A General Geometric Method for Identifying Singular Configurations of One-DOF Planar Mechanisms

2006 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Scientific Community ◽  
Singularity Analysis ◽  
Parallel Architectures ◽  
Geometric Method ◽  
Systems Of Equations ◽  
Planar Mechanisms ◽  
Main Interest ◽  
Singular Configurations ◽  
Geometric Conditions ◽  
General Method

The importance of finding singular configurations (singularities) of mechanisms has become clear since the interest of the scientific community for parallel architectures arose. Regarding the singularity analysis, the main interest has been devoted to architectures with more-than-one degree of freedom (dof) without realizing that one-dof mechanisms are commonly used and deserve the same attention. This paper addresses the singularity analysis of one-dof planar mechanisms. A general method for implementing this analysis will be presented. The presented method relies on the possibility of giving geometric conditions for any type of singularity. It can be used to generate systems of equations to solve either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

Singularities of Single-DOF Spherical Mechanisms Identified by Means of Pole Axes’ Properties

2010 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Singularity Analysis ◽  
Systems Of Equations ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Spherical Mechanism ◽  
General Method

Instantaneous pole axes (IPAs) play, in spherical-mechanism kinematics, the same role as instant centers in planar-mechanism kinematics. IPA-based techniques have not been proposed yet for the singularity analysis of spherical mechanisms, even though instant-center-based algorithms have been already presented for planar mechanisms’ singularity analysis. This paper addresses the singularity analysis of single-dof spherical mechanisms by exploiting the properties of pole axes. A general method for implementing this analysis is presented. The presented method relies on the possibility of giving geometric conditions for any type of singularity, and it is the spherical counterpart of an instant-center-based algorithm previously proposed by the author for single-dof planar mechanisms. It can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

Analytical method for the singularity analysis and exhaustive enumeration of the singularity conditions in single-degree-of-freedom spherical mechanisms

2012 ◽  
Vol 227 (8) ◽  
pp. 1830-1840 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytical Method ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Systems Of Equations ◽  
Single Degree Of Freedom ◽  
Planar Mechanism ◽  
Single Degree ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Spherical Mechanism

In spherical-mechanism kinematics, instantaneous pole axes play the same role as, in planar-mechanism kinematics, instant centres. Their locations only depend on the mechanism configuration when spherical single-degree-of-freedom mechanisms are considered. Such a property makes them a tool to visualize and/or to analyse the instantaneous kinematics of those mechanisms. This article addresses the singularity analysis of single-degree-of-freedom spherical mechanisms by exploiting the properties of instantaneous pole axes. An exhaustive enumeration of the geometric conditions which occur for all the singularity types is given, and a general analytical method based on this enumeration is proposed for implementing the singularity analysis. The proposed analytical method can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

Singularity Analysis of a Single-Loop Underactuated Wrist

2013 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Path Planning ◽  
Closed Form ◽  
Nonholonomic Constraint ◽  
Singularity Analysis ◽  
The Novel ◽  
Single Loop ◽  
Position Analysis ◽  
Singular Configurations ◽  
Geometric Conditions

In a previous paper, this author proposed a novel type of underactuated parallel wrist (PW) with a single-loop architecture containing only one nonholonomic constraint. Moreover, he addressed its position analysis and path planning and showed that closed-form formulas can be used to solve all the finite-kinematics problems involved in the path planning of the novel PW. Here, the instantaneous kinematics and the singularity analysis of this PW are addressed. In particular, both the analytic and geometric conditions which identify the singular configurations are presented together with their static interpretation. The presented results are relevant for designing this type of PWs.

A new geometric method for singularity analysis of spherical mechanisms

Robotica ◽  
2011 ◽  
Vol 29 (7) ◽  
pp. 1083-1092 ◽  
Author(s):  
Soheil Zarkandi
Keyword(s):  
Trajectory Planning ◽  
Singularity Analysis ◽  
Systematic Method ◽  
Singular Configurations ◽  
Planning And Control ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Input And Output ◽  
And Control ◽  
Trajectory Planning And Control

SUMMARYFinding singular configurations (singularities) has an important role during the design, trajectory planning, and control stages of mechanisms because in these configurations, the instantaneous kinematics is locally undetermined. In this paper, a systematic method is presented to obtain singular configurations of spherical mechanisms with input and output links. The method extends the use of instantaneous poles to singularity analysis of spherical mechanisms and offers geometric conditions for any type of singularities occurring in these mechanisms.

Singularity Analysis of Multi-DOF Planar Mechanisms

2007 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Motion Control ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Static Behavior ◽  
Planar Mechanisms ◽  
New Approach ◽  
Singular Configurations

Singular configurations (singularities) are mechanism configurations where the instantaneous kinematics is locally undetermined. Since the indetermination of the instantaneous kinematics causes serious problems both to the static behavior and to the motion control of the mechanism, the research of all the singularities (singularity analysis) is a mandatory step during the design of mechanisms. This paper presents a new approach to implement the singularity analysis of planar mechanisms. The proposed technique extends the use of the instant center properties to the singularity analysis of planar mechanisms with more than one degree of freedom (dof). It exploits the results of previous works by the author in which a geometric and analytic technique has been presented to address the singularity analysis of single-dof planar mechanisms.

