27 research outputs found
Singularity Analysis of Limited-dof Parallel Manipulators using Grassmann-Cayley Algebra
This paper characterizes geometrically the singularities of limited DOF
parallel manipulators. The geometric conditions associated with the dependency
of six Pl\"ucker vector of lines (finite and infinite) constituting the rows of
the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra.
Manipulators under consideration do not need to have a passive spherical joint
somewhere in each leg. This study is illustrated with three example robot
Singularity Analysis of Lower-Mobility Parallel Manipulators Using Grassmann-Cayley Algebra
This paper introduces a methodology to analyze geometrically the
singularities of manipulators, of which legs apply both actuation forces and
constraint moments to their moving platform. Lower-mobility parallel
manipulators and parallel manipulators, of which some legs do not have any
spherical joint, are such manipulators. The geometric conditions associated
with the dependency of six Pl\"ucker vectors of finite lines or lines at
infinity constituting the rows of the inverse Jacobian matrix are formulated
using Grassmann-Cayley Algebra. Accordingly, the singularity conditions are
obtained in vector form. This study is illustrated with the singularity
analysis of four manipulators
Kinematics and workspace analysis of a 3ppps parallel robot with u-shaped base
This paper presents the kinematic analysis of the 3-PPPS parallel robot with
an equilateral mobile platform and a U-shape base. The proposed design and
appropriate selection of parameters allow to formulate simpler direct and
inverse kinematics for the manipulator under study. The parallel singularities
associated with the manipulator depend only on the orientation of the
end-effector, and thus depend only on the orientation of the end effector. The
quaternion parameters are used to represent the aspects, i.e. the singularity
free regions of the workspace. A cylindrical algebraic decomposition is used to
characterize the workspace and joint space with a low number of cells. The
dis-criminant variety is obtained to describe the boundaries of each cell. With
these simplifications, the 3-PPPS parallel robot with proposed design can be
claimed as the simplest 6 DOF robot, which further makes it useful for the
industrial applications
A Six-Dof Epicyclic-Parallel Manipulator
International audienceA new six-dof epicyclic-parallel manipulator with all actuators allocated on the ground is introduced. It is shown that the system has a considerably simple kinematics relationship, with the complete direct and inverse kinematics analysis provided. Further, the first and second links of each leg can be driven independently by two motors. The serial and parallel singularities of the system are determined, with an interesting feature of the system being that the parallel singularity is independent of the position of the end-effector. The workspace of the manipulator is also analyzed with future applications in haptics in mind
New geometric approaches to the analysis and design of Stewart-Gough platforms
In general, rearranging the legs of a Stewart-Gough platform, i.e., changing the locations of its leg attachments, modifies the platform singularity locus in a rather unexpected way. Nevertheless, some leg rearrangements have been recently found to leave singularities invariant. Identification of such rearrangements is useful not only for the kinematic analysis of the platforms, but also as a tool to redesign manipulators avoiding the implementation of multiple spherical joints, which are difficult to construct and have a small motion range. In this study, a summary of these singularity-invariant leg rearrangements is presented, and their practical implications are illustrated with several examples including well-known architectures.The authors gratefully acknowledge funding from the Generalitat de Catalunya through the Robotics group (SRG0155).Peer Reviewe
A general method for the numerical computation of manipulator singularity sets
The analysis of singularities is central to the development and control of a manipulator. However, existing methods for singularity set computation still concentrate on specific classes of manipulators. The absence of general methods able to perform such computation on a large class of manipulators is problematic because it hinders the analysis of unconventional manipulators and the development of new robot topologies. The purpose of this paper is to provide such a method for nonredundant mechanisms with algebraic lower pairs and designated input and output speeds. We formulate systems of equations that describe the whole singularity set and each one of the singularity types independently, and show how to compute the configurations in each type using a numerical technique based on linear relaxations. The method can be used to analyze manipulators with arbitrary geometry, and it isolates the singularities with the desired accuracy. We illustrate the formulation of the conditions and their numerical solution with examples, and use 3-D projections to visualize the complex partitions of the configuration space induced by the singularities.Preprin
Contribution à l'étude cinématique et dynamique des machines parallèles
