forschungsschwerpunkte fakultät für bauingenieurwesen symbolic computation in mechanism and...
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TRANSCRIPT
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Symbolic Computation in Mechanism and Machine
Science
Manfred L. Husty
Inst. f. Basic Sciences in Engineering Unit Geometry and CAD
Overview
• Introduction
• Kinematic Mapping, Study Model of SE(3)
• Constraint Varieties for Mechanism Analysis and Synthesis
• Application to Mechanism Analysis– Direct Kinematics of Stewart-Gough Platforms
– Assembly modes of a nine-bar structure – Dixon’s mechanisms
– Architecture Singularity and Self Motions of Platform Manipulators (Griffis-Duffy Platforms)
– 6-AS-Manipulator
– Discussion of the Inverse Kinematics of General 6-R Manipulators
– 3UPU Analysis
• Application to Mechanism Synthesis – Synthesis of Bennett Mechanisms
• Conclusions
H-P. Schröcker, K. Brunnthaler, M. Pfurner, Dominic Walter, Jim Robinson
Basics
• Design parameter: parameters that determine the geometry and topology of the mechanism
• Joint coordinates: Lengths or angles of the actuators
• Cartesian coordinates: Parameters that determine the relative position and orientation of end-effector frame to base frame
• Workspace: set of all poses that can be reached by the manipulator in presence of limits of active and passive joints
• Direct Kinematics: Given: Design of the manipulator and joint parameter
Find: possible positions and orientations of the manipulator
• Inverse KinematicsGiven: Design of the manipulator and the pose of the end-effector
Find: joint parameters
Kinematic Mapping
kinematic image space (P7)
moving coordinate system
fixed coordinate system
Study quadric S62