scholarly journals Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Clément Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Constraint Analysis ◽  
Fixed Direction ◽  
Geometric Singularity ◽  
Grassmann Geometry ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction (3T1R). Eleven architectures obtained from a recent type synthesis of such manipulators are analyzed. The constraint analysis shows that these architectures are all overconstrained and share some common properties between the actuation and the constraint wrenches. The singularities of such manipulators are examined through the singularity analysis of the 4-RUU parallel manipulator. A wrench graph representing the constraint wrenches and the actuation forces of the manipulator is introduced to formulate its superbracket. Grassmann–Cayley Algebra is used to obtain geometric singularity conditions. Based on the concept of wrench graph, Grassmann geometry is used to show the rank deficiency of the Jacobian matrix for the singularity conditions. Finally, this paper shows the general aspect of the obtained singularity conditions and their validity for 3T1R parallel manipulators with identical limb structures.

Singularity Analysis of the 4-RUU Parallel Manipulator Based on Grassmann-Cayley Algebra and Grassmann Geometry

2011 ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Ste´phane Caro ◽  
Philippe Wenger ◽  
Cle´ment Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Graph Representation ◽  
Fixed Direction ◽  
Cayley Algebra ◽  
Geometric Singularity ◽  
Grassmann Geometry ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Scho¨nflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The study is developed through the singularity analysis of the 4-RUU parallel manipulator. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity, namely, two constraint moments, among its six Plu¨cker lines. The Grassmann-Cayley Algebra is used to obtain geometric singularity conditions. However, due to the presence of lines at infinity, the rank deficiency of the Jacobian matrix for the singularity conditions is not easy to grasp. Therefore, a wrench graph representation for some singularity conditions emphasizes the linear dependence of the Plu¨cker lines of the Jacobian matrix and highlights the correspondence between Grassmann-Cayley algebra and Grassmann geometry.

scholarly journals SINGULARITY ANALYSIS OF THE 4 RUU PARALLEL MANIPULATOR USING GRASSMANN-CAYLEY ALGEBRA

2011 ◽  
Vol 35 (4) ◽  
pp. 515-528 ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Clément Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Fixed Direction ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of four degrees of freedom parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity among its six Plücker vectors. Some points at infinity are thus introduced to formulate the superbracket of Grassmann-Cayley algebra, which corresponds to the determinant of the Jacobian matrix. By exploring this superbracket, all the singularity conditions of such manipulators can be enumerated. The study is illustrated through the singularity analysis of the 4-RUU parallel manipulator.

scholarly journals Singularity analysis of the H4 robot using Grassmann–Cayley algebra

Robotica ◽  
2012 ◽  
Vol 30 (7) ◽  
pp. 1109-1118 ◽  
Author(s):  
Semaan Amine ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Daniel Kanaan
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Analysis Method ◽  
Rank Deficiency ◽  
Constraint Analysis ◽  
Cayley Algebra ◽  
Lower Mobility ◽  
Grassmann Cayley Algebra

SUMMARYThis paper extends a recently proposed singularity analysis method to lower-mobility parallel manipulators having an articulated nacelle. Using screw theory, a twist graph is introduced in order to simplify the constraint analysis of such manipulators. Then, a wrench graph is obtained in order to represent some points at infinity on the Plücker lines of the Jacobian matrix. Using Grassmann–Cayley algebra, the rank deficiency of the Jacobian matrix amounts to the vanishing condition of the superbracket. Accordingly, the parallel singularities are expressed in three different forms involving superbrackets, meet and join operators, and vector cross and dot products, respectively. The approach is explained through the singularity analysis of the H4 robot. All the parallel singularity conditions of this robot are enumerated and the motions associated with these singularities are characterized.

A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 511-520 ◽  
Author(s):  
Kefei Wen ◽  
TaeWon Seo ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Singular Configurations ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

Statics, Instantaneous Kinematics and Singularity Analysis of Planar Parallel Manipulators via Grassmann-Cayley Algebra

2014 ◽  
Vol 532 ◽  
pp. 378-381 ◽  
Author(s):  
Ke Fei Wen ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
New Approach ◽  
Coordinate Method ◽  
Cayley Algebra ◽  
Symbolic Formula ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

The wrench Jacobian matrix plays an important role in statics and singularity analysis of planar parallel manipulators (PPMs). It is easy to obtain this matrix based on plücker coordinate method. In this paper, a new approach is proposed to the analysis of the forward and inverse wrench Jacobian matrix used by Grassmann-Cayley algebra (GCA). A symbolic formula for the inverse statics and a coordinate free formula for the singularity analysis are obtained based on this Jacobian. As an example, this approach is implemented for the 3-RPR PPMs.

