89 research outputs found
An Algorithm for Computing Cusp Points in the Joint Space of 3-RPR Parallel Manipulators
This paper presents an algorithm for detecting and computing the cusp points
in the joint space of 3-RPR planar parallel manipulators. In manipulator
kinematics, cusp points are special points, which appear on the singular curves
of the manipulators. The nonsingular change of assembly mode of 3-RPR parallel
manipulators was shown to be associated with the existence of cusp points. At
each of these points, three direct kinematic solutions coincide. In the
literature, a condition for the existence of three coincident direct kinematic
solutions was established, but has never been exploited, because the algebra
involved was too complicated to be solved. The algorithm presented in this
paper solves this equation and detects all the cusp points in the joint space
of these manipulators
Changing Assembly Modes without Passing Parallel Singularities in Non-Cuspidal 3-R\underline{P}R Planar Parallel Robots
This paper demonstrates that any general 3-DOF three-legged planar parallel
robot with extensible legs can change assembly modes without passing through
parallel singularities (configurations where the mobile platform loses its
stiffness). While the results are purely theoretical, this paper questions the
very definition of parallel singularities.Comment: 2nd International Workshop on Fundamental Issues and Future Research
Directions for Parallel Mechanisms and Manipulators, Montpellier : France
(2008
A study of the singularity locus in the joint space of planar parallel manipulators: special focus on cusps and nodes
Cusps and nodes on plane sections of the singularity locus in the joint space
of parallel manipulators play an important role in nonsingular assembly-mode
changing motions. This paper analyses in detail such points, both in the joint
space and in the workspace. It is shown that a cusp (resp. a node) defines a
point of tangency (resp. a crossing point) in the workspace between the
singular curves and the curves associated with the so-called characteristics
surfaces. The study is conducted on a planar 3-RPR manipulator for illustrative
purposes.Comment: 4th International Congress Design and Modeling of Mechanical Systems,
Sousse : Tunisia (2011
On the determination of cusp points of 3-R\underline{P}R parallel manipulators
This paper investigates the cuspidal configurations of 3-RPR parallel
manipulators that may appear on their singular surfaces in the joint space.
Cusp points play an important role in the kinematic behavior of parallel
manipulators since they make possible a non-singular change of assembly mode.
In previous works, the cusp points were calculated in sections of the joint
space by solving a 24th-degree polynomial without any proof that this
polynomial was the only one that gives all solutions. The purpose of this study
is to propose a rigorous methodology to determine the cusp points of
3-R\underline{P}R manipulators and to certify that all cusp points are found.
This methodology uses the notion of discriminant varieties and resorts to
Gr\"obner bases for the solutions of systems of equations
Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot
Having non-singular assembly modes changing trajectories for the 3-RPS
parallel robot is a well-known feature. The only known solution for defining
such trajectory is to encircle a cusp point in the joint space. In this paper,
the aspects and the characteristic surfaces are computed for each operation
mode to define the uniqueness of the domains. Thus, we can easily see in the
workspace that at least three assembly modes can be reached for each operation
mode. To validate this property, the mathematical analysis of the determinant
of the Jacobian is done. The image of these trajectories in the joint space is
depicted with the curves associated with the cusp points
Uniqueness domains and non singular assembly mode changing trajectories
Parallel robots admit generally several solutions to the direct kinematics
problem. The aspects are associated with the maximal singularity free domains
without any singular configurations. Inside these regions, some trajectories
are possible between two solutions of the direct kinematic problem without
meeting any type of singularity: non-singular assembly mode trajectories. An
established condition for such trajectories is to have cusp points inside the
joint space that must be encircled. This paper presents an approach based on
the notion of uniqueness domains to explain this behaviour
Cusp Points in the Parameter Space of Degenerate 3-RPR Planar 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 non-singular 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,
Gr\"obner 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.Comment: ASME Journal of Mechanisms and Robotics (2012) 1-1
Non-Singular Assembly Mode Changing Trajectories of a 6-DOF Parallel Robot
International audienceThis paper deals with the non-singular assembly mode changing of a six degrees of freedom parallel manipulator. The manipulator is composed of three identical limbs and one moving platform. Each limb is composed of three prismatic joints of directions orthogonal to each other and one spherical joint. The first two prismatic joints of each limb are actuated. The planes normal to the directions of the first two prismatic joints of each limb are orthogonal to each other. It appears that the parallel singularities of the manipulator depend only on the orientation of its moving platform. Moreover, the manipulator turns to have two aspects, namely, two maximal singularity free domains without any singular configuration, in its orientation workspace. As the manipulator can get up to eight solutions to its direct kinematic model, several assembly modes can be connected by non-singular trajectories. It is noteworthy that the images of those trajectories in the joint space of the manipulator encircle one or several cusp point(s). This property can be depicted in a three dimensional space because the singularities depend only on the orientation of the moving-platform and the mapping between the orientation parameters of the manipulator and three joint variables can be obtained with a simple change of variables. Finally, to the best of the authors' knowledge, this is the first spatial parallel manipulator for which non-singular assembly mode changing trajectories have been found and shown
Kinematic analysis of a class of analytic planar 3-RPR parallel manipulators
A class of analytic planar 3-RPR manipulators is analyzed in this paper.
These manipulators have congruent base and moving platforms and the moving
platform is rotated of 180 deg about an axis in the plane. The forward
kinematics is reduced to the solution of a 3rd-degree polynomial and a
quadratic equation in sequence. The singularities are calculated and plotted in
the joint space. The second-order singularities (cups points), which play an
important role in non-singular change of assembly-mode motions, are also
analyzed
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