Classification of Screw Systems Composed of Three Planar Pencils of Lines for Singularity Analysis of Parallel Mechanisms1

2014 ◽  
Vol 6 (2) ◽  
Author(s):  
Xianwen Kong ◽  
Andrew Johnson
Keyword(s):  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Spherical Joint ◽  
Geometric Characteristics ◽  
Singular Configurations ◽  
Kinematic Joint

Screw systems composed of (the sum of) three planar pencils of lines are closely related to the singularity analysis of a number of three-legged parallel manipulators (PMs) 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 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 singular configurations of a number of three-legged parallel manipulators.

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.

Geometric Interpretation of Singular Configurations of a Class of Parallel Manipulators

2011 ◽  
Author(s):  
Xianwen Kong ◽  
Jingjun Yu ◽  
Cle´ment Gosselin
Keyword(s):  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Geometric Interpretation ◽  
Spherical Joint ◽  
Kinematic Singularity ◽  
Geometric Characteristics ◽  
Singular Configurations ◽  
Parallel Kinematic ◽  
Forward Kinematic

This paper proposes an equivalent serial kinematic chain approach to identify the geometric characteristics of singular configurations of a class of parallel manipulators, which can be reduced to a structure composed of three XS and/or SX legs. Here, S and X denote respectively a spherical joint and a one-degree-of-freedom joint or generalized joint. The equivalent serial kinematic chain associated with a parallel kinematic chain composed of two XS legs is first obtained using the concept of reciprocal screws. The forward kinematic singularity (also static singularity) analysis of the parallel manipulators is then reduced to the singularity (stability) analysis of a single-loop structure. Finally, the geometric characteristics of singular configurations of the class of parallel manipulators are obtained with almost no algebraic derivation.

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.

Singularity Analysis of Planar Multiple-DOF Linkages

2014 ◽  
Author(s):  
Jun Wang ◽  
Liangyi Nie ◽  
Quan Wang ◽  
Jinfeng Sun ◽  
Ying You ◽  
...  
Keyword(s):  
Singularity Analysis ◽  
General Concept ◽  
Degree Of Freedom ◽  
Simple Explanation ◽  
Constrained Motion ◽  
Singular Configurations ◽  
N Input ◽  
Center Position ◽  
Kinematic Loop ◽  
Planar Linkages

Singularity analysis of multi-DOF (multiple-degree-of-freedom) multiloop planar linkages is much more complicated than the single-DOF planar linkages. This paper offers a degeneration method to analyze the singularity (dead center position) of multi-DOF multiloop planar linkages. The proposed method is based on the singularity analysis results of single-DOF planar linkages and the less-DOF linkages. For an N-DOF (N>1) planar linkage, it generally requires N inputs for a constrained motion. By fixing M (M<N) input joints or links, the N-DOF planar linkage degenerates an (N-M)-DOF linkage. If any one of the degenerated linkages is at the dead center position, the whole N-DOF linkage must be also at the position of singularity. With the proposed method, one may find out that it is easy to obtain the singular configurations of a multiple-DOF multiloop linkage. The proposed method is a general concept in sense that it can be systematically applied to analyze the singularity for any multiple-DOF planar linkage regardless of the number of kinematic loop or the types of joints. The velocity method for singularity analysis is also used to verify the results. The proposed method offers simple explanation and straightforward geometric insights for the singularity identification of multiple-DOF multiloop planar linkages. Examples are also employed to demonstrate the proposed method.

scholarly journals SINGULARITY ANALYSIS OF A 3-PRRR KINEMATICALLY REDUNDANT PLANAR PARALLEL MANIPULATOR

1970 ◽  
Vol 41 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Soheil Zarkandi
Keyword(s):  
Motion Control ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Redundant Manipulators ◽  
Static Behavior ◽  
Singular Configurations ◽  
Planar Parallel Manipulator ◽  
And Control ◽  
Planar Parallel Manipulators

Finding Singular configurations (singularities) is one of the mandatory steps during the design and control of mechanisms. Because, in these configurations, the instantaneous kinematics is locally undetermined that causes serious problems both to static behavior and to motion control of the mechanism. This paper addresses the problem of determining singularities of a 3-PRRR kinematically redundant planar parallel manipulator by use of an analytic technique. The technique leads to an input –output relationship that can be used to find all types of singularities occurring in this type of manipulators.Key Words: Planar parallel manipulators; Redundant manipulators; Singularity analysis; Jacobian matrices.DOI: 10.3329/jme.v41i1.5356Journal of Mechanical Engineering, Vol. ME 41, No. 1, June 2010 1-6