This thesis deals with the kinematic and dynamic modelling of limited degree-of-freedom parallel robots. These robots with less than six degrees of freedom are able to carry out several industrial tasks. The main reason of using such robots is to reduce the production costs by using less legs and motors. However, in some cases, these structures can produce a complex motion defined as a simultaneous combination of translation and rotation of the moving platform, which is the case of the Verne parallel module having three translation degrees of freedom. The modelling of this type of robots can prove to be complicated. This report includes five chapters. In the first chapter, a classification of parallel architectures is presented and a state of the art on important notions on kinematics and design of manipulators is exposed. The second and the third chapters are devoted to the kinematic modelling, serial singularity analysis and workspace calculation of the Verne machine. The fourth chapter deals with parallel singularity analysis of limited degrees of freedom robots using Grassmann-Cayley algebra. The geometrical conditions of existence of parallel singularities of three classes of parallel manipulators are found. Finally, the fifth chapter covers the dynamic modelling of limited degree-of-freedom parallel manipulators. A general method based on the Newton-Euler algorithm is developed. The proposed method takes in consideration all the dynamics of these robots including the legs dynamics as well as the mobile platform dynamics.Les travaux présentés dans cette thèse portent sur l’étude cinématique et dynamique des robots parallèles à mobilités restreintes. Ces robots à moins de 6 degrés de liberté permettent d’effectuer de multiples tâches demandées par l’industrie. La raison principale de l’utilisation de ces robots est la volonté de réduire le coût en utilisant moins de jambes et moins de moteurs. Cependant, ces structures peuvent dans certains cas produire un mouvement de la plate-forme contraint par un couplage entre la position et l’orientation comme pour le module parallèle de la machine Verne ayant trois degrés de liberté de translation. Dans ce cas, la modélisation peut s’avérer compliquée. Ce mémoire comporte cinq chapitres. Dans le premier chapitre, une classification des architectures parallèles est présentée et des notions importantes liées à la cinématique et à la conception des manipulateurs sont exposées. Les deuxième et troisième chapitres sont consacrés à la modélisation géométrique, à l’étude des singularités sérielles et au calcul de l’espace de travail de la machine Verne. Le quatrième chapitre traite les singularités parallèles des manipulateurs à mobilités restreintes en utilisant l’algèbre de Grassmann-Cayley. Les conditions géométriques d’existence des singularités pour trois classes de manipulateurs sont trouvées. Les chaînes de ces manipulateurs transmettent des forces et/ou couples à la plate-forme mobile. Finalement, le cinquième chapitre concerne la modélisation dynamique des manipulateurs à mobilités restreintes. Une méthode générale basée sur les algorithmes de type Newton-Euler est développée. La méthode proposée prend en compte la dynamique des jambes et de la plate-forme. Nous obtenons ainsi des modèles dynamiques complets de ces robots
New geometric approaches to the singularity analysis of parallel platforms
In general, rearranging the legs of a Stewart-
Gough platform, i.e., changing the locations of its leg attachments,
modifies the platform singularity locus in a rather
unexpected way. Nevertheless, some leg rearrangements have
been recently found to leave singularities invariant. In this
work, a summary of the some of such singularity-invariant leg
rearrangements are presented, and their practical consequences
are illustrated with several examples including well-known
architectures.Postprint (author’s final draft
A general method for the numerical computation of manipulator singularity sets
The analysis of singularities is central to the development and control of a manipulator. However, existing methods for singularity set computation still concentrate on specific classes of manipulators. The absence of general methods able to perform such computation on a large class of manipulators is problematic because it hinders the analysis of unconventional manipulators and the development of new robot topologies. The purpose of this paper is to provide such a method for nonredundant mechanisms with algebraic lower pairs and designated input and output speeds. We formulate systems of equations that describe the whole singularity set and each one of the singularity types independently, and show how to compute the configurations in each type using a numerical technique based on linear relaxations. The method can be used to analyze manipulators with arbitrary geometry, and it isolates the singularities with the desired accuracy. We illustrate the formulation of the conditions and their numerical solution with examples, and use 3-D projections to visualize the complex partitions of the configuration space induced by the singularities.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness under contract DPI2010-18449, and by a Juan de la Cierva contract supporting the fourth author.Peer Reviewe