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.

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

A New Approach for Locating the Instantaneous Centers of Zero Velocity for 1-DOF Planar Linkages

2018 ◽  
Author(s):  
Nadim Diab
Keyword(s):  
Degree Of Freedom ◽  
Planar Mechanisms ◽  
New Approach ◽  
Zero Velocity ◽  
Graphical Technique ◽  
Instantaneous Center ◽  
Planar Linkages ◽  
Consistent Approach

This paper presents a new graphical technique to locate the secondary instantaneous centers of zero velocity (ICs) for one-degree-of-freedom (1-DOF) kinematically indeterminate planar mechanisms. The proposed approach is based on transforming the 1-DOF mechanism into a 2-DOF counterpart by converting any ground-pivoted ternary link into two ground-pivoted binary links. Fixing each of these two new binary links, one at a time, results in two different 1-DOF mechanisms where the intersection of the loci of their instantaneous centers will determine the location of the desired instantaneous center for the original 1-DOF mechanism. This single and consistent approach proved to be successful in locating the ICs of various mechanisms reported in the literature that required different techniques to reach the same results obtained herein.

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.

Singularity Analysis of Planar Multiple-DOF Linkages

2014 ◽  
Author(s):  
Jun Wang ◽  
Liangyi Nie ◽  
Quan Wang ◽  
Jinfeng Sun ◽  
Ying You ◽  
...  
Keyword(s):  
Singularity Analysis ◽  
General Concept ◽  
Degree Of Freedom ◽  
Simple Explanation ◽  
Constrained Motion ◽  
Singular Configurations ◽  
N Input ◽  
Center Position ◽  
Kinematic Loop ◽  
Planar Linkages

Singularity analysis of multi-DOF (multiple-degree-of-freedom) multiloop planar linkages is much more complicated than the single-DOF planar linkages. This paper offers a degeneration method to analyze the singularity (dead center position) of multi-DOF multiloop planar linkages. The proposed method is based on the singularity analysis results of single-DOF planar linkages and the less-DOF linkages. For an N-DOF (N>1) planar linkage, it generally requires N inputs for a constrained motion. By fixing M (M<N) input joints or links, the N-DOF planar linkage degenerates an (N-M)-DOF linkage. If any one of the degenerated linkages is at the dead center position, the whole N-DOF linkage must be also at the position of singularity. With the proposed method, one may find out that it is easy to obtain the singular configurations of a multiple-DOF multiloop linkage. The proposed method is a general concept in sense that it can be systematically applied to analyze the singularity for any multiple-DOF planar linkage regardless of the number of kinematic loop or the types of joints. The velocity method for singularity analysis is also used to verify the results. The proposed method offers simple explanation and straightforward geometric insights for the singularity identification of multiple-DOF multiloop planar linkages. Examples are also employed to demonstrate the proposed method.

Singularity Analysis of 5-RPRRR Parallel Mechanisms via Grassmann Line Geometry

2009 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Line Geometry ◽  
Singular Configurations ◽  
Highly Nonlinear ◽  
Grassmann Line Geometry

This paper investigates the singular configurations of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical legs of the RPUR type. The general mechanism was recently revealed by performing the type synthesis for symmetrical 5-DOF parallel mechanisms. In this study, some simplified designs are proposed for which the singular configurations can be predicted by means of the so-called Grassmann line geometry. This technique can be regarded as a powerful tool for analyzing the degeneration of the Plu¨cker screw set. The main focus of this contribution is to predict the actuation singularity, for a general and simplified design, without expanding the determinant of the inverse Jacobian matrix (actuated constraints system) which is highly nonlinear and difficult to analyze.

A DEPENDENT-SCREW SUPPRESSION APPROACH TO THE SINGULARITY ANALYSIS OF A 7-DOF REDUNDANT MANIPULATOR: CANADARM2

2005 ◽  
Vol 29 (4) ◽  
pp. 593-604 ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Singular Configurations

A dependent-screw suppression approach is proposed for the singularity analysis of 7-DOF (degree-of-freedom) redundant manipulators. This approach is applied to the singularity analysis of the Canadarm2. Five families of singular configurations are identified for the Canadarm2. The singular configurations obtained are identical to those obtained using the reciprocity-based method. Unlike the results presented previously, there are no denominators in the equations describing the singular configurations.

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.

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.

Analytic and Geometric Technique for the Singularity Analysis of Multi-Degree-of-Freedom Spherical Mechanisms

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Virtual Work ◽  
Superposition Principle ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Static Behavior ◽  
Virtual Work Principle ◽  
Spherical Mechanisms ◽  
Homogeneous Models ◽  
Homogeneous Mappings ◽  
Geometric Technique

Mechanisms' instantaneous kinematics is modeled by linear and homogeneous mappings whose coefficient matrices are also meaningful to understand their static behavior through the virtual work principle. The analysis of these models is a mandatory step during design. The superposition principle can be used for building and studying linear and homogeneous models. Here, multi-degree-of-freedom (multi-DOF) spherical mechanisms are considered. Their instantaneous-kinematics model is written by exploiting instantaneous-pole-axes' (IPA) properties and the superposition principle. Then, this general model is analyzed and an exhaustive analytic and geometric technique to identify all their singular configurations is deduced. Eventually, the effectiveness of the deduced technique is shown with two relevant case studies.

Sign in / Sign up

Export Citation Format

Share Document