Singularity Analysis of 5-RPRRR Parallel Mechanisms via Grassmann Line Geometry

2009 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Line Geometry ◽  
Singular Configurations ◽  
Highly Nonlinear ◽  
Grassmann Line Geometry

This paper investigates the singular configurations of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical legs of the RPUR type. The general mechanism was recently revealed by performing the type synthesis for symmetrical 5-DOF parallel mechanisms. In this study, some simplified designs are proposed for which the singular configurations can be predicted by means of the so-called Grassmann line geometry. This technique can be regarded as a powerful tool for analyzing the degeneration of the Plu¨cker screw set. The main focus of this contribution is to predict the actuation singularity, for a general and simplified design, without expanding the determinant of the inverse Jacobian matrix (actuated constraints system) which is highly nonlinear and difficult to analyze.

A DEPENDENT-SCREW SUPPRESSION APPROACH TO THE SINGULARITY ANALYSIS OF A 7-DOF REDUNDANT MANIPULATOR: CANADARM2

2005 ◽  
Vol 29 (4) ◽  
pp. 593-604 ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Singular Configurations

A dependent-screw suppression approach is proposed for the singularity analysis of 7-DOF (degree-of-freedom) redundant manipulators. This approach is applied to the singularity analysis of the Canadarm2. Five families of singular configurations are identified for the Canadarm2. The singular configurations obtained are identical to those obtained using the reciprocity-based method. Unlike the results presented previously, there are no denominators in the equations describing the singular configurations.

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.

Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms

2004 ◽  
Vol 126 (1) ◽  
pp. 109-118 ◽  
Author(s):  
Jing Wang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Main Idea ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Redundant Manipulators ◽  
Parallel Mechanisms ◽  
Jacobian Matrices ◽  
Kinematic Chains ◽  
Analysis And Design

This paper addresses the singularity analysis and the design of three new types of kinematically redundant parallel mechanisms, i.e., the four-degree-of-freedom planar and spherical parallel mechanisms and the seven-degree-of-freedom spatial Stewart platform. The main idea in the design of these parallel manipulators is the addition of one redundant degree of freedom in one of the kinematic chains of the nonredundant manipulator. Such manipulators can be used to avoid the singularities inside the workspace of nonredundant manipulators. After describing the geometry of the manipulators, the velocity equations are derived and the expressions for the Jacobian matrices are obtained. Then, the singularity conditions are discussed. Finally, the expressions of the singularity loci of the kinematically redundant mechanisms are obtained and the singularity loci of the nonredundant and redundant manipulators are compared. It is shown here that the conditions for the singularity of the redundant manipulators are reduced drastically relative to the nonredundant ones. As a result, the proposed kinematically redundant parallel manipulators may be of great interest in several applications.

Instantaneous Kinematics and Singularity Analysis of a Novel Three-Legged Mobile Robot With Active S-R-R-R Legs

2008 ◽  
Author(s):  
Ping Ren ◽  
Dennis Hong
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
The Body ◽  
Jacobian Matrices ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Grassmann Line Geometry ◽  
Actuation Scheme ◽  
Complete Investigation

STriDER (Self-excited Tripedal Dynamic Experimental Robot) is a unique three-legged walking robot that utilizes its innovative tripedal gait to walk. Previous work on the kinematic analysis of STriDER mainly focused on solving the forward and inverse displacement problems. As a continuation, this paper addresses the instantaneous kinematics and singularity analysis. The kinematic configuration of STriDER is modeled as a three-legged in-parallel manipulator when all three feet of the robot are in contact with the ground without slipping. The results obtained from this study can be implemented to the velocity control and the resistance of disturbance forces, thus improving the motion accuracy and stability of the robot. By using screw theory, the screw-based Jacobian matrices of the manipulator can be derived since the forward displacement problems have already been solved. Based on these Jacobian matrices, the transformation equations from the active joint rates to the velocities of the body and vice versa are derived. Then, a complete investigation on the identification and elimination of singularities is presented. Unlike serial manipulators, in-parallel manipulators have two types of singularities, i.e., forward and inverse singularities. The inverse singularities are identified by checking the singular configurations of individual legs and the determinant of the inverse Jacobian matrix. By using Grassmann line geometry, the analytical conditions under which the forward singularities occur are obtained. A study on each case of these singular configurations shows that the redundant-actuation scheme of the active joints can effectively eliminate forward singularities.

Sign in / Sign up

Export Citation Format

Share Document