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.

Improving Motion Stability of the Plane 3-RPR Parallel Manipulator at Singular Configuration

2018 ◽  
Author(s):  
Yu-Tong Li ◽  
Yu-Xin Wang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Angular Speed ◽  
Motion Stability ◽  
Singular Configurations ◽  
Movable Platform ◽  
Singular Configuration ◽  
Translation Type ◽  
External Forces ◽  
Gerschgorin Circle

Kinematic parameters have significant influences on the motion stability of parallel manipulators at singular configureations. Taking the plane 3-RPR parallel manipulator as an example, the motion stability at different types of singular configurations corresponding to the angular speed and velocity of the movable platform are investigated. At first, the second order of uncoupled dynamics equation for the 3-RPR parallel manipulator is established with the aid of the second class Lagrange approach. According to the Lyapunov first approximate stability criterion, the approximate conditions for the 3-RPR parallel manipulator with a stabile motion at singular configurations are determined based on the Gerschgorin circle theorem. Next, the exact Hurwitz criterion is utilized to study the motion stability and the load capability of the manipulator corresponding to the angular speed and velocity of the movable platform, as well as the directions of the external forces at two kinds of singular configurations: with a gained rotation-type DOF, and with a gained translation-type DOF, respectively. The results show that increasing both the angular speed and the velocity of the mass center of the movable platform can efficiently improve the motion stability of the 3-RPR parallel manipulator at singular configurations.

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.

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.

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.

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.

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

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.

A new approach to determine the maximal singularity-free zone of 3-RPR planar parallel manipulator

Robotica ◽  
2011 ◽  
Vol 30 (6) ◽  
pp. 1005-1012 ◽  
Author(s):  
G. Abbasnejad ◽  
H. M. Daniali ◽  
S. M. Kazemi
Keyword(s):  
Parallel Manipulator ◽  
Orientation Angle ◽  
Parallel Manipulators ◽  
Swarm Optimization ◽  
New Approach ◽  
Free Zone ◽  
Reference Orientation ◽  
Planar Parallel Manipulator ◽  
Different Types ◽  
Moving Platform

SUMMARYThis paper presents a new algorithm to find the singularity-free cylindrical workspace of parallel manipulators. Because of the limited workspace of parallel manipulators cluttered with different types of singularities, a simple and robust technique to determine continuous singularity-free zones in the workspace of parallel manipulators is required. Here, the largest singularity-free cylinder within the workspace for any prescribed orientation ranging around a reference orientation angle of moving platform is determined. To this end, Particle Swarm Optimization is utilized to find the closest point on the singularity surface to the axis of the cylinder. By implementing the algorithm on 3-RPR planar parallel manipulator, the results show that this algorithm improves the efficiency and leads to significantly larger singularity-free workspace than those reported earlier.

Singular Configuration and Workspace of a Parallel Manipulator With New Architecture

2000 ◽  
Author(s):  
Abbas Fattah ◽  
Mojtaba Oghbaei
Keyword(s):  
Parallel Manipulator ◽  
Singularity Analysis ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Singular Configurations ◽  
Input And Output ◽  
Points Of View ◽  
Singular Configuration

Abstract In this paper singularity analysis and workspace of a 3DOF parallel manipulator with new architecture are studied. Singular configurations of the manipulator at hand are analysed first. To this end, upon differentiating the kinematic constraint equations of the manipulator with respect to time, the relation between input and output speeds is obtained in terms of two kinds of Jacobians. These two Jacobians are then used to determine singular configurations. Next the workspace of the manipulator is studied from two points of view.

Determination of the Workspace of Parallel Manipulators Using a CAD Software and the Concept of Virtual Chains

2013 ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Performance Indices ◽  
Workspace Analysis ◽  
Static Calculation

Development of a new parallel manipulator can be very time consuming due to the traditional method of producing kinematic, dynamic and static calculation models and then evaluating them to determine aspects of the manipulator’s performance indices such as the mechanism’s workspace and singularity analysis. By extending the virtual chain approach to the type synthesis of parallel manipulators, this paper proposes a virtual-chain approach to the workspace analysis of parallel manipulators. This method is illustrated by producing and evaluating the workspace of several parallel robots including the well known DELTA robot by utilising the three-dimensional CAD software SolidWorks to produce a virtual prototype of a manipulator with an embedded virtual chain. The virtual chain represents the motion pattern of a manipulator’s end-effector and is very useful in the production of a graphical representation of the workspace of the manipulator. Using this approach, the link interferences and transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

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