Comparison of 3-RPR Planar Parallel Manipulators with regard to their Dexterity and Sensitivity to Geometric Uncertainties

International audienceThis paper deals with the sensitivity analysis of 3-RPR planar parallel manipulators. First, the manipulators under study as well as their degeneracy conditions are presented. Then, an optimization problem is formulated in order to obtain their maximal regular dexterous workspace. Moreover, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically. Two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, we compare two non-degenerate and two degenerate 3-R\underline{P}R planar parallel manipulators with regard to their dexterity, workspace size and sensitivity. Finally, two actuating modes are compared with regard to their sensitivity

Kinematics, workspace and singularity analysis of a multi-mode parallel robot

A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity analysis of a 3-PRPiR parallel robot involving lockable Pi and R (revolute) joints. Here a Pi joint may act as a 1-DOF planar parallelogram if its lock-able P (prismatic) joint is locked or a 2-DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation modes to three 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation modes are dealt with in detail. The workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. A prototype built at Heriot-Watt University is used to illustrate the results of this work.Comment: International Design Engineering Technical Conferences \& Computers and Information in Engineering Conference, Aug 2017, Cleveland, United States. 201

The 3-PPPS parallel robot with U-shape Base, a 6-DOF parallel robot with simple kinematics

International audienceOne of the main problems associated with the use of 6 DOF parallel robots remains the solving of their kinematic models. This is rarely possible to analytically solve their models thereby justifying the application of numerical methods. These methods are difficult to implement in an industrial controller and can cause solution bifurcations close to singularities resulting in following an unplanned trajectory. Recently, a 3-PPPS robot with U-shaped base was introduced where an analytical kinematic model can be derived. Previously, quaternion parameters were used to represent the orientation of the mobile platform. To allow for simpler model handling, this article introduces the use of Euler angles which have a physical meaning for the users. Compact writing of the direct and inverse kinematic model is thus obtained. Using algebraic and cylindrical decomposition for the workspace, this provides a simpler representation of the largest domain without singularity around the " home " configuration

Workspace, Joint space and Singularities of a family of Delta-Like Robot

International audienceThis paper presents the workspace, the joint space and the singularities of a family of delta-like parallel robots by using algebraic tools. The different functions of SIROPA library are introduced, which is used to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Groebner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three-dimensional plotting describing the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations

Augmentation de la taille de l’espace de travail opérationnel des robots parallèles en traversant les singularités de Type 2 :Génération de trajectoires optimales et commande avancée

In order to increase the size of the operational workspace of parallel robots (largely reduced by the presence of singularities), the approach proposed in this thesis consists of directly moving a mechanism through those singularities.To do so, the conditions of degeneracy of the dynamic model of parallel robots are first studied. From those conditions, it is possible to create criteria that ensure the non-degeneracy of the mechanism in a singular configuration. This allows the planning of trajectories that go from one aspect of the workspace to another through a singularity, and without anydegeneracy of the dynamic model. In order to track those trajectories, a multi-model computed torque control is presented, coupled with an optimal trajectory planning strategy.Every development presented have been validated in simulation and experimentally on a prototype of a five-bar mechanism designed and manufactured during the thesis.Afin d’augmenter la taille de l’espace de travail opérationnel des robots parallèles (largement réduit par la présence de singularités), cette thèse propose une approche consistant à traverser ces singularités.Pour permettre cette traversée, les conditions de dégénérescence du modèle dynamique des mécanismes parallèles sont d’abord étudiées. Cette étude permet de mettre en place des conditions de non dégénérescence sous forme de critères. En planifiant une trajectoire respectant ces critères, un mécanisme parallèle peut théoriquement traverserune singularité sans que les efforts ne divergent. Un contrôleur basé sur une commande en couples-calculés multi-modèle et dédié à la traversée de singularité, couplé avec une stratégie de planification de trajectoire optimale est par la suite proposé. L’ensemble des travaux présentés est validé en simulation puis expérimentalement sur un prototype de mécanismes à cinq barres développé et conçu durant la thèse

Cusp points in the parameter space of degenerate planar 3-RPR parallel manipulators

This paper investigates the conditions in the design parameter space for the existence and distribution of the cusp locus for planar parallel manipulators. Cusp points make possible nonsingular assembly-mode changing motion, which increases the maximum singularity-free workspace. An accurate algorithm for the determination is proposed amending some imprecisions done by previous existing algorithms. This is combined with methods of cylindric algebraic decomposition, Gröbner bases, and discriminant varieties in order to partition the parameter space into cells with constant number of cusp points. These algorithms will allow us to classify a family of degenerate 3-RPR manipulators. © 2012 American Society of Mechanical Engineers.The authors would like to acknowledge the financial support of this research by ANR Project SiRoPa. The first and second authors have been supported for this research by two postdoctoral contracts at the Institut de Recherche en Communications et Cybernétique de Nantes under the sponsorship of the same project. .Peer Reviewe