A General Method for Constructing Planar Cognate Mechanisms

2021 ◽  
pp. 1-18
Author(s):  
Samantha N. Sherman ◽  
Jonathan D. Hauenstein ◽  
Charles W. Wampler
Keyword(s):  
Mechanical Design ◽  
Planar Mechanisms ◽  
Planar Curve ◽  
Straightforward Method ◽  
General Method

Abstract Cognate linkages are mechanisms that share the same motion, a property that can be useful in mechanical design. This paper treats planar curve cognates, that is, planar mechanisms with rotational joints whose coupler points draw the same curve, as well as coupler cognates and timed curve cognates. The purpose of this article is to develop a straightforward method based solely on kinematic equations to construct cognates. The approach computes cognates that arise from permuting link rotations and is shown to reproduce all of the known results for cognates of four-bar and six-bar linkages. This approach is then used to construct a cognate of an eight-bar and a ten-bar linkage.

Curve Cognate Constructions Made Easy

2020 ◽  
Author(s):  
Samantha N. Sherman ◽  
Jonathan D. Hauenstein ◽  
Charles W. Wampler
Keyword(s):  
Mechanical Design ◽  
Planar Mechanisms ◽  
Simple Method ◽  
Planar Curve ◽  
Geometric Drawing

Abstract Cognate linkages are mechanisms that share the same motion, a property that can be useful in mechanical design. This paper treats planar curve cognates, that is, planar mechanisms whose tracing point draws the same curve. While Roberts cognates for planar four-bars are relatively simple to understand from a geometric drawing, the same cannot be said for planar six-bar cognates, especially the intricate diagrams Dijksman presented in cataloging all the known six-bar curve cognates. The purpose of this article is to show how the six-bar cognates can be easily understood using kinematic equations written using complex vectors, giving a simple method for generating these cognates as alternatives in a mechanical design. The simplicity of the approach enables the derivation of cognates for eight-bars and possibly beyond.

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 Two-Swim Operators in the Modified Bacterial Foraging Algorithm for the Optimal Synthesis of Four-Bar Mechanisms

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Betania Hernández-Ocaña ◽  
Ma. Del Pilar Pozos-Parra ◽  
Efrén Mezura-Montes ◽  
Edgar Alfredo Portilla-Flores ◽  
Eduardo Vega-Alvarado ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Mechanical Design ◽  
Differential Evolution Algorithm ◽  
Fine Tuning ◽  
Local Optimum ◽  
Bacterial Foraging Optimization ◽  
Planar Mechanisms ◽  
Bacterial Foraging ◽  
Evolution Algorithm ◽  
Parameter Values

This paper presents two-swim operators to be added to the chemotaxis process of the modified bacterial foraging optimization algorithm to solve three instances of the synthesis of four-bar planar mechanisms. One swim favors exploration while the second one promotes fine movements in the neighborhood of each bacterium. The combined effect of the new operators looks to increase the production of better solutions during the search. As a consequence, the ability of the algorithm to escape from local optimum solutions is enhanced. The algorithm is tested through four experiments and its results are compared against two BFOA-based algorithms and also against a differential evolution algorithm designed for mechanical design problems. The overall results indicate that the proposed algorithm outperforms other BFOA-based approaches and finds highly competitive mechanisms, with a single set of parameter values and with less evaluations in the first synthesis problem, with respect to those mechanisms obtained by the differential evolution algorithm, which needed a parameter fine-tuning process for each optimization problem.

Configuration and Dimensional Synthesis in Mechanical Design: an Application for Planar Mechanisms

CIRP Annals ◽  
1994 ◽  
Vol 43 (1) ◽  
pp. 145-148 ◽  
Author(s):  
Petri Makkonen ◽  
Jan-Gunnar Persson
Keyword(s):  
Mechanical Design ◽  
Dimensional Synthesis ◽  
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.

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.

A fairly general method for optimum synthesis of planar mechanisms

1985 ◽  
Vol 20 (4) ◽  
pp. 321-328 ◽  
Author(s):  
R Avilés ◽  
M.B Ajuria ◽  
J García De Jalón
Keyword(s):  
Planar Mechanisms ◽  
Optimum Synthesis ◽  
General Method

A general method for analysis of planar mechanisms using a modular approach

1996 ◽  
Vol 31 (8) ◽  
pp. 1155-1166 ◽  
Author(s):  
Michael R. Hansen
Keyword(s):  
Modular Approach ◽  
Planar Mechanisms ◽  
General Method

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.

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