgebraicFoundation_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Wampler: Algebraic Foundations of Kinematics
2&#= 13;
Overview
nWhy kinematics is (mostly) algebraic geometry =
n= Rigid bodies with algebraic surfaces in contact &#= 13;
nA good approximation to the most common devices= 3;
nMechanism & robot types
n= Families and sub-families
n= Classification via type graphs <= /div>
nTypes of kinematic problems
n= Analysis: how does this mechanism move?
nMotion paths, workspace limits, singularities =
n= Synthesis: what mechanism will move this w= ay?
n= Exceptional (“overconstrained”) mechan= isms
n
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Kinematics: Then & Now
Model of Watt Engine, 1784
(http://kmoddl.library.cornell.edu/tutorials/05/)
Stewart-Gough robot
(Fanuc F200)
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Griffis-Duffy Platform
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Definition of a Mechanism
nA collection of links connected by joints.
nLinks are rigid bodies
nIn reality, not quite, but a good approximation
n“Compliant mechanisms” are another story
nJoints = are mechanical contacts between surfaces of two links
nPin joint (hinge), Ball-and-socket, etc.
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Rigid-Body Motion
nA rigid body has two defining properties:
nPreservation of distance
nPreservation of chirality (handedness)
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