An Interval Discretization Method for Workspace Determination of Parallel Mechanisms

2022 ◽  
Author(s):  
Pengda Ye ◽  
Jingjing You ◽  
Fengfeng Xi ◽  
Jieyu Wang ◽  
Yu Ru
Keyword(s):  
Discretization Method ◽  
Parallel Mechanisms

Analytic Determination of Wrench Closure Workspace of Spatial Cable Driven Parallel Mechanisms

2015 ◽  
Author(s):  
Zhiyu Sheng ◽  
Joon-Hyuk Park ◽  
Paul Stegall ◽  
Sunil K. Agrawal
Keyword(s):  
Simulation Study ◽  
Null Space ◽  
Boundary Surface ◽  
Parallel Mechanisms ◽  
Analytic Determination ◽  
Structure Matrix ◽  
Feasible Solutions

This paper proposes an efficient way of determining analytically the Wrench Closure Workspace (WCW) of spatial redundant cable-driven parallel mechanisms (CDPM). The method builds upon the boundary surface equations obtained from the null space of the structure matrix of CDPM. The set of feasible solutions is obtained that satisfies positive tension in the cables. This method was applied to characterize the WCW of spatial CDPM which has redundancy of 1 or 2. A simulation study was carried out to validate the accuracy and efficiency of the method. Several advantages over conventional approaches for determining the WCW were identified through simulation.

Determination of Singularity-Free Zones in the Workspace of Planar 3-P̱RR Parallel Mechanisms

2006 ◽  
Vol 129 (6) ◽  
pp. 649-652 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanisms ◽  
Numerical Examples ◽  
Mathematical Derivation

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-P̱RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach.

A novel numerical approach for workspace determination of parallel mechanisms

2017 ◽  
Vol 31 (6) ◽  
pp. 3005-3015 ◽  
Author(s):  
Yiqun Zhou ◽  
Junchuan Niu ◽  
Zhihui Liu ◽  
Fuliang Zhang
Keyword(s):  
Numerical Approach ◽  
Parallel Mechanisms

Determination of Maximal Singularity-Free Workspace of Parallel Mechanisms Using Constructive Geometric Approach

2013 ◽  
pp. 307-314
Author(s):  
Mohammad Hadi Farzaneh Kaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Behnam Mashhadi Gholamali
Keyword(s):  
Geometric Approach ◽  
Parallel Mechanisms ◽  
Maximal Singularity

scholarly journals Automatic Mobility Analysis of Parallel Mechanisms: An Algorithm Approach Based on Position and Orientation Characteristic Equations

2019 ◽  
Author(s):  
Xiaorong Zhu ◽  
Huiping Shen ◽  
Chengqi Wu ◽  
Damien Chablat ◽  
Tingli Yang
Keyword(s):  
Systematic Approach ◽  
Fundamental Problem ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Topological Structures ◽  
Design And Optimization ◽  
Logical Operations ◽  
Intelligent Analysis ◽  
Position And Orientation

Abstract The determination of the mobility of parallel mechanisms (PM) is a fundamental problem. An automatic and intelligent analysis software will be a significant tool for the design and optimization of mechanical systems. Based on the theory of position and orientation characteristics (POC) equations, a systematic approach to computer-aided mobility analysis of PMs is presented in this paper. First, a digital model for topological structures which has a mapping relationship with position and orientation characteristics of mechanism is proposed. It describes not only the dimension of the motion output, but also gives the mapping relationship between the output characteristic and the axis of the kinematic joints. Secondly, algorithmic rules are established that convert the union and intersection operations of POC into the binary logical operations and the automatic analysis of POC are realized. Then, the algorithm of the automatic mobility analysis of PMs and its implementation with VC++ are written. The mobility and its properties (POC) will also be analyzed and displayed automatically after introducing by users of the data of topological structures representation. Finally, typical examples are provided to show the effectiveness of the software platform.

Determination of Singularity-Free Zones in the Workspace of Planar Parallel Mechanisms with Revolute Actuators

2011 ◽  
Vol 121-126 ◽  
pp. 1992-1996 ◽  
Author(s):  
Shu Jun Li ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Parallel Mechanism ◽  
Numerical Results ◽  
Parallel Mechanisms ◽  
Kinematic Design ◽  
Cartesian Space ◽  
Singularity Locus

The singularity-free workspace of parallel mechanisms is important in the trajectory planning and the kinematic design of the mechanisms. The planar parallel mechanism with revolute actuators, which the expression for the singularity locus and the algorithms for determining the singularity-free zones involve both the Cartesian and the joint variables, has been studied in the paper. Algorithms are proposed here to simplify the determination of the singularity-free zones in Cartesian space. The methodology and procedures for determining the singularity-free zones of planar parallel mechanisms with revolute actuators are introduced. The numerical results show that the simplified algorithms and the techniques are correct and efficient in determining singularity-free zones in the workspace of planar parallel mechanisms.

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.

A Deterministic Method of Application Region of Clamping Forces for Fixture Design

2011 ◽  
Vol 697-698 ◽  
pp. 345-348
Author(s):  
X.Y. Guo ◽  
Guo Hua Qin ◽  
Hai Chao Ye
Keyword(s):  
Screw Theory ◽  
Deterministic Algorithm ◽  
Fixture Design ◽  
Clamping Force ◽  
Discretization Method ◽  
Deterministic Method ◽  
Analysis Algorithm ◽  
Production Safety ◽  
Workpiece Stability

After being located, cutting force and torques will exert on a workpiece during the machining operation. In order to guarantee the location accuracy and production safety, the feasible clamping forces must be planned to stabilize the workpiece in the entire processing. Therefore, the workpiece stability is taken as a core to create a deterministic algorithm to the application region of clamping forces for the complex workpiece. Firstly, on the basis of the combination of the screw theory with the linear programming technology, an analysis algorithm is subjected to judge the workpiece stability. Secondly, according to the surface discretization method, a deterministic algorithm is further established to plan the application region of clamping force by analyzing the workpiece stability at all nodes in sequence. The proposed method can be utilized for the determination of the application region of clamping forces as well as the verification of the feasibility of the magnitudes of clamping forces.

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.

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