Singularity Locus of 6–4 Fully-Parallel Manipulators

2010 ◽  
pp. 437-445 ◽  
Author(s):  
R. Di Gregorio
Keyword(s):  
Parallel Manipulators ◽  
Singularity Locus

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

Considering the Ability for Nonsingular Transitions of Assembly Mode for Dimensional Synthesis

2009 ◽  
Author(s):  
Oscar Altuzarra ◽  
Vi´ctor Petuya ◽  
Mo´nica Uri´zar ◽  
Alfonso Herna´ndez
Keyword(s):  
Parallel Manipulator ◽  
Analytical Procedure ◽  
Parallel Manipulators ◽  
Dimensional Synthesis ◽  
Complex Singularity ◽  
Algebraic Expressions ◽  
Free Region ◽  
Dimensional Parameters ◽  
Cusp Points ◽  
Singularity Locus

An important difficulty in the design of parallel manipulators is their reduced practical workspace, due mainly to the existence of a complex singularity locus within the workspace. The workspace is divided into singularity-free regions according to assembly modes and working modes, and the dimensioning of parallel manipulators aims at the maximization of those regions. It is a common practice to restrict the manipulator’s motion to a specific singularity-free region. However, a suitable motion planning can enlarge the operational workspace by means of transitions of working mode and/or assembly mode. In this paper, the authors present an analytical procedure for obtaining the loci of cusp points of a parallel manipulator as algebraic expressions of its dimensional parameters. The purpose is to find an optimal design for non-singular transitions to be possible.

A new family of spherical parallel manipulators

Robotica ◽  
2002 ◽  
Vol 20 (4) ◽  
pp. 353-358 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
End Effector ◽  
Singular Configurations ◽  
New Family ◽  
Geometric Conditions ◽  
Singularity Locus ◽  
The Given ◽  
Spherical Parallel Manipulator ◽  
Spherical Motion

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

scholarly journals Kinematic analysis of the X4 translational–rotational parallel robot

2018 ◽  
Vol 15 (5) ◽  
pp. 172988141880384 ◽  
Author(s):  
Stefan Staicu ◽  
Zhufeng Shao ◽  
Zhaokun Zhang ◽  
Xiaoqiang Tang ◽  
Liping Wang
Keyword(s):  
High Speed ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Commercial Applications ◽  
Recursive Matrix ◽  
Singularity Locus

High-speed pick-and-place parallel manipulators have attracted considerable academic and industrial attention because of their numerous commercial applications. The X4 parallel robot was recently presented at Tsinghua University. This robot is a four-degree-of-freedom spatial parallel manipulator that consists of high-speed closed kinematic chains. Each of its limbs comprises an active pendulum and a passive parallelogram, which are connected to the end effector with other revolute joints. Kinematic issues of the X4 parallel robot, such as degree of freedom analysis, inverse kinematics, and singularity locus, are investigated in this study. Recursive matrix relations of kinematics are established, and expressions that determine the position, velocity, and acceleration of each robot element are developed. Finally, kinematic simulations of actuators and passive joints are conducted. The analysis and modeling methods illustrated in this study can be further applied to the kinematics research of other parallel mechanisms.

Orientation-singularity analysis and orientationability evaluation of a special class of the Stewart–Gough parallel manipulators

Robotica ◽  
2013 ◽  
Vol 31 (8) ◽  
pp. 1361-1372 ◽  
Author(s):  
Yi Cao ◽  
Clément Gosselin ◽  
Hui Zhou ◽  
Ping Ren ◽  
Weixi Ji
Keyword(s):  
Performance Index ◽  
Special Class ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Design Parameters ◽  
Graphical Representations ◽  
Practical Orientation ◽  
Discretization Algorithm ◽  
Half Angle ◽  
Singularity Locus

SUMMARYThis paper addresses the orientation-singularity analysis and the orientationability evaluation of a special class of the Stewart–Gough parallel manipulators in which the moving and base platforms are two similar semi-symmetrical hexagons. Based on the half-angle transformation, an analytical polynomial of degree 13 that represents the orientation-singularity locus of this special class of parallel manipulators at a given position is derived. Graphical representations of the orientation-singularity locus of this class of manipulators are illustrated with examples to demonstrate the results. Based on the description of the orientation-singularity and nonsingular orientation region of this class of parallel manipulators, a performance index, referred to as orientationability, which describes the orientation capability of this class of manipulators at a given position, is introduced. A discretization algorithm is proposed for computing the orientationability of the special class of parallel manipulators at a given position in the workspace. Moreover, the effects of the design parameters and position parameters on the orientationability are also investigated in detail. Based on the orientationability performance index, another performance index, referred to as practical orientationability, representing the practical orientation capability of the manipulators at a given position, is introduced. In this performance index, singularities, the limitations of active and passive joints and link interferences are all taken into consideration. Furthermore, the practical orientationability of the special class of parallel manipulators studied here is also analyzed over several plane sections of the position-workspace in detail.

