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.

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.

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.

scholarly journals A general method for the determination of the instantaneous screw axes of one-degree-of-freedom spatial mechanisms

2020 ◽  
Vol 11 (1) ◽  
pp. 91-99
Author(s):  
Juan Ignacio Valderrama-Rodríguez ◽  
José M. Rico ◽  
J. Jesús Cervantes-Sánchez
Keyword(s):  
Degree Of Freedom ◽  
Euclidean Group ◽  
Spatial Mechanisms ◽  
Instantaneous Screw ◽  
General Method

Abstract. This contribution shows that a method proposed previously, for the determination of the instantaneous centers of rotation of planar closed chains, can be generalized for the determination of the instantaneous screw axes of general one-degree-of-freedom spatial mechanisms. Hence, the approach presented in this paper can be applied to any of the closed chains that belong to any of the subgroups of the Euclidean group, SE(3), namely planar, spherical or chains associated with the Schönflies subgroups, among others. Furthermore it can be also applied to multi-loop mechanisms and even to closed chains that are exceptional o paradoxical, as indicated by Hervé.

Determination of overconstraint and mobility analysis for planar mechanisms

2016 ◽  
Vol 230 (20) ◽  
pp. 3743-3754 ◽  
Author(s):  
Daxing Zeng ◽  
Wenjuan Lu ◽  
Zhen Huang
Keyword(s):  
Closed Loop ◽  
Degree Of Freedom ◽  
Mobility Analysis ◽  
Planar Mechanisms ◽  
New Concepts ◽  
Core Problem

The mobility(or degree of freedom) analysis of planar mechanisms is traditionally calculated using the Grübler–Kutzbach formula. However, this method often fails in practice due to overconstraint, which is a core problem in all mobility analysis. Analyzing the cause of overconstraint, it is presented that overconstraint in closed-loop mechanisms can be recognized by analyzing the relative movements of the two elements in a rigidity re-closure. A solution to determine the overconstraint in multiloop mechanisms is also proposed. In this method, each loop is opened and the overconstraint can be calculated when the loop is reclosed. A mobility analysis must begin by determining the overconstraint. However, given that most planar mechanisms do not have any overconstraint, it is important to identify rapidly whether overconstraint exists in a mechanism. This paper proposes a concise technique to determine the existence of overconstraint based on the concept of “Assur groups”. To simplify the process of mobility analysis, three new concepts and four relevant theories are introduced. In this paper, the proposed methodology is applied to several types of planar mechanisms, producing results in accordance with the prototype. This shows that the proposed methodology makes performing the mobility analysis of planar mechanisms, including complicated planar mechanisms, accurate, convenient, and fast.

MANUFACTURE INVESTIGATION OF CARTRIDGE WITH BOTTOM-MOST PART FLANGE BY DIRECT EXTRUSION WITH COUNTERPUNCH. REPORT 13. DETERMINATION OF DEFORMED STATE UNDER STRAITENED EXTRUSION IN FOURTH CENTRAL AREA OF PLASTIC DEFORMATION

2020 ◽  
Vol 0 (4) ◽  
pp. 43-51
Author(s):  
A. L. Vorontsov ◽  
◽  
I. A. Nikiforov ◽  
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Central Area ◽  
Direct Extrusion ◽  
Deformed State ◽  
Cumulative Deformation ◽  
The Given ◽  
General Method

Formulae have been obtained that are necessary to calculate cumulative deformation in the process of straitened extrusion in the central area closed to the working end of the counterpunch. The general method of plastic flow proposed by A. L. Vorontsov was used. The obtained formulae allow one to determine the deformed state of a billet in any point of the given area. The formulae should be used to take into account the strengthening of the extruded material.

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.

Kinematic and Workspace Modelling of a 6-PUS Parallel Mechanism

2018 ◽  
Author(s):  
Jérôme Landuré ◽  
Clément Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Accurate Description ◽  
Transmission Ratio ◽  
Inverse Kinematic Problem ◽  
Jacobian Matrices ◽  
Six Degree Of Freedom

This article presents the kinematic analysis of a six-degree-of-freedom six-legged parallel mechanism of the 6-PUS architecture. The inverse kinematic problem is recalled and the Jacobian matrices are derived. Then, an algorithm for the geometric determination of the workspace is presented, which yields a very fast and accurate description of the workspace of the mechanism. Singular boundaries and a transmission ratio index are then introduced and studied for a set of architectural parameters. The proposed analysis yields conceptual architectures whose properties can be adjusted to fit given applications.

A New Method and Automatic Generation for Dynamic Analysis of Complex Planar Mechanisms Based on the Ordered Single-Opened-Chains

1994 ◽  
Author(s):  
Jian-Qing Zhang ◽  
Ting-Li Yang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Equation ◽  
Automatic Generation ◽  
The Other ◽  
New Method ◽  
Complex Mechanism ◽  
Planar Mechanisms ◽  
Spatial Mechanisms ◽  
General Dynamic

Abstract This work presents a new method for kinetostatic analysis and dynamic analysis of complex planar mechanisms, i.e. the ordered single-opened-chains method. This method makes use of the ordered single-opened chains (in short, SOC,) along with the properties of SOC, and the network constraints relationship between SOC,. By this method, any planar complex mechanism can be automatically decomposed into a series of the ordered single-opened chains and the optimal structural decomposition route (s) can be automatically selected for dynamic analysis, the paper present the dynamic equation which can be used to solve both the kinetostatic problem and the general dynamic problem. The main advantage of the proposed approach is the possibility to reduce the number of equations to be solved simultaneously to the minimum, and its high automation as well. The other advantage is the simplification of the determination of the coefficients in the equations, and thus it maybe result in a much less time-consuming algorthem. The proposed approach is illustrated with three examples. The presented method can be easily extended to the dynamic analysis of spatial mechanisms.

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