A Robust Solution of the Spherical Burmester Problem

2010 ◽  
Author(s):  
Jorge Angeles ◽  
Shaoping Bai
Keyword(s):  
Solution Method ◽  
Synthesis Method ◽  
Robust Solution ◽  
Equation Solving ◽  
Prismatic Joints ◽  
Four Bar Linkage ◽  
Special Case ◽  
Robust Synthesis ◽  
Linkage Synthesis

The problem of spherical four-bar linkage synthesis is revisited in this paper. The work is aimed at developing a robust synthesis method by taking into account both the formulation and the solution method. In addition, the synthesis of linkages with spherical prismatic joints is considered by treating them as a special case of the linkages under study. A two-step synthesis method is developed, which sequentially deals with equation-solving by a semigraphical approach and branching-detection. Examples are included to demonstrate the proposed method.

Four-Bar Linkage Synthesis Methods for Two Precision Positions Combined With N Quasi-Positions

1995 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Synthesis Method ◽  
Synthesis Methods ◽  
Bounded Motion ◽  
Transmission Angle ◽  
Pass Through ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Exact Positions ◽  
Linkage Synthesis

Abstract Mechanisms seldom need to pass through more than one or two exact positions. The method of quasi-position synthesis combines a number of approximate or “quasi” positions with two exact positions to design four-bar linkages that will produce a specified, bounded motion. Quasi-position synthesis allows for the optimization of some linkage characteristic (such as link lengths or transmission angles) by using the three variables that describe a single quasi-position. Procedures for circuit and transmission angle rectification are also easily incorporated into the quasi-position synthesis method.

Some Special Cases of the Burmester Problem for Four and Five Poses

2005 ◽  
Author(s):  
Jorge Angeles ◽  
Shaoping Bai
Keyword(s):  
Synthesis Method ◽  
Geometric Parameters ◽  
Special Treatment ◽  
End Point ◽  
Displacement Vectors ◽  
Special Cases ◽  
Common Intersection ◽  
Four Bar Linkage ◽  
Special Case

The Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with both revolute-revolute (RR) and prismatic-revolute (PR) dyads. A PR dyad is a special case of RR dyad, i.e., a dyad with one end-point at infinity. The special nature of PR dyads warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In this paper, we study the synthesis of planar four-bar linkages addressing the problem of the determination of PR dyads. The conditions for the presence of PR dyads with the prescribed poses are derived. A synthesis method is developed by resorting to the parallelism condition of the displacement vectors of the circle points of PR dyads. We show that the “circle” point of a PR dyad can be determined as one common intersection of three or four circles, depending on whether four or, correspondingly, five poses are prescribed.

A Method for Adjustable Planar and Spherical Four-Bar Linkage Synthesis

2004 ◽  
Vol 127 (3) ◽  
pp. 456-463 ◽  
Author(s):  
Boyang Hong ◽  
Arthur G. Erdman
Keyword(s):  
Synthesis Method ◽  
New Method ◽  
Spherical Form ◽  
Numerical Example ◽  
Input And Output ◽  
Special Cases ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

This paper describes a new method to synthesize adjustable four-bar linkages, both in planar and spherical form. This method uses fixed ground pivots and an adjustable length for input and output links. A new application of Burmester curves for adjustable linkages is introduced, and a numerical example is discussed. This paper also compares a conventional synthesis method (nonadjustable linkage) to the new method. Nonadjustable four-bar linkages provide limited solutions for five-position synthesis. Adjustable linkages generate one infinity of solution choices. This paper also shows that the nonadjustable solutions are special cases of adjustable solutions. This new method can be extended to six position synthesis, with adjustable ground pivots locations.

The Synthesis of Dyads With One Prismatic Joint

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Chao Chen ◽  
Shaoping Bai ◽  
Jorge Angeles
Keyword(s):  
Geometric Parameters ◽  
Special Treatment ◽  
Prismatic Joint ◽  
Invariant Formulation ◽  
Underlying Geometry ◽  
Joint Center ◽  
Four Bar Linkage ◽  
Special Case ◽  
Linkage Synthesis

The classic Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with revolute-revolute (RR), prismatic-revolute (PR), and revolute-prismatic (RP) dyads. A PR dyad is a special case of the RR dyad, namely, a dyad of this kind with its fixed joint center at infinity; a similar interpretation applies to the RP dyad. The special nature of dyads with one P joint warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In proposing robust computational means to synthesize PR and RP dyads, we adopt an invariant formulation, which, additionally, sheds light on the underlying geometry.

Planar Linkage Synthesis for Rigid Body Guidance Using Poles and Rotation Angles

2013 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Rigid Body ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
Center Point ◽  
Circle Center ◽  
Previous Solution ◽  
Design Software ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

A graphical four bar linkage synthesis method for planar rigid body guidance is presented. This method, capable of synthesis for up to five specified coupler positions, uses the poles and rotation angles, which are constraints, to define guiding links. Faster and simpler than traditional graphical synthesis methods, this method, allows the designer to see and consider most or all the possible solutions within a few seconds before making any free choices. All of the guiding links satisfying five specified coupler positions can be obtained graphically within 30 minutes without plotting any Burmester curves and without any mechanism design software. For four positions, both the circle and center point curves are simultaneously traced by corresponding circle-center point pairs using three poles having a common subscript and the corresponding rotation angles without any additional construction. This method eliminates the iterative construction required in previous methods which were based on free choices rather than constraints. The tedious plotting of Burmester curves graphically using pole quadrilaterals is also eliminated. The simplicity of the method makes four and five position synthesis practical to do graphically. A corresponding analytical solution is presented which provides a simpler formulation than the previous solution method. This new method requires two fewer equations and provides a new way to plot Burmester curves analytically.