Designing a Translational Parallel Manipulator Based on the 3SS Kinematic Joint

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Erik Macho ◽  
Mónica Urízar ◽  
Víctor Petuya ◽  
Alfonso Hernández
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Modular Design ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Point Of View ◽  
Pick And Place ◽  
Prismatic Joints ◽  
Singularity Locus ◽  
Kinematic Joint

Abstract Nowadays, translational parallel manipulators are widely used in industrial applications related to pick and place tasks. In this paper, a new architecture of a translational parallel manipulator without floating prismatic joints and without redundant constraints is presented, which leads to a robust design from the manufacturing and maintenance point of view. The frame configuration has been chosen with the aim of achieving the widest and most regular operational workspace completely free of singularities. Besides, the position equations of the proposed design are obtained in a closed form, as well as the singularity locus. It will be shown that the proposed design owns a very simple kinematics so that the related equations can be efficiently implemented in the control of the robot. In addition, the Jacobian condition number assessment shows that a wide part of the operational workspace is well-conditioned, and also the existence of an isotropic configuration will be proved. Finally, a prototype has been built by following a modular design approach.

scholarly journals Position-Singularity Analysis of a Class of the 3/6-Gough-Stewart Manipulators Based on Singularity-Equivalent-Mechanism

10.5772/45664 ◽  
2012 ◽  
Vol 9 (1) ◽  
pp. 9 ◽  
Author(s):  
Hui Zhou ◽  
Yi Cao ◽  
Baokun Li ◽  
Meiping Wu ◽  
Jinghu Yu ◽  
...  
Keyword(s):  
Screw Theory ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Polynomial Expression ◽  
Moving Platform ◽  
Singularity Locus ◽  
Three Dimensional Space ◽  
Equivalent Mechanism

This paper addresses the problem of identifying the property of the singularity loci of a class of 3/6-Gough-Stewart manipulators for general orientations in which the moving platform is an equilateral triangle and the base is a semiregular hexagon. After constructing the Jacobian matrix of this class of 3/6-Gough-Stewart manipulators according to the screw theory, a cubic polynomial expression in the moving platform position parameters that represents the position-singularity locus of the manipulator in a three-dimensional space is derived. Graphical representations of the position-singularity locus for different orientations are given so as to demonstrate the results. Based on the singularity kinematics principle, a novel method referred to as ‘singularity-equivalent-mechanism' is proposed, by which the complicated singularity analysis of the parallel manipulator is transformed into a simpler direct position analysis of the planar singularity-equivalent-mechanism. The property of the position-singularity locus of this class of parallel manipulators for general orientations in the principal-section, where the moving platform lies, is identified. It shows that the position-singularity loci of this class of 3/6-Gough-Stewart manipulators for general orientations in parallel principal-sections are all quadratic expressions, including a parabola, four pairs of intersecting lines and infinite hyperbolas. Finally, the properties of the position-singularity loci of this class of 3/6-Gough-Stewart parallel manipulators in a three-dimensional space for all orientations are presented.

Orientation workspace analysis of a special class of the Stewart–Gough parallel manipulators

Robotica ◽  
2010 ◽  
Vol 28 (7) ◽  
pp. 989-1000 ◽  
Author(s):  
Yi Cao ◽  
Zhen Huang ◽  
Hui Zhou ◽  
Weixi Ji
Keyword(s):  
Special Class ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Discretization Method ◽  
Practical Orientation ◽  
Workspace Analysis ◽  
Half Angle ◽  
Polynomial Expression ◽  
Singularity Locus ◽  
Orientation Workspace

SUMMARYThe workspace of a robotic manipulator is a very important issue and design criteria in the context of optimum design of robots, especially for parallel manipulators. Though, considerable research has been paid to the investigations of the three-dimensional (3D) constant orientation workspace or position workspace of parallel manipulators, very few works exist on the topic of the 3D orientation workspace, especially the nonsingular orientation workspace and practical orientation workspace. This paper addresses the orientation workspace analysis of a special class of the Stewart–Gough parallel manipulators in which the moving and base platforms are two similar semisymmetrical hexagons. Based on the half-angle transformation, a polynomial expression of 13 degree that represents the orientation singularity locus of this special class of the Stewart–Gough parallel manipulators at a fixed position is derived and graphical representations of the orientation singularity locus of this special class of the Stewart–Gough manipulators are illustrated with examples to demonstrate the result. Exploiting this half-angle transformation and the inverse kinematics solution of this special class of the Stewart–Gough parallel manipulators, a discretization method is proposed for computing the orientation workspace of this special class of the Stewart–Gough parallel manipulators taking limitations of active and passive joints and the link interference all into consideration. Based on this algorithm, this paper also presents a new discretization method for computing the nonsingular orientation workspace of this class of the manipulators, which not only can satisfy all the kinematics demand of this class of the manipulators but also can guarantee the manipulator is nonsingular in the whole orientation workspace, and the practical orientation workspace of this class of the manipulators, which not only can guarantee the manipulator is nonsingular and will never encounter any kinematic interference but also can satisfy the demand of the orientation workspace with a regular shape in practical application, respectively. Examples of a 6/6-SPS Stewart–Gough parallel manipulator of this special class are given to demonstrate these theoretical results.

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