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.

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.

Constraint and Singularity Analysis of the Exechon Tripod

2012 ◽  
Author(s):  
Dimiter Zlatanov ◽  
Matteo Zoppi ◽  
Rezia Molfino
Keyword(s):  
Machine Tool ◽  
System Approach ◽  
Parallel Mechanism ◽  
Singularity Analysis ◽  
Geometric Interpretation ◽  
End Effector ◽  
Singular Configurations ◽  
Parallel Kinematic ◽  
Three Degree Of Freedom ◽  
Fixture System

The paper discusses mobility and singularities of the Exechon three-degree-of-freedom (dof) parallel mechanism (PM) on which a family of parallel kinematic machines is based. Exechon designs are used by a number of machine-tool makers. A new version of the manipulator has been developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. The PM has two UPR (4-dof) legs, constrained to move in a common rotating plane, and an SPR (5-dof) leg. The paper focuses on the constraint and singularity analysis of the mechanism. The screw systems of end-effector freedoms and constraints are identified. The singular configurations are classified in detail and their geometric interpretation is discussed. The velocity kinematics and the Jacobian operator are formulated via a screw-system approach. A fully parameterized package of Maple tools has been developed and used to visualize singularities and their consequences.

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.

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.

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.

scholarly journals Position and Singularity Analysis of a Class of Planar Parallel Manipulators with a Reconfigurable End-Effector

Machines ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 7
Author(s):  
Tommaso Marchi ◽  
Giovanni Mottola ◽  
Josep M. Porta ◽  
Federico Thomas ◽  
Marco Carricato
Keyword(s):  
Inverse Kinematics ◽  
Kinematic Chain ◽  
Experimental Tests ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
End Effector ◽  
Revolute Joints ◽  
A Chain ◽  
And Control

Parallel robots with configurable platforms are a class of robots in which the end-effector has an inner mobility, so that its overall shape can be reconfigured: in most cases, the end-effector is thus a closed-loop kinematic chain composed of rigid links. These robots have a greater flexibility in their motion and control with respect to rigid-platform parallel architectures, but their kinematics is more challenging to analyze. In our work, we consider n-RRR planar configurable robots, in which the end-effector is a chain composed of n links and revolute joints, and is controlled by n rotary actuators located on the base of the mechanism. In particular, we study the geometrical design of such robots and their direct and inverse kinematics for n=4, n=5 and n=6; we employ the bilateration method, which can simplify the kinematic analysis and allows us to generalize the approach and the results obtained for the 3-RRR mechanism to n-RRR robots (with n>3). Then, we study the singularity configurations of these robot architectures. Finally, we present the results from experimental tests that have been performed on a 5–RRR robot prototype.

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 Design of a Lockable Spherical Joint for a Reconfigurable 3-URU Parallel Platform

Robotics ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 42 ◽  
Author(s):  
Matteo Palpacelli ◽  
Luca Carbonari ◽  
Giacomo Palmieri ◽  
Massimo Callegari
Keyword(s):  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Preliminary Design ◽  
Kinematic Structure ◽  
Spherical Joint ◽  
Pure Rotation ◽  
Fixed Base ◽  
Lower Mobility ◽  
Parallel Platform ◽  
Robotic Applications

This article deals with the functional and preliminary design of a reconfigurable joint for robotic applications. Such mechanism is a key element for a class of lower mobility parallel manipulators, allowing a local reconfiguration of the kinematic chain that enables a change in platform’s mobility. The mechanism can be integrated in the kinematic structure of a 3-URU manipulator, which shall accordingly gain the ability to change mobility from pure translation to pure rotation. As a matter of fact, special kinematics conditions must be met for the accomplishment of this task. Such peculiar requirements are described and properly exploited for the design of an effective reconfigurable mechanism. A detailed description of the joint operational principle is provided, also showing how to design it when is physically located at the fixed base of the manipulator.

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.

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