160,042 research outputs found
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
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
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
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
Working and Assembly Modes of the Agile Eye
This paper deals with the in-depth kinematic analysis of a special spherical
parallel wrist, called the Agile Eye. The Agile Eye is a three-legged spherical
parallel robot with revolute joints in which all pairs of adjacent joint axes
are orthogonal. Its most peculiar feature, demonstrated in this paper for the
first time, is that its (orientation) workspace is unlimited and flawed only by
six singularity curves (rather than surfaces). Furthermore, these curves
correspond to self-motions of the mobile platform. This paper also demonstrates
that, unlike for any other such complex spatial robots, the four solutions to
the direct kinematics of the Agile Eye (assembly modes) have a simple geometric
relationship with the eight solutions to the inverse kinematics (working
modes)
A Framework to Illustrate Kinematic Behavior of Mechanisms by Haptic Feedback
The kinematic properties of mechanisms are well known by the researchers and
teachers. The theory based on the study of Jacobian matrices allows us to
explain, for example, the singular configuration. However, in many cases, the
physical sense of such properties is difficult to explain to students. The aim
of this article is to use haptic feedback to render to the user the
signification of different kinematic indices. The framework uses a Phantom Omni
and a serial and parallel mechanism with two degrees of freedom. The
end-effector of both mechanisms can be moved either by classical mouse, or
Phantom Omni with or without feedback
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
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