Investigation of Parallel Manipulators Using Linear Complex Approximation

2003 ◽  
Vol 125 (3) ◽  
pp. 564-572 ◽  
Author(s):  
A. Wolf ◽  
M. Shoham
Keyword(s):  
Singular Point ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Line Geometry ◽  
Complex Approximation ◽  
Linear Complex ◽  
Additional Information ◽  
Physical Understanding ◽  
Singular Configuration

This investigation deals with singularity analysis of parallel manipulators and their instantaneous behavior while in or close to a singular configuration. The method presented utilizes line geometry tools and screw theory to describe a manipulator in a given position. Then, this description is used to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines of the manipulator. The linear complex axis and pitch provide additional information and a better physical understanding of the type of singularity and the motion the manipulator tends to perform in a singular point and in its neighborhood. Examples of Hunt’s, Fichter’s and 3-UPU singularities, along with a few selected examples taken from Merlet’s work [1], are presented and analyzed using this method.

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.

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.

Geometrical method to determine the reciprocal screws and applications to parallel manipulators

Robotica ◽  
2009 ◽  
Vol 27 (6) ◽  
pp. 929-940 ◽  
Author(s):  
Jianguo Zhao ◽  
Bing Li ◽  
Xiaojun Yang ◽  
Hongjian Yu
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Algebraic Manipulation ◽  
Robot Kinematics ◽  
Geometrical Approach ◽  
New Approach ◽  
Geometrical Relation ◽  
Manipulator Design

SUMMARYScrew theory has demonstrated its wide applications in robot kinematics and statics. We aim to propose an intuitive geometrical approach to obtain the reciprocal screws for a given screw system. Compared with the traditional Plücker coordinate method, the new approach is free from algebraic manipulation and can be used to obtain the reciprocal screws just by inspecting the structure of manipulator. The approach is based on three observations that describe the geometrical relation for zero pitch screw and infinite pitch screw. Based on the observations, the reciprocal screw systems of several common kinematic elements are analyzed, including usual kinematic pairs and chains. We also demonstrate usefulness of the geometrical approach by a variety of applications in mobility analysis, Jacobian formulation, and singularity analysis for parallel manipulator. This new approach can facilitate the parallel manipulator design process and provide sufficient insights for existing manipulators.

Forward Displacement Analysis and Singularity Analysis of a Special 2-DOF 5R Spherical Parallel Manipulator

2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type I ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Self Motion ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

This paper deals with the forward displacement analysis and singularity analysis of a special 2-DOF 5R spherical parallel manipulator, in which the angle between the axes of any two adjacent revolute joints is a right angle. An alternative formulation of the kinematic equations of the 5R spherical parallel manipulator is proposed. A formula is then derived to produce directly the unique current solution to the forward displacement analysis of the 5R spherical parallel manipulator. It will also be addressed to keep the spherical parallel manipulator in the same working mode and assembly mode by simply restraining the range of an input angle. Unlike other parallel manipulators, the 5R spherical parallel manipulator always undergoes self-motion in a type-II singular configuration, and the 3R leg of the 5R spherical parallel manipulator also always undergoes self-motion in a type-I singular configuration.

Classification of Screw Systems Composed of Three Planar Pencils of Lines

2012 ◽  
Author(s):  
Xianwen Kong ◽  
Andrew Johnson
Keyword(s):  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Spherical Joint ◽  
Geometric Characteristics ◽  
Singular Configuration ◽  
Kinematic Joint

Screw systems composed of three planar pencils of lines are closely related to the singularity analysis of a number of 3-legged parallel manipulators in which the passive joints in each leg are a spherical joint and a single-DOF (degree-of-freedom) kinematic joint or generalized kinematic joint. This paper systematically classifies the screw systems composed of three planar pencils of lines. The classification is based on the intersection of two planar pencils of lines, the classification of screw systems of order 2, and the reciprocal screw system of the three planar pencils of lines. The classification in this paper is more comprehensive than those in the literature. The above results are illustrated using CAD figures. This work may help readers better understand the geometric characteristics of the singular configuration of a number of 3-legged parallel manipulators.

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 New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Xin-Jun Liu ◽  
Chao Wu ◽  
Jinsong Wang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Challenging Problem ◽  
Performance Indices ◽  
New Approach ◽  
Singular Configurations ◽  
Different Types ◽  
Force Transmissibility ◽  
Singular Configuration

Singularity analysis is one of the most important issues in the field of parallel manipulators. An approach for singularity analysis should be able to not only identify all possible singularities but also explain their physical meanings. Since a parallel manipulator is always out of control at a singularity and its neighborhood, it should work far from singular configurations. However, how to measure the closeness between a pose and a singular configuration is still a challenging problem. This paper presents a new approach for singularity analysis of parallel manipulators by taking into account motion/force transmissibility. Several performance indices are introduced to measure the closeness to singularities. By using these indices, a uniform “metric” can be found to represent the closeness to singularities for different types of nonredundant parallel manipulators.

Singularity Analysis of Large Workspace 3RRRS Parallel Mechanism Using Line Geometry and Linear Complex Approximation

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Alon Wolf ◽  
Daniel Glozman
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Community Research ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Equilibrium Equations ◽  
Six Degrees Of Freedom ◽  
Singular Configurations

During the last 15 years, parallel mechanisms (robots) have become more and more popular among the robotics and mechanism community. Research done in this field revealed the significant advantage of these mechanisms for several specific tasks, such as those that require high rigidity, low inertia of the mechanism, and/or high accuracy. Consequently, parallel mechanisms have been widely investigated in the last few years. There are tens of proposed structures for parallel mechanisms, with some capable of six degrees of freedom and some less (normally three degrees of freedom). One of the major drawbacks of parallel mechanisms is their relatively limited workspace and their behavior near or at singular configurations. In this paper, we analyze the kinematics of a new architecture for a six degrees of freedom parallel mechanism composed of three identical kinematic limbs: revolute-revolute-revolute-spherical. We solve the inverse and show the forward kinematics of the mechanism and then use the screw theory to develop the Jacobian matrix of the manipulator. We demonstrate how to use screw and line geometry tools for the singularity analysis of the mechanism. Both Jacobian matrices developed by using screw theory and static equilibrium equations are similar. Forward and inverse kinematic solutions are given and solved, and the singularity map of the mechanism was generated. We then demonstrate and analyze three representative singular configurations of the mechanism. Finally, we generate the singularity-free workspace of the mechanism.

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.

Sign in / Sign up

Export Citation Format

Share Document