24 research outputs found
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
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
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
An Exhaustive Study of the Workspaces Tolopogies of all 3R Orthogonal Manipulators with Geometric Simplifications
International audienceThis paper proposes a classification of three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The manipulators are classified into different types with similar kinematic properties. Each type is evaluated according to interesting kinematic properties such as, whether the workspace is fully reachable with four inverse kinematic solutions or not, the existence of voids, and the feasibility of continuous trajectories in the workspace. It is found that several orthogonal manipulators have a "well-connected" workspace, that is, their workspace is fully accessible with four inverse kinematic solutions and any continuous trajectory is feasible. This result is of interest for the design of alternative manipulator geometries