Dr M. Bouri, Septembre Partie 2 Robotique Parallèle - PDF

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1 Partie 2 Robotique Parallèle 2 Robots Parallèles Définitions Robots à chaines cinématiques fermées Moteurs sur la base Nacelle Fermeture de la boucle 3 Parallel structures are characterized by two aspects

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1 Partie 2 Robotique Parallèle 2 Robots Parallèles Définitions Robots à chaines cinématiques fermées Moteurs sur la base Nacelle Fermeture de la boucle 3 Parallel structures are characterized by two aspects 1. All the kinematic chains from the basis to the mobile parts are closed to the basis. 2. All the motors are on the basis and no one is on the structure. The intermediate joints in the structure are all passive. 4 4-bar linkage mechanism 5 Parallel link to remote an actuator and make the link stiffer 6 Parallel link to remote an actuator and make the link stiffer 7 Parallel Robots Since When? The oldest «known» is Pollard robot (Pollard 1938) invented by Mr Pollard 8 The Pollard developed at EPFL The Movie Observe the motors 9 Parallel robotics : The key! 1. No actuated joints (no motors) on the structure 2. The mouvement of the mobile plate (Nacelle) depends on the type of the passive joints So obvious! 10 Parallel kinematics. The Most known 11 A particular parallel robot The Delta robot Patented by R. Clavel (EPFL) in 1985 Has been the precursor for the parallel robotics market. Figure Principle It is industrialized since 1988 by the Swiss company Demaurex SA (currently Bosch Packaging Technology Unit, Romanel). Figure Pattent 12 Currently, numerous big companies are proposing parallel robots in their catalog: 1. Mitsubishi that proposes the double Scara robot. 2. ABB (with his Delta FlexPicker). 3. Bosch that acquired the company Demaurex proposing the Delta robot. 4. Adept that is proposing the Quattro robot 5. Fanuc that proposes different variants of the Delta robot. Fanuc ABB Bosch 13 The Delta.. 14 Dr M. Bouri, Septembre 2013 15 The joints 16 Simplicity of the Delta Moteur + réducteur + Bras + Barres parallèles Moteur + réducteur + Bras + Barres parallèles Moteur + réducteur + Bras + Barres parallèles + Nacelle 17 Some Variants of the Delta Angular Delta with 4 DOF Additional DOF : Serial or Parallel? 18 Dr M. Bouri, Septembre 2013 19 Linear Variants of the Delta Link_Delta Vert 20 Linear Variants of the Delta - inclinated axis : The Keops Movie Keops 21 Some Variants of the Delta Angular and linear Delta : The IBIS 22 Rotations. With the Delta The Thales Movie Thales Dr M. Bouri, Septembre 2013 23 Thales Another realisation Initial kinematics Dedicated kinematics for laparoscopic surgery with an ex-centered tool 24 The Tricept 25 The Tricept Which DOF? 26 The Colibri 27 Platforms 6 DDL 28 Robots Parallèles Les +connus : La plateforme de Stewart 29 Platforms 6 DDL The Stewart platform 30 Platforms 6 DDL 31 Platforms 5 DDL The Alfa5 32 Calcul de mobilité d un robot. La mobilité d un robot est une image de son nombre de degrés de liberté. C est l ensemble des mobilités des éléments constituants le robots en considérant bien sûre les contraintes cinématiques de la structure. Dans le cas d un robot sériel, la mobilité est égale au nombre de moteurs : c est la dimension de l espace articulaire. Dans le cas d un robot parallèle, Il existe des formule permettant de calculer la mobilité Formule de Grübler. Formule des boucles. Formule de Grübler By considering a kinematic structure composed by n solid elements, the degrees of freedom (called DOF or Mobility MO) of this set of elements before any assembly is obviously equal to MO = 6. n (each element has 6 spatial DOF). Each link between 2 elements reduces the total mobility by a value corresponding to the number of the generalized forces (NGF) in the considered link. With k joints, the mobility is computed as follows: MO = 6n k i=1 NGF i The number of the generalized forces (NGF i ) involved in a considered joint is a complementary to 6 of the number of the degrees of freedom (MO i ). We then obtain: NGF i = 6 MO i k And hence: MO = 6n 6k + i=1 MO i k That gives: MO = 6(n k) + i=1 MO i By considering that one element of the structure is fixed on the frame, its 6 DOF must be differentiated from the total mobility number MO. We obtain: 33 MO = 6(n k 1) + k i=1 MO i 34 Computing Mobility of a robot Using the loops 35 Exemple 1, Donner la représentation cinématique d un Delta avec des cardans. Calculer sa mobilité. Que conclure. Representation of one kinematic chain 36 Représentation cinématique Basis Active Pivot Pivot Cardan Cardan joints Spherical joint Mobile Plate 37 Calcul de la mobilité By applying the Grübler formula, we have: The number of elements of the structure is n = 8 ( ) {1 basis + 1 mobile plate + 3 arms + 3 forearms}. The number of joints k =9 {(1 pivot + 2 cardans) X 3 identical links}. The mobility of the pivot is equal to 1. The mobility of each cardan is equal to 2. The total mobility of this Delta is then computed as follows: MO = = = 3 38 Exercice, Donner la représentation cinématique d un Delta avec des barres parallèles. Calculer sa mobilité. Que conclure. Basis Active Pivot Cardan joints Mobile Plate Dr M. Bouri, Septembre 2013 39 Représentation cinématique Basis Active Pivot Pivot Cardan Spherical joints Spherical joint Mobile Plate 40 Calcul de la mobilité By applying the Grübler formula to the spherical joint based Delta robot, we have: The number of elements of the structure is n = 11 ( ) {1 basis + 1 mobile plate + 3 arms + 6 bars}. The number of joints k =15 {(1 pivot + 4 spherical joints) X 3 identical links}. The mobility of the pivot is equal to 1. The mobility of each spherical joint is equal to 3. The total mobility of this Delta is then computed as follows: MO = = = 9 41 Observation The Delta robot as designed with the parallel bars and spherical joints has 6 supplementary mobilities. These mobilities concern internal mobilities not affecting the pure translation of the mobile plate. They are actually related to the rotation of each bar around its principal axis. 42 Hyperguidage Robot Omega à retour de force 43 Représentation cinématique Pivot Cardan Spherical joint 44 Calcul de la mobilité By applying the Grübler formula to the Omega Delta robot, we have: The number of elements of the structure is n = 17 (1+1+5 X 3) {1 basis + 1 mobile plate + 5 elements X 3}. The number of joints k =21 {(1 pivot + 4 spherical joints) X 3 identical links}. The mobility of each pivot is equal to 1. The total mobility of this Delta is then computed as follows: MO = = 9 Hyperguidage of order 12 45 Dr M. Bouri, Septembre 2013 46 Dr M. Bouri, Septembre 2013 47 Dr M. Bouri, Septembre 2013 48 Dr M. Bouri, Septembre 2013 49 Pourquoi la Nacelle du Delta est-elle totalement bloquée en rotation? 50 Exemple de singularités du Delta Moments de blockage Rotations libres (non bloquées) Aucun moment de blockage vertical- La nacelle tourney autour d elle même 51 Video Tokyo 52 Dr M. Bouri, Septembre 2013
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