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

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.

Determination of the maximal singularity-free zone of 4-RRR redundant parallel manipulators and its application on investigating length ratios of links

Robotica ◽  
2014 ◽  
Vol 34 (9) ◽  
pp. 2039-2055 ◽  
Author(s):  
Yuzhe Liu ◽  
Jun Wu ◽  
Liping Wang ◽  
Jinsong Wang
Keyword(s):  
Parallel Manipulators ◽  
Numerical Approach ◽  
Previous Method ◽  
Joint Position ◽  
Parallel Mechanisms ◽  
3 Dimensional ◽  
Free Zone ◽  
Maximal Singularity ◽  
Three Degree Of Freedom

SUMMARYThis paper presents a new numerical approach using a Genetic algorithm (GA) to search for the singularity-free cylindrical space of a 4-RRR planar redundant parallel manipulator and investigates the effects of the joint position (namely the length ratios of two links) of each leg on the singularity-free cylindrical space. A previous method investigated the maximal singularity-free zone in a 3-dimensional (3-D) space within a given workspace. The method in this paper is improved by optimizing the maximal singularity-free zone in a 2-dimensional (2-D) plane while considering the whole workspace. This improvement can be helpful for reducing the searching time and for finding a larger singularity-free zone. Furthermore, the effect of the joint position of each leg on the maximal singularity-free zone is studied in this paper, which reveals a larger singularity-free zone than before. This result shows that changing the joint positions of one or two legs may be more practical than changing the joint positions of more legs. The approach in this paper can be used to analyze the maximal singularity-free zone of any other three-degree-of-freedom (3-DOF) planar parallel mechanisms and will be useful for the optimal design of redundant parallel manipulators.

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

New Investigation on the Geometry of the Contact in Gear Generation

2003 ◽  
Author(s):  
Marco Gabiccini ◽  
Massimo Guiggiani ◽  
Francesca Di Puccio
Keyword(s):  
Reference Frame ◽  
Relative Position ◽  
Geometric Approach ◽  
Gear Ratio ◽  
Reference Systems ◽  
Geometric Properties ◽  
Envelope Surface ◽  
Enveloping Surface ◽  
Contact Matrix

Based on a recently developed geometric approach to the theory of gearing that does not make use of any reference systems [1], this paper presents some useful relations between the geometric properties of the enveloping surface and those of its envelope. Treating vectors as such, that is without expressing their components in any reference systems, it is possible to obtain compact expressions for the coefficients of the first and second fundamental forms of the envelope surface. These coefficients show to be central in the determination of the contact matrix between mating surfaces. Moreover, since this approach is coordinate free, it is valid regardless of the reference frame actually employed to perform calculations and allows a, hopefully, clearer understanding of the roles played by the intrinsic geometric properties of the enveloping surface, the relative position of the gear axes and the gear ratio.

BREAKING OF LINEAR SYMMETRIES AND MICHEL'S THEORY: GRASSMANN MANIFOLDS, AND INVARIANT SUBSPACES

2008 ◽  
Vol 23 (03n04) ◽  
pp. 547-565
Author(s):  
GIUSEPPE GAETA
Keyword(s):  
Symmetry Breaking ◽  
Group Action ◽  
Invariant Manifolds ◽  
Invariant Subspaces ◽  
Geometric Approach ◽  
Symmetry Type ◽  
Original Formulation ◽  
Grassmann Manifolds ◽  
Nonlinear Flows

Michel's theory of symmetry breaking in its original formulation has some difficulty in dealing with problems with a linear symmetry, due to the degeneration in the symmetry type implied by the linearity of group action. Here we propose a fully geometric, approach to the problem, making use of Grassmann manifolds. In this way Michel theory can also be applied to the determination of dynamically invariant manifolds for equivariant nonlinear flows.

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