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.

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.

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.

scholarly journals Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation

2000 ◽  
Vol 123 (3) ◽  
pp. 382-387 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
Numerical Solutions ◽  
Minimal Size ◽  
Input Output ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Revolute Joints ◽  
Generalized Eigenvalue ◽  
General Method

This paper presents a general method for the analysis of any planar mechanism consisting of rigid links connected by revolute joints. The method combines a complex plane formulation [1] with the Dixon determinant procedure of Nielsen and Roth [2]. The result is simple to derive and implement, so in addition to providing numerical solutions, the approach facilitates analytical explorations. The procedure leads to a generalized eigenvalue problem of minimal size. Both input/output problems and the derivation of tracing curve equations are addressed, as is the extension of the method to treat slider joints.

A general algorithm for analytically determining all the instantaneous pole axis locations in single-DOF spherical mechanisms

2011 ◽  
Vol 225 (9) ◽  
pp. 2062-2075 ◽  
Author(s):  
R Di Gregorio
Keyword(s):  
Degree Of Freedom ◽  
General Algorithm ◽  
Planar Mechanisms ◽  
Spherical Mechanisms ◽  
Kinematic Analyses ◽  
General Method

In spherical mechanisms (SMs), instantaneous pole axes (IPAs) play the same role as instant centres in planar mechanisms. Their use in kinematic analyses requires general techniques to determine them. In the literature, such techniques have not been proposed yet. That is why they are not used for studying the kinematics of SMs in all the problems whose planar counterparts are efficiently solved by exploiting instant centres’ properties. This article aims to fill this lack of techniques. For SMs with one degree of freedom (DOF), a general method to analytically locate all the IPAs as a function of the mechanism configuration is presented. The presented method is directly deduced from an algorithm already proposed by the author for the determination of the instant centres in single-DOF planar mechanisms.

scholarly journals Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation

2000 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
Numerical Solutions ◽  
Generalized Eigenvalue Problem ◽  
Minimal Size ◽  
Input Output ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Generalized Eigenvalue ◽  
General Method

Abstract This paper presents a general method for the analysis of any planar mechanism consisting of rigid links connected by revolute and slider joints. The method combines the complex plane formulation of Wampler (1999) with the Dixon determinant procedure of Nielsen and Roth (1999). The result is simple to derive and implement, so in addition to providing numerical solutions, the approach facilitates analytical explorations. The procedure leads to a generalized eigenvalue problem of minimal size. Both input/output problems and the derivation of tracing curve equations are addessed.

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.

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 Spherical Mechanism Synthesis in Virtual Reality

1998 ◽  
Author(s):  
Todd J. Furlong ◽  
Judy M. Vance ◽  
Pierre M. Larochelle
Keyword(s):  
Virtual Reality ◽  
Design Space ◽  
Three Dimensional ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
New Approach ◽  
Spherical Mechanisms ◽  
Input Design ◽  
Previous Design ◽  
Spherical Mechanism

Abstract This paper presents a new approach to using virtual reality (VR) to design spherical mechanisms. VR provides a three dimensional design space where a designer can input design positions using a combination of hand gestures and motions and view the resultant mechanism in stereo using natural head movement to change the viewpoint. Because of the three dimensional nature of the design and verification of spherical mechanisms, VR is examined as a new design interface in this research. In addition to providing a VR environment for design, the research presented in this paper has focused on developing a “design in context” approach to spherical mechanism design. Previous design methods have involved placing coordinate frames along the surface of a constraint sphere. The new “design in context” approach allows a designer to freely place geometric models of movable objects inside an environment consisting of fixed objects. The fixed objects could either act as a base for a mechanism or be potential sources of interference with the motion of the mechanism. This approach allows a designer to perform kinematic synthesis of a mechanism while giving consideration to the interaction of that mechanism with its application environment.

Instantaneous kinematics and singularity analysis of three-legged parallel manipulators

Robotica ◽  
2004 ◽  
Vol 22 (2) ◽  
pp. 189-203 ◽  
Author(s):  
Anjan Kumar Dash ◽  
I-Ming Chen ◽  
Song Huat Yeo ◽  
Guilin Yang
Keyword(s):  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Physical Structure ◽  
Inverse Kinematic ◽  
New Approach ◽  
Kinematics Model ◽  
Passive Joint ◽  
Geometric Conditions ◽  
Joint Plane ◽  
Inverse Kinematic Analysis

Instantaneous kinematics and singularity analysis of a class of three-legged, 6-DOF parallel manipulators are addressed in this paper. A generic method of derivation of reciprocal screw and consequently, the instantaneous kinematics model is presented. The advantage of this formulation is that the instantaneous kinematics model possesses well-defined geometric meaning and algebraic structure. Singularity analysis is performed under three categories, namely forward, inverse and combined singularities. A new concept of Passive Joint Plane is introduced to correlate the physical structure of the manipulator and these geometric conditions. In the inverse kinematic analysis, a new approach is introduced. At each leg end point a characteristic parallel- epiped is defined whose sides are the linear velocity components from three main joints of the leg. An inverse singularity occurs when the volume of this parallelepiped becomes zero. Examples are demonstrated using RRRS and RPRS-type parallel manipulators.

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