304 research outputs found
Kinematic analysis of the 3-RPR parallel manipulator
The aim of this paper is the kinematic study of a 3-RPR planar parallel
manipulator where the three fixed revolute joints are actuated. The direct and
inverse kinematic problem as well as the singular configuration is
characterized. On parallel singular configurations, the motion produce by the
mobile platform can be compared to the Reuleaux straight-line mechanism
Pose, posture, formation and contortion in kinematic systems
The concepts of pose, posture, formation and contortion are defined for serial, parallel and hybrid kinematic systems. Workspace and jointspace structure is examined in terms of these concepts. The inter-relationships of pose, posture, formation and contortion are explored for a range of robot workspace and jointspace types
Design of reconfigurable planar parallel robot
A 3-RPR planar parallel robot is a kind of planar mechanism; three prismatic actuators connected with the end effector in parallel.
This thesis will begin with the kinematic analysis for the manipulator to determinate the optimized dimension of the manipulator, including the workspace analysis, determinate of Jacobian analysis, and Direction Selective Index (DSI) analysis.
Secondly, a multi-body bond graph system will be built for the 3-RPR planar parallel manipulator (PPM), along with three PID controllers, which give commands to three DC motors respectively. The advantage of bond graphs is that they can integrate different types of dynamics systems. The manipulator, the control and the motor can be modelled and simulated altogether in the same process. The bond graph will be established for each rigid body with body-fixed coordinate’s reference frames, which are connected with parasitic elements (damping and compliance) to each other. Furthermore, Virtual Work method will be used to evaluate the previous dynamic analysis result.
Eventually, the Solidworks design will be demonstrated with images, which show the overall appearance and a detailed drawing of this project. After the mechanical design of the manipulator is finished, the controller design is considered as a future work to conduct
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
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
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
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
On the false positives and false negatives of the Jacobian Matrix in kinematically redundant parallel mechanisms
The Jacobian matrix is a highly popular tool for the control and performance analysis of closed-loop robots. Its usefulness in parallel mechanisms is certainly apparent, and its application to solve motion planning problems, or other higher level questions, has been seldom queried, or limited to non-redundant systems. In this paper, we discuss the shortcomings of the use of the Jacobian matrix under redundancy, in particular when applied to kinematically redundant parallel architectures with non-serially connected actuators. These architectures have become fairly popular recently as they allow the end-effector to achieve full rotations, which is an impossible task with traditional topologies. The problems with the Jacobian matrix in these novel systems arise from the need to eliminate redundant variables when forming it, resulting in both situations where the Jacobian incorrectly identifies singularities (false positive), and where it fails to identify singularities (false negative). These issues have thus far remained unaddressed in the literature. We highlight these limitations herein by demonstrating several cases using numerical examples of both planar and spatial architectures
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
- …