Quasi-Precision Position Synthesis of Four-Bar Linkages

1994 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Two Dimensional ◽  
Exact Position ◽  
Planar Linkages ◽  
Position Synthesis ◽  
Exact Positions

Abstract Quasi positions describe portions of a mechanism’s motion that do not require an exact position. Quasi positions are combined with three exact positions to define a two-dimensional design plane for the synthesis of planar linkages. Quasi-precision position synthesis is based on precision position techniques. The method preserves the computational advantages of precision position synthesis with the added advantage of being able to specify a much greater number of design positions.

Two Precision Position Synthesis of Planar Linkages With Positional Rectification

1996 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Numerical Algorithms ◽  
All Solutions ◽  
Pass Through ◽  
Planar Linkages ◽  
Position Synthesis ◽  
Exact Positions

Abstract Precision position synthesis is used to generate planar linkages that pass through two exact positions and an additional number of approximate positions. The approximate positions provide a means of rectifying the solution linkages such that all solutions presented are more likely to describe a motion that remains within acceptable positional bounds. The rectification method involves the development of three different numerical algorithms that may be applied to a particular step in the dyad/triad method of precision position synthesis. The three algorithms presented can be applied in a variety of combinations to allow for the synthesis of both simple (four-bar) and complex (multiloop) planar linkages.

Approximate Velocities in Mixed Exact-Approximate Position Synthesis of Planar Mechanisms

1999 ◽  
Vol 123 (3) ◽  
pp. 388-394 ◽  
Author(s):  
Jennifer E. Holte ◽  
Thomas R. Chase ◽  
Arthur G. Erdman
Keyword(s):  
Two Dimensional ◽  
Computer Implementation ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Form Complex ◽  
New Approach ◽  
Realistic Representation ◽  
Velocity Constraints ◽  
Position Synthesis ◽  
Exact Positions

A new approach to the synthesis of planar linkage mechanisms with approximate velocity constraints is proposed. The paper presents the first closed-form complex-number dyad solution to the ground pivot specification problem for two precision positions with velocity specified at one of the positions. The solution is then manipulated in order to add approximate velocity constraints to design methods for two exact positions and an unlimited number of approximate positions. The approximate position and velocity constraints facilitate more realistic representation of design objectives. Solution spaces are presented using two-dimensional ground-pivot maps. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation.

An X-ray examination of substituted edingtonites

1935 ◽  
Vol 24 (151) ◽  
pp. 208-220 ◽  
Author(s):  
W. H. Taylor
Keyword(s):  
British Museum ◽  
Systematic Investigation ◽  
Sodium Ion ◽  
Base Exchange ◽  
Barium Ions ◽  
X Ray ◽  
Exact Position ◽  
Ray Methods ◽  
Thallium Ions ◽  
Exact Positions

The rare barium zeolite edingtonite has been examined in the course of the systematic investigation of the zeolites now being made at the British Museum, and several substitution derivatives have been prepared. The structure of natural edingtonite has also been completely determined by X-ray methods, and in the present paper an account is given of an attempt to discover the exact positions occupied in the substituted edingtonites by the potassium and thallium ions which replace the barium ions of ordinary edingtonite.Base-exchange products obtained from some other zeolites have already been examined in detail by X-ray methods. In silveranalcime and silver-natrolite the intensities of X-ray reflections are explained satisfactorily on the assumption that each silver ion occupies the exact position previously occupied by the sodium ion which it replaces.

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.

The Synthesis of Planar Linkages to Satisfy an Approximate Motion Specification

1993 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Design Space ◽  
Accurate Position ◽  
Solution Region ◽  
Pass Through ◽  
Position Problem ◽  
The Individual ◽  
Planar Linkages ◽  
Position Synthesis ◽  
Individual Design ◽  
Complete Process

Abstract This paper introduces the method of quasi-precision position synthesis for planar linkages. A quasi-precision position is defined by an approximate region that the mechanism must pass through. The quasi-precision position problem specification generates an increased design region by not requiring the accurate position specification that is characteristic of optimization and precision position methods. The design space is generated by intersecting the individual design regions of different four position sets. Each four position set consists of three exact positions plus one quasi-precision position. The method allows for the use of any number of quasi-precision positions. The result of using quasi-precision positions is an increase in the available design space without violating the basic problem constraints. The increased solution region gives the designer a greater variety of choices while reducing the number of required design iterations. The complete process of quasi-precision position synthesis is presented through the use of an example.