Kinematics and Singularity Analysis of the Hexaglide Parallel Robot

2008 ◽  
Author(s):  
Mansour Abtahi ◽  
Hodjat Pendar ◽  
Aria Alasty ◽  
Gholamreza Vossoughi
Keyword(s):  
Machine Tools ◽  
Parallel Manipulator ◽  
High Speed ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
The Past ◽  
Different Types ◽  
Forward Kinematic

In the past few years, parallel manipulators have become increasingly popular in industry, especially, in the field of machine tools. Hexaglide is a 6 DOF parallel manipulator that can be used as a high speed milling machine. In this paper, the kinematics and singularity of Hexaglide parallel manipulator are studied systematically. At first, this robot has been modeled and its inverse and forward kinematic problems have been solved. Then, formulas for solving inverse velocity are derived and Jacobian matrix is obtained. After that, three different types of singularity for this type of robot have been investigated. Finally a numerical example is presented.

Type Synthesis of Six-DOF Wrist-Partitioned Parallel Manipulators

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
General Structure ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Forward Displacement ◽  
Serial Manipulators ◽  
Six Dof ◽  
Moving Platform ◽  
Actuated Joints

A six-DOF wrist-partitioned parallel manipulator is a parallel manipulator in which three of the six actuated joints are used to control the position of a point on the moving platform while the other three are further used to control the orientation of the moving platform. Such parallel manipulators are, in fact, the parallel counterparts of the wrist-partitioned serial manipulators, which are widely used in industry. Unlike parallel manipulators of a general structure, a six-DOF wrist-partitioned parallel manipulator usually has simple kinematic characteristics such as its forward displacement analysis and singularity analysis are easy to solve. This paper deals with the type synthesis of six-DOF wrist-partitioned parallel manipulators. An approach is first proposed for the type synthesis of this class of parallel manipulators. Using the proposed approach, six-DOF wrist-partitioned parallel manipulators can be constructed from the types of three-DOF nonoverconstrained spherical parallel manipulators. A large number of six-DOF wrist-partitioned parallel manipulators are then obtained, and several types of practical relevance are also identified.

Constraint and Singularity Analysis of Lower-Mobility Parallel Manipulators With Parallelogram Joints

2010 ◽  
Author(s):  
Semaan Amine ◽  
Daniel Kanaan ◽  
Ste´phane Caro ◽  
Philippe Wenger
Keyword(s):  
Projective Space ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
3 Dimensional ◽  
Geometric Conditions ◽  
Constraint Analysis ◽  
Lower Mobility ◽  
Dimensional Projective Space ◽  
Grassmann Cayley Algebra

This paper presents a general approach to analyze the singularities of lower-mobility parallel manipulators with parallelogram joints. Using screw theory, the concept of twist graph is introduced and the twist graphs of two types of parallelogram joints are established in order to simplify the constraint analysis of the manipulators under study. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six Plu¨cker vectors of finite and infinite lines in the 3-dimensional projective space are reformulated in the superbracket in order to derive the geometric conditions for parallel singularities. The methodology is applied to three lower-mobility parallel manipulators with parallelogram joints: the Delta-linear robot, the Orthoglide robot and the H4 robot. The geometric interpretations of the singularities of these robots are given.

Type Synthesis of Six-DOF Wrist-Partitioned Fully Parallel Manipulators

2007 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
General Structure ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Forward Displacement ◽  
Serial Manipulators ◽  
Six Dof ◽  
Moving Platform ◽  
Actuated Joints

A six-DOF wrist-partitioned fully parallel manipulator is a parallel manipulator in which three of the six actuated joints are used to control the position of a point on the moving platform while the other three are further used to control the orientation of the moving platform. Such parallel manipulators are in fact the parallel counterparts of the wrist-partitioned serial manipulators, which are widely used in industry. Unlike parallel manipulators of a general structure, a six-DOF wrist-partitioned fully parallel manipulator usually has simple kinematic characteristics such as its forward displacement analysis and singularity analysis are easy to solve. This paper deals with the type synthesis of six-DOF wrist-partitioned fully parallel manipulators. An approach is first proposed for the type synthesis of this class of parallel manipulators. Using the proposed approach, six-DOF wrist-partitioned fully parallel manipulators can be constructed from the types of three-DOF non-overconstrained spherical parallel manipulators. A large number of six-DOF wrist-partitioned fully parallel manipulators are then obtained, and several types of practical relevance are also identified.

Singularity Analysis of Limited-DOF Parallel Manipulator Based on Jacobian Matrixes

2011 ◽  
Vol 141 ◽  
pp. 488-492
Author(s):  
Xin You Li ◽  
W.Y. Chen
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Machine ◽  
Singularity Analysis ◽  
Mechanical Analysis ◽  
Singular Problem ◽  
Velocity Analysis ◽  
Force Transformation ◽  
The Relationship

To analyze effects of singularity on parallel manipulator, the Jacobian matrixes were introduced as the indexes for analyzing the 3UPS/S parallel machine. The relationship between the velocity Jacobian matrix and the force-transformation matrix was established, and their equivalence was verified through the determinant and condition number’ reciprocal of the matrixes. Effects of singularity on motion accuracy, actuator forces and constrained forces were investigated within the nutation angle’range. The result showed that velocity analysis and mechanical analysis were consistent for 3UPS/S parallel machine in the aspect of singularity, and proved that the accuracy and actuator force properties were deteriorated when approach to singularity. The approach could be applied to other parallel manipulators in the research on singular problem as a reference.

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