Determination of maximal singularity-free zones in the workspace of planar three-degree-of-freedom parallel mechanisms

2006 ◽  
Vol 41 (10) ◽  
pp. 1157-1167 ◽  
Author(s):  
Haidong Li ◽  
Clément M. Gosselin ◽  
Marc J. Richard
Keyword(s):  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Maximal Singularity ◽  
Three Degree Of Freedom

On the Properties and the Determination of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms

2004 ◽  
Author(s):  
Marc Gouttefarde ◽  
Cle´ment M. Gosselin
Keyword(s):  
Detailed Analysis ◽  
Graphical Representation ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Conic Sections ◽  
Moving Platform ◽  
Three Degree Of Freedom ◽  
Disconnected Sets

This paper presents a detailed analysis of the constant-orientation wrench-closure workspace of planar three-degree-of-freedom parallel mechanisms driven by four cables. The constant-orientation wrench-closure workspace is defined as the subset of the plane wherein, for a given orientation of the moving platform, any planar wrench applied on the moving platform can be balanced by the cable-driven mechanism. Based on mathematical observations, this workspace is proved to be the union of two disconnected sets that may or may not exist. Moreover, if the constant-orientation wrench-closure workspace (WCW) exists, its boundary is shown to be composed of portions of conic sections. Then, an algorithm that determines the constant-orientation wrench-closure workspace by means of a graphical representation of its boundary is introduced. Several examples are also included.

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.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

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 3-ṞPR Parallel Mechanism With Singularities That are Self-Motions

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Novona Rakotomanga ◽  
Ilian A. Bonev
Keyword(s):  
Parallel Mechanism ◽  
Control Strategies ◽  
Joint Space ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Active Joint ◽  
Cartesian Space ◽  
Three Degree Of Freedom

The Cartesian workspace of most three-degree-of-freedom parallel mechanisms is divided by Type 2 (also called parallel) singularity surfaces into several regions. Accessing more than one such region requires crossing a Type 2 singularity, which is risky and calls for sophisticated control strategies. Some mechanisms can still cross these Type 2 singularity surfaces through “holes” that represent Type 1 (also called serial) singularities only. However, what is even more desirable is if these Type 2 singularity surfaces were curves instead. Indeed, there exists at least one such parallel mechanism (the agile eye) and all of its singularities are self-motions. This paper presents another parallel mechanism, a planar one, whose singularities are self-motions. The singularities of this novel mechanism are studied in detail. While the Type 2 singularities in the Cartesian space still constitute a surface, they degenerate into lines in the active-joint space, which is the main result of this paper.

Synthesis and Design of Reactionless Three-Degree-of-Freedom Parallel Mechanisms

2004 ◽  
Vol 20 (2) ◽  
pp. 191-199 ◽  
Author(s):  
C.M. Gosselin ◽  
F. Vollmer ◽  
G. Cote ◽  
Y. Wu
Keyword(s):  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Three Degree Of Freedom

A New Algorithm for the Determination of the Workspace of Complex Planar Kinematic Chains

1995 ◽  
Author(s):  
Pascal Lê-Huu ◽  
Clément M. Gosselin
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degree Of Freedom ◽  
Topological Graph ◽  
Kinematic Chains ◽  
Cartesian Space ◽  
Hybrid Manipulator ◽  
Three Degree Of Freedom ◽  
Two Degree Of Freedom

Abstract A new algorithm for the determination of the workspace of complex planar kinematic chains is presented in this paper. This algorithm is completely general since it can deal with any kind of topological graph and any set of parameters defined in a convention of notation. It uses the numerical solution of the inverse kinematics and is based on a wavefront expansion in the Cartesian space. Three examples are presented here, and lead to a dexterity mapping for two two-degree-of-freedom multi-loop manipulators and a three-degree-of-freedom hybrid manipulator.

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