Flagged Parallel Manipulators. F. Thomas (joint work with M. Alberich and C. Torras) Institut de Robòtica i Informàtica Industrial. Talk outline. PART I. Trilatelable Parallel Robots Forward kinematics Singularities Formulation using determinants

Download Presentation

Flagged Parallel Manipulators

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

Flagged Parallel Manipulators F. Thomas (joint work with M. Alberich and C. Torras) Institut de Robòtica i Informàtica Industrial

Talk outline PART I • Trilatelable Parallel Robots • Forward kinematics • Singularities • Formulation using determinants • Singularities as basic contacts between polyhedra • Generalization to serial robots

Talk outline PART II • Technical problems at singularities • The direct kinematics problem and singularities • The singularity locus • How to get rid of singularities? • Goal: Characterization of the singularity locus • Stratification of the singularity locus • Basic flagged parallel robot

Talk outline PART II • Why flagged? • Ataching flags to parallel robots • Equilalence between basic contacts and volumes of tetrahedra • Deriving the whole family of flagged parallel robots • Local transformations • Substituting of 2-leg groups by serial chains • Examples

Talk outline PART II • The direct kinematics of flagged parallel robots • Invariance of flags to certain transformations • Classical result from the flag manifold • Stratification of the flag manifold • From projective flags to affine flags • From afine flags to the configuration space of the platform • Strata of dimension 6 and 5 • Redundant flagged parallel robots

Talk outline PART II • Technical problems at singularities • The direct kinematics problem and singularities • The singularity locus • How to get rid of singularities? • Goal: Characterization of the singularity locus • Stratification of the singularity locus • Basic flagged parallel robot

Talk outline PART II • Why flagged? • Ataching flags to parallel robots • Equilalence between basic contacts and volumes of tetrahedra • Deriving the whole family of flagged parallel robots • Local transformations • Substituting of 2-leg groups by serial chains • Examples

Talk outline PART II • The direct kinematics of flagged parallel robots • Invariance of flags to certain transformations • Classical result from the flag manifold • Stratification of the flag manifold • From projective flags to affine flags • From afine flags to the configuration space of the platform • Strata of dimension 6 and 5 • Redundant flagged parallel robots

platform 6 legs base Technical problems at singularities The platform becomes uncontrollable at certain locations • It is not able to support weights • The actuator forces in the legs may become very large. Breakdown of the robot

The Direct Kinematics Problem and Singularities Direct finding location of platform with Kinematics respect to base from 6 leg lengths problem finding preimages of the forward kinematics mapping configuration spaceleg lengths space

The Singularity Locus Rank of the Jacobian of the kinematics mapping Singularity locus Branching locus of the number of ways of assembling the platform

How to get rid of singularities? • By operating in reduced workspaces • By adding redundant actuators Problems: • how to plan trajectories? • where to place the extra leg? In both cases we need a complete and precise characterization of the singularity locus

Goal: characterization of the singularity locus(nature and location) Configuration space Configuration space Two assembly modes are always separated by a singular region Branching locus Branching locus Leg lengths space Leg lengths space Two assembly modes can be connected by singularity-free paths

Basic flagged parallel robot • Three possible architectures for 3-3 parallel manipulators: octahedral flagged 3-2-1

Basic flagged parallel robot • One of the three possible architectures for 3-3 parallel manipulators: Trilaterable octahedral flagged 3-2-1

Attaching flags vertex - face contact edge - edge contact face - vertex contact

Attaching flags Attached flag to the platform Attached flag to the base

Why flagged? Because their singularities can be described in terms of incidences between two flags. But, what’s a flag?