The scientific bibliography of Roberto Lawley (1818–1881) and his contribution to the study of fossil sharks

2006 ◽  
Vol 33 (2) ◽  
pp. 267-281
Author(s):  
Giuseppe Manganelli ◽  
Andrea Benocci ◽  
Valeriano Spadini
Keyword(s):  
New Taxa ◽  
Scientific Community ◽  
Publishing House ◽  
Main Interest ◽  
Private Collection ◽  
Scientific Papers

Roberto Massimo Lawley (1818–1881) was a non-academic naturalist who made a major contribution to the Tuscan scientific community of his time. He was involved in the foundation of two societies (Società Italiana di Malacologia, 1874–1899; Società Toscana di Scienze Naturali, 1874–today) and a publishing house (Biblioteca Malacologica Italiana). He first devoted himself to malacology, but Neogene fossil fishes became his main interest. Over the years, he gathered a huge private collection of fossils and produced 18 scientific papers, dealing mainly with fossil sharks. Subsequent revisers criticized his approach to fossil taxa: their observations were generally sound, but they failed to fully recognize Lawley's scientific merits. His scientific papers, new taxa established by him and eponymys are given in the Appendix.

Determination of the Instantaneous Pole Axes in Single-DOF Spherical Mechanisms

2008 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
A Algorithm ◽  
Planar Mechanisms ◽  
Spherical Mechanisms ◽  
Kinematic Behavior ◽  
General Method

In spherical mechanisms, the instantaneous pole axes play the same role as the instant centers in planar mechanisms. Notwithstanding this, they are not fully exploited to study the kinematic behavior of spherical mechanisms as the instant centers are for planar mechanisms. The first step to make their use possible and friendly is the availability of efficient techniques to determine them. This paper presents a general method to determine the instantaneous pole axes in single-dof spherical mechanisms as a function of the mechanism configuration. The presented method is directly deduced from a algorithm already proposed by the author for the determination of the instant centers in single-dof planar mechanisms.

Solving the Kinematics of Planar Mechanisms

1998 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
System Of Equations ◽  
Polynomial Equations ◽  
Input Output ◽  
Planar Mechanisms ◽  
General Method

Abstract This paper presents a general method for the analysis of planar mechanisms consisting of rigid links connected by rotational and/or translational joints. After describing the links as vectors in the complex plane, a simple recipe is outlined for formulating a set of polynomial equations which determine the locations of the links when the mechanism is assembled. It is then shown how to reduce this system of equations to a standard eigenvalue problem, or if preferred, a single resultant polynomial. Both input/output problems and tracing-curve equations are treated.

scholarly journals A Novel Kinematically Redundant Planar Parallel Robot Manipulator With Full Rotatability

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Nicholas Baron ◽  
Andrew Philippides ◽  
Nicolas Rojas
Keyword(s):  
Potential Application ◽  
Robot Manipulator ◽  
Video Recording ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Geometric Method ◽  
Forward Kinematics ◽  
Online Video ◽  
End Effector ◽  
Moving Platform

This paper presents a novel kinematically redundant planar parallel robot manipulator, which has full rotatability. The proposed robot manipulator has an architecture that corresponds to a fundamental truss, meaning that it does not contain internal rigid structures when the actuators are locked. This also implies that its rigidity is not inherited from more general architectures or resulting from the combination of other fundamental structures. The introduced topology is a departure from the standard 3-RPR (or 3-RRR) mechanism on which most kinematically redundant planar parallel robot manipulators are based. The robot manipulator consists of a moving platform that is connected to the base via two RRR legs and connected to a ternary link, which is joined to the base by a passive revolute joint, via two other RRR legs. The resulting robot mechanism is kinematically redundant, being able to avoid the production of singularities and having unlimited rotational capability. The inverse and forward kinematics analyses of this novel robot manipulator are derived using distance-based techniques, and the singularity analysis is performed using a geometric method based on the properties of instantaneous centers of rotation. An example robot mechanism is analyzed numerically and physically tested; and a test trajectory where the end effector completes a full cycle rotation is reported. A link to an online video recording of such a capability, along with the avoidance of singularities and a potential application, is also provided.

Singularity Analysis of Serial Robot-Manipulators

1996 ◽  
Vol 118 (4) ◽  
pp. 520-525 ◽  
Author(s):  
A. Karger
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Singularity Analysis ◽  
Singular Set ◽  
Singular Configurations ◽  
Special Cases ◽  
Serial Robot ◽  
Singular Configuration ◽  
Actual Configuration

This paper is devoted to the description of the set of all singular configurations of serial robot-manipulators. For 6 degrees of freedom serial robot-manipulators we have developed a theory which allows to describe higher order singularities. By using Lie algebra properties of the screw space we give an algorithm, which determines the degree of a singularity from the knowledge of the actual configuration of axes of the robot-manipulator only. The local shape of the singular set in a neighbourhood of a singular configuration can be determined as well. We also solve the problem of escapement from a singular configuration. For serial robot-manipulators with the number of degrees of freedom different from six we show that up to certain exceptions singular configurations can be avoided by a small change of the motion of the end-effector. We also give an algorithm which allows to determine equations of the singular set for any serial robot-manipulator. We discuss some special cases and give examples of singular sets including PUMA 560.

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