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.

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.

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.

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.

Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy

Robotica ◽  
2009 ◽  
Vol 27 (1) ◽  
pp. 51-57 ◽  
Author(s):  
Jinsong Wang ◽  
Jun Wu ◽  
Tiemin Li ◽  
Xinjun Liu
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Actuation Redundancy ◽  
Hybrid Machine Tool ◽  
Planar Parallel Manipulator ◽  
Redundantly Actuated ◽  
Value Decomposition ◽  
The Relationship ◽  
Orientation Workspace

SUMMARYThis paper deals with the position workspace, orientation workspace, and singularity of a 3-degree-of-freedom (DOF) planar parallel manipulator with actuation redundancy, which is created by introducing a redundant link with active actuator to a 3-DOF nonredundant parallel manipulator. Based on the kinematic analysis, the position workspace and orientation workspace of the redundantly actuated parallel manipulator and its corresponding nonredundant parallel manipulator are analyzed, respectively. In the singularity analysis phase, the relationship between the generalized input velocity and the generalized output velocity is researched on the basis of the theory of singular value decomposition. Then a method to investigate the singularity of parallel manipulators is presented, which is used to determine the singularity of the redundantly actuated parallel manipulator. In contrast to the corresponding nonredundant parallel manipulator, the redundant one has larger orientation workspace and less singular configurations. The redundantly actuated parallel manipulator is incorporated into a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

scholarly journals Interior singularity analysis for a 2(3HUS+S) parallel manipulator with descending matrix rank method

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141982684
Author(s):  
Feng Guo ◽  
Gang Cheng ◽  
Zunzhong Zhao
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singular Locus ◽  
Singularity Analysis ◽  
Normal Operation ◽  
Motion Path ◽  
Moving Platforms ◽  
Singular Configuration ◽  
The Relationship ◽  
Interior Singularity

Singularity analysis is one of the basic problems for parallel manipulators. When a manipulator moves in a singular configuration, the motion and transmission performance are poor. In certain serious cases, the normal operation could be damaged. Based on the topology structure and kinematics analysis of a 2(3HUS+S) parallel manipulator, the Jacobian matrices were established. Then, the singular locus surface was obtained by numerical simulation. In addition, the relationship between the motion path curve and the singular locus surface was analyzed. In this study, α, β, and γ are the attitude angles that describe the motion of moving platforms. There is a nonsingular attitude space in singular locus surfaces, and the singular locus surface is a single surface in a small attitude angle range. The nonsingular attitude space increases as the absolute value of γ increases, and singularity could be avoided when γ is large. Furthermore, the motion path curve passes through the singular locus surface two times, and the two intersection points are consistent with the positions where the motion dexterity is equal to zero. This study provides new insights on the singularity analysis of parallel manipulators, particularly for the structure parameter optimization of the nonsingular attitude space.

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.

Kinematic and Singularity Analysis of a Novel 4-DOF Parallel Manipulator

2011 ◽  
Vol 101-102 ◽  
pp. 685-688 ◽  
Author(s):  
Meng Guan ◽  
Yi Min Song ◽  
Tao Sun ◽  
Gang Dong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Velocity Analysis ◽  
Inverse Kinematic Analysis ◽  
In Virtue Of

This paper presents a novel 4-DOF (Degree of Freedom) parallel manipulator called 2-PSS&(2-PRR)R manipulator. Firstly, the architecture of this manipulator is described and the mobility is analyzed via screw theory. Secondly, the inverse kinematic analysis including position analysis and velocity analysis is performed. Finally, the Jacobian matrix is obtained through velocity analysis, and then three kinds of singularity configurations are observed in virtue of the Jacobian matrix. This paper lays the foundation for further research of this manipulator.

Effect of links deformation on motion precision of parallel manipulator based on flexible dynamics

2017 ◽  
Vol 44 (6) ◽  
pp. 776-787 ◽  
Author(s):  
Chunxia Zhu ◽  
Jay Katupitiya ◽  
Jing Wang
Keyword(s):  
Parallel Manipulator ◽  
High Speed ◽  
Beam Theory ◽  
Parallel Manipulators ◽  
Dynamic Responses ◽  
Axial Deformation ◽  
Content Type ◽  
High Performing ◽  
Coupling Equations ◽  
The Relationship

Purpose Manipulator motion accuracy is a fundamental requirement for precision manufacturing equipment. Light weight manipulators in high speed motions are vulnerable to deformations. The purpose of this work is to analyze the effect of link deformation on the motion precision of parallel manipulators. Design/methodology/approach The flexible dynamics model of the links is first established by applying the Euler–Bernoulli beam theory and the assumed modal method. The rigid-flexible coupling equations of the parallel mechanism are further derived by using the Lagrange multiplier approach. The elastic energy resulting from spiral motion and link deformations are computed and analyzed. Motion errors of the 3-link torque-prismatic-torque parallel manipulator are then evaluated based on its inverse kinematics. The validation experiments are also conducted to verify the numerical results. Findings The lateral deformation and axial deformation are largest at the middle of the driven links. The axial deformation at the middle of the driven link is approximately one-tenth of the transversal deformation. However, the elastic potential energy of the transversal deformation is much smaller than the elastic force generated from axial deformation. Practical implications Knowledge on the relationship between link deformation and motion precision is useful in the design of parallel manipulators for high performing dynamic responses. Originality/value This work establishes the relationship between motion precision and the amount of link deformation in parallel manipulators.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator

2010 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment Gosselin ◽  
James M. Ritchie
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Alternative Formulation ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Actuated Joints ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators — leg actuation singularity — is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator.

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