An Optimization-Based Algorithm for Determination of Inclusive and Constant Orientation Workspace of Parallel Mechanisms

2009 ◽  
Author(s):  
Gholamreza Vossoughi ◽  
Soroosh Hassanpour ◽  
Amir Fazeli ◽  
Mehdi Paak
Keyword(s):  
Optimization Technique ◽  
Optimization Methods ◽  
Optimization Approach ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Boundary Determination ◽  
Spatial Parallel Mechanism ◽  
Forward Kinematic ◽  
Orientation Workspace

Workspace of a mechanism is generally defined as the region of space which end-effector of that mechanism can reach. Determination of workspace is an important task in the design of a mechanism. However, for parallel mechanisms, due to the complexity of solving the forward kinematic equations, determination of workspace is much more complicated than for serial mechanisms. In the literature, time-consuming numerical methods, such as point-by-point searching, are usually employed for this purpose. In this paper, an optimization-based algorithm is introduced for the boundary determination of inclusive and constant orientation workspaces of parallel mechanisms. In the proposed algorithm, thanks to applying the optimization approach along with point-by-point searching, the dimension of the point-by-point searched space (and hence, the consumed time) are significantly reduced. While different optimization methods can be used in the proposed algorithm, Particle Swarm Optimization is utilized as the optimization technique in this paper. The proposed algorithm is illustrated through its application to a planar and a spatial parallel mechanism.

A Geometric Constructive Approach for the Workspace Analysis of Symmetrical 5-PRUR Parallel Mechanisms (3T2R)

2010 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Mohammad Hossein Saadatzi ◽  
Cle´ment Gosselin ◽  
Hamid D. Taghirad
Keyword(s):  
Geometric Approach ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
End Effector ◽  
Workspace Analysis ◽  
Architecture Optimization ◽  
Insight Into ◽  
Orientation Workspace

This paper investigates an important kinematic property, the constant-orientation workspace, of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical limbs of the PRUR type. The general mechanism originates from the type synthesis performed for symmetrical 5-DOF parallel mechanism. In this study, the emphasis is placed on the determination of constant-orientation workspace using geometrical interpretation of the so-called vertex space, i.e., motion generated by a limb for a given orientation, rather than relying on classical recipes, such as discretization methods. For the sake of better understanding a CAD model is also provided for the vertex space. The constructive geometric approach presented in this paper provides some insight into the architecture optimization. Moreover, this approach facilitates the computation of the evolution of the volume of the constant-orientation workspace for different orientations of the end-effector.

Analyses of Error and Precision of 6-DOF Platform

2012 ◽  
Vol 591-593 ◽  
pp. 2081-2086 ◽  
Author(s):  
Rui Ren ◽  
Chang Chun Ye ◽  
Guo Bin Fan
Keyword(s):  
Inverse Kinematics ◽  
Newton Iteration ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
C Programming Language ◽  
C Programming ◽  
Manufacturing Tolerances ◽  
Parallel Robotics ◽  
Forward Kinematic

A particular subset of 6-DOF parallel mechanisms is known as Stewart platforms (or hexapod). Stewart platform characteristic analyzed in this paper is the effect of small errors within its elements (strut lengths, joint placement) which can be caused by manufacturing tolerances or setting up errors or other even unknown sources to end effector. The biggest kinematics problem is parallel robotics which is the forward kinematics. On the basis of forward kinematic of 6-DOF platform, the algorithm model was built by Newton iteration, several computer programs were written in the MATLAB and Visual C++ programming language. The model is effective and real-time approved by forwards kinematics, inverse kinematics iteration and practical experiment. Analyzing the resource of error, get some related spectra map, top plat position and posture error corresponding every error resource respectively. By researching and comparing the error spectra map, some general results is concluded.

Extending the workspace of parallel working mechanisms

2008 ◽  
Vol 222 (7) ◽  
pp. 1305-1313 ◽  
Author(s):  
H Alp ◽  
İ Özkol
Keyword(s):  
Material Processing ◽  
Flight Simulation ◽  
Parallel Mechanisms ◽  
Working Mechanism ◽  
Workspace Analysis ◽  
Cylindrical Coordinate ◽  
Robotic Applications ◽  
Orientation Workspace ◽  
Working Mechanisms

The aim of this study is to present a new model to extend the workspace of a parallel working machine in a chosen direction. Therefore, the existing mathematical models are combined and developed to represent the extension of the workspace of a 6° parallel working machine. For this purpose, the 6-3 Stewart platform mechanism (SPM), which is commonly used in robotic applications, material processing, and flight simulation, and the 6-4 SPM have been chosen. Although there are many studies on parallel mechanisms, the workspace analysis of a parallel working mechanism has not yet been generalized. This study determines the workspace of a parallel working mechanism in the direction perpendicular to the moving platform, which is the most workable direction. For these types of working mechanisms, i.e. mechanical tools used for material processing that is forced to move in a certain chosen direction, the determination of the point in that direction at which the workspace is maximum has to be outlined. After carrying out a kinematic analysis, the discretization method, which is based on Euler angles, is used to represent the orientation workspace of these parallel working mechanisms. Additionally, the orientation workspaces of the 6-3 SPM and the 6-4 SPM are compared. Results are presented in a cylindrical coordinate system.