A Simple Synthesis Method for Spherical 4R Linkages Reaching Four Positions

2011 ◽  
Vol 199-200 ◽  
pp. 1236-1239 ◽  
Author(s):  
Tong Yang ◽  
Jian You Han ◽  
Lai Rong Yin
Keyword(s):  
Matrix Method ◽  
Synthesis Method ◽  
Simple Synthesis ◽  
Simple Derivation ◽  
Derivation Method ◽  
Curve Equation ◽  
Linkage Synthesis

For spherical 4R linkage synthesis reaching four specified task positions, we introduce a simple derivation method of spherical Burmester curve equation by employing a displacement matrix method. Then we presented a method to calculate the coordinates of circle and center points, so the spherical Burmester curves can be drawn by the software developed.

scholarly journals METHOD OF PROJECT MULTICRITERIA DECISION SYNTHESIS ON THE BASIS OF DECISION SUCCESS CRITERION/PROJEKTŲ DAUGIAKRITERINIŲ SPRENDIMŲ SINTEZĖS REMIANTIS PRIIMAMO SPRENDIMO SĖKMĖS KRITERIJUMI METODAS

2000 ◽  
Vol 6 (3) ◽  
pp. 193-201 ◽  
Author(s):  
Vaidotas Šarka ◽  
Edmundas Kazimieras Zavadskas ◽  
Leonas Ustinovičius
Keyword(s):  
Decision Process ◽  
Construction Projects ◽  
Solution Method ◽  
Synthesis Method ◽  
Multicriteria Decision ◽  
Success Criterion ◽  
Decision Methods ◽  
Close Relationship ◽  
Relationship Of ◽  
Proper Analysis

Method of project multicriteria decision synthesis with decision success criterion is used for realisation of construction projects which require a proper analysis of constituent parts in close relationship of components. Scheme of this method is presented in Fig 3. Multicriteria decision project may be divided into several interrelated building processes and smaller projects. On every level of the whole project, the decision of closeness to ideal solution method is made and, on the basis of the obtained results, several alternatives are chosen. On every separate level, a number of alternatives is selected by the method user. It depends on complexity of the project and on requirements of interested parties. At the last decision stage, there is performed a synthesis using the chosen alternatives and relying on their interrelations. During decision process on the intermediate stages, having eliminated irrational alternatives, effective and precise results are achieved. The developed multicriteria decision synthesis method is one of the elements of the newly created group of multicriteria decision methods. Using this method algorithm, software is prepared that entirely manages the whole decision process from database filling to calculation and result processing.

scholarly journals Four-Bar Linkage Synthesis Using Non-convex Optimization

2016 ◽  
pp. 618-635 ◽  
Author(s):  
Vincent Goulet ◽  
Wei Li ◽  
Hyunmin Cheong ◽  
Francesco Iorio ◽  
Claude-Guy Quimper
Keyword(s):  
Convex Optimization ◽  
Four Bar Linkage ◽  
Linkage Synthesis

Linkage Synthesis of a Four-Bar Mechanism for N Precision Points Using Simulated Annealing

1998 ◽  
Author(s):  
Horacio Martínez-Alfaro ◽  
Homero Valdez ◽  
Jaime Ortega
Keyword(s):  
Simulated Annealing ◽  
Computational Intelligence ◽  
Simulated Annealing Algorithm ◽  
Alternative Synthesis ◽  
Computational Intelligence Technique ◽  
Annealing Algorithm ◽  
Four Bar Linkage ◽  
Generation Problem ◽  
Intelligence Technique ◽  
Linkage Synthesis

Abstract This paper presents an alternative way of linkage synthesis by using a computational intelligence technique: Simulated Annealing. The technique allows to define n precision points of a desired path to be followed by a four-bar linkage (path generation problem). The synthesis problem is transformed into an optimization one in order to use the Simulated Annealing algorithm. With this approach, a path can be better specified since the user will be able to provide more “samples” than the usual limited number of five allowed by the classical methods. Several examples are shown to demonstrate the advantages of this alternative synthesis technique.

A Matrix-Vector Operation-Based Numerical Solution Method for Linear m-th Order Ordinary Differential Equations: Application to Engineering Problems

2013 ◽  
Vol 5 (03) ◽  
pp. 269-308 ◽  
Author(s):  
M. Aminbaghai ◽  
M. Dorn ◽  
J. Eberhardsteiner ◽  
B. Pichler
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Solution Method ◽  
Variable Coefficients ◽  
Exact Integration ◽  
Robust Solution ◽  
Vector Operation ◽  
Engineering Sciences ◽  
Engineering Problems ◽  
Matrix Vector

AbstractMany problems in engineering sciences can be described by linear, inhomogeneous,m-th order ordinary differential equations (ODEs) with variable coefficients. For this wide class of problems, we here present a new, simple, flexible, and robust solution method, based on piecewise exact integration of local approximation polynomials as well as on averaging local integrals. The method is designed for modern mathematical software providing efficient environments for numerical matrix-vector operation-based calculus. Based on cubic approximation polynomials, the presented method can be expected to perform (i) similar to the Runge-Kutta method, when applied to stiff initial value problems, and (ii) significantly better than the finite difference method, when applied to boundary value problems. Therefore, we use the presented method for the analysis of engineering problems including the oscillation of a modulated torsional spring pendulum, steady-state heat transfer through a cooling web, and the structural analysis of a slender tower based on second-order beam theory. Related convergence studies provide insight into the satisfying characteristics of the proposed solution scheme.

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