Kinematic Analysis and Design of Planar Parallel Mechanisms Actuated With Cables

2000 ◽  
Author(s):  
Guillaume Barrette ◽  
Clément M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Analysis And Design ◽  
Spring Mechanism

Abstract In this paper, we present a general and systematic analysis of planar parallel mechanisms actuated with cables. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is denned, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable sub-workspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Guillaume Barrette ◽  
Cle´ment M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Two Dimensional ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Spring Mechanism

In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Kinematic Analysis and Singularity Representation of 5-RPRRR Parallel Mechanisms

2007 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin
Keyword(s):  
Algebraic Geometry ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Parallel Mechanisms ◽  
Inverse Kinematic Problem ◽  
Kinematic Geometry ◽  
Kinematic Properties ◽  
Orientation Workspace ◽  
Principal Contribution

This paper presents a novel type of five-degree-of-freedom parallel mechanism generating the 3T2R motion with linear inputs. The kinematic geometry of the mechanism is presented and several important kinematic issues including the inverse kinematic problem, the vector-loop velocity equations, the constant orientation workspace and the singularity configurations are investigated. The principal contribution of this study is the determination of the workspace based on algebraic geometry (Bohemian domes) and the study of the the singularity configurations. Based on the results, some optimization hints are proposed to refine the kinematic properties.

Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system

Robotica ◽  
2014 ◽  
Vol 33 (08) ◽  
pp. 1686-1703 ◽  
Author(s):  
Mohammad Reza Chalak Qazani ◽  
Siamak Pedrammehr ◽  
Arash Rahmani ◽  
Behzad Danaei ◽  
Mir Mohammad Ettefagh ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
High Acceleration ◽  
Workspace Analysis ◽  
Rotation Symmetric ◽  
Cloud Of Points

SUMMARYParallel mechanisms possess several advantages such as the possibilities for high acceleration and high accuracy positioning of the end effector. However, most of the proposed parallel manipulators suffer from a limited workspace. In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced. Since parallel mechanisms have more workspace limitations compared to that of serial mechanisms, determination of the workspace in parallel manipulators is of the utmost importance. For finding position, angular velocity, and acceleration, in this paper, inverse and forward kinematics of the mechanism are studied and after presenting the workspace limitations, workspace analysis of the hexarot manipulator is performed by using MATLAB software. Next, using the obtained cloud of points from simulation, the overall borders of the workspace are illustrated. Finally, it is shown that this manipulator has the important benefits of combining a large positional workspace in relation to its footprint with a sizable range of platform rotations.

Geometric Determination of the Interference-Free Constant-Orientation Workspace of Parallel Cable-Driven Mechanisms

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Simon Perreault ◽  
Philippe Cardou ◽  
Clément M. Gosselin ◽  
Martin J.-D. Otis
Keyword(s):  
High Probability ◽  
Three Dimensional ◽  
Design Stage ◽  
Fast Method ◽  
Dimensional Problem ◽  
Mechanical Contact ◽  
End Effector ◽  
Free Constant ◽  
Orientation Workspace

The increasing use of parallel cable-driven mechanisms calls for a better understanding of their behavior and highly efficient algorithms to attenuate their drawbacks at the design stage. One of these drawbacks is the high probability of mechanical interferences between the moving parts of the mechanism. In this paper, the phenomenon is described under the assumption that a cable is a line segment in space. When a mechanical contact occurs between two cables or between a cable and an edge of the end effector, these entities necessarily lie in the same plane, and then the three-dimensional problem becomes two-dimensional. This fact is used to simplify the equations, and leads to exhaustive descriptions of the associated interference loci in the constant-orientation workspace of a cable-driven mechanism. These results provide a fast method to graphically represent all interference regions in the manipulator workspace, given its geometry and the orientation of its end effector.

scholarly journals Heuristic Optimization of Overloading Due to Electric Vehicles in a Low Voltage Grid

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6069
Author(s):  
Sajjad Haider ◽  
Peter Schegner
Keyword(s):  
Electric Vehicles ◽  
Low Voltage ◽  
Optimization Methods ◽  
Monte Carlo Analysis ◽  
Heuristic Optimization ◽  
Optimization Approach ◽  
Worst Case ◽  
Voltage Drops ◽  
The Individual ◽  
Nodal Voltage

It is important to understand the effect of increasing electric vehicles (EV) penetrations on the existing electricity transmission infrastructure and to find ways to mitigate it. While, the easiest solution is to opt for equipment upgrades, the potential for reducing overloading, in terms of voltage drops, and line loading by way of optimization of the locations at which EVs can charge, is significant. To investigate this, a heuristic optimization approach is proposed to optimize EV charging locations within one feeder, while minimizing nodal voltage drops, cable loading and overall cable losses. The optimization approach is compared to typical unoptimized results of a monte-carlo analysis. The results show a reduction in peak line loading in a typical benchmark 0.4 kV by up to 10%. Further results show an increase in voltage available at different nodes by up to 7 V in the worst case and 1.5 V on average. Optimization for a reduction in transmission losses shows insignificant savings for subsequent simulation. These optimization methods may allow for the introduction of spatial pricing across multiple nodes within a low voltage network, to allow for an electricity price for EVs independent of temporal pricing models already in place, to reflect the individual impact of EVs charging at different nodes across the network.

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