A Linkage Type Map for Spherical 4 Position Synthesis

1995 ◽  
Author(s):  
Andrew P. Murray ◽  
J. Michael McCarthy
Keyword(s):  
Two Dimensional ◽  
Planar Case ◽  
Position Synthesis ◽  
Spherical Mechanism

Abstract This paper classifies and evaluates the solutions to the four orientation synthesis of spherical 4R linkages. Burmester’s result that a one-parameter set of planar RR dyads exists that guide a body through the four planar positions has an analogous form for spherical RR dyads given four orientations. The theory provides a two dimensional set of spherical 4R linkages that can be assembled in each of the four chosen orientations. A map of linkage types is obtained by classifying each spherical mechanism at the vertices of a finite grid on this set; Erdman titles this a “Map of Solutions” for the planar case. Each mechanism is then checked for input drivability, that is, whether or not the input link can drive the coupler smoothly through all four positions. The result is a map of the spherical 4R mechanisms that the designer can use to find practical solutions to the spherical synthesis problems.

scholarly journals A Novel Approach to the Teaching of Planar Mechanism Dynamics – A Case Study

2003 ◽  
Vol 31 (3) ◽  
pp. 201-214 ◽  
Author(s):  
Rosario Sinatra ◽  
Jorge Angeles
Keyword(s):  
Dynamic Model ◽  
Cross Product ◽  
Two Dimensional ◽  
Dynamic Balancing ◽  
Planar Mechanism ◽  
Systematic Procedure ◽  
Novel Approach ◽  
Planar Linkages ◽  
Crank Mechanism

We propose a novel approach to the teaching of undergraduate planar mechanism dynamics. To illustrate the approach, we use a case study, the dynamics of the planar slider-crank mechanism. In this case study, we make extensive use of an operator representing in two-dimensional form the cross-product of two vectors. Furthermore, by using the natural orthogonal complement, introduced elsewhere, we produce a systematic procedure to derive a dynamic model of the same class of mechanism. Subsequently, we illustrate how, with the use of the aforementioned operator, the dynamic balancing of this mechanism, as first proposed by Berkof and Lowen for RRRR planar linkages, and extended by Bagci to the slider-crank mechanism, simplifies tremendously.

Mixed Exact-Approximate Position Synthesis of Planar Mechanisms

1998 ◽  
Vol 122 (3) ◽  
pp. 278-286 ◽  
Author(s):  
Jennifer E. Holte ◽  
Thomas R. Chase ◽  
Arthur G. Erdman
Keyword(s):  
Three Dimensional ◽  
Solution Space ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Dimensional Solution ◽  
New Approach ◽  
Fuzzy Constraints ◽  
Position Synthesis ◽  
Synthesis Approach ◽  
Exact Positions

A new approach to the synthesis of planar linkage mechanisms with fuzzy constraints is proposed. Design methods for two exact positions and an unlimited number of approximate positions are presented. The use of approximate specifications allows the designer to represent design objectives more realistically. A precision position synthesis approach is used to generate a three-dimensional solution space of dyads satisfying all exact and approximate constraints. The three-dimensional solution space is reduced to a two-dimensional ground-pivot map. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation. [S1050-0472(00)00803-5]

IX. Lines of induction in a magnetic field

1901 ◽  
Vol 195 (262-273) ◽  
pp. 303-327 ◽  
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Viscous Liquid ◽  
Thin Sheet ◽  
The Body ◽  
Two Dimensional ◽  
Transparent Medium ◽  
Exact Position ◽  
Stream Lines ◽  
Lines Of Force

The following paper, which is partly experimental and partly mathematical, has arisen from the discovery that two-dimensional cases of magnetic lines of force could apparently be represented by the flow of a viscous liquid.* The original experiments upon which this assumption was made, showed that the stream lines which were obtained by the method in question, gave results very similar to those which had been calculated and plotted for the cases of an elliptical and circular cylinder. In order to ascertain definitely that the stream lines under these circum­stances actually gave the exact position and direction of the corresponding magnetic lines of force, a result which, if verified, could be used for many practical investi­gations—it was necessary to undertake a long research dealing with the various points involved, a research which has proved extremely laborious, extending without intermission over a period of nearly two years. In the first place it was necessary to devise some method by which a thin sheet of transparent or semi-transparent medium could be obtained of any required thickness, and on which, when placed between two sheets of glass, the required section of the body to be investigated could be formed.

Patterned Bootstrap: A New Method Which Gives Efficiency for Precision Position Synthesis of Planar Linkages

2005 ◽  
Author(s):  
Zhenjun Luo ◽  
Jian S. Dai
Keyword(s):  
New Method ◽  
Continuation Methods ◽  
Interval Methods ◽  
Homotopy Continuation ◽  
Root Finding ◽  
Starting Point ◽  
Homotopy Continuation Methods ◽  
Upper Level ◽  
Planar Linkages ◽  
Position Synthesis

This paper presents a new method, termed as patterned bootstrap (PB), which is suitable for precision position synthesis of planar linkages. The method solves a determined system of equations using a new bootstrapping strategy. In principle, a randomly generated starting point is advanced to a final solution through solving a number of intermediate systems. The structure and the associated parameters of each intermediate system is defined as a pattern. In practice, a PB procedure generally consists of two levels: an upper level which controls the transition of patterns, and a lower level which solves intermediate systems using globally convergent root-finding algorithms. Besides introducing the new method, tunnelling functions have been added to several systems of polynomials derived by formal researchers in order to exclude degenerated solutions. Our numerical experiments demonstrate that many precision position synthesis problems can be solved efficiently without resorting to time-consuming polynomial homotopy continuation methods or interval methods. Finding over 95 percentages of the complete solutions of the 11 precision position function generation problem of a Stephenson-III linkage has been achieved for the first time.

Sign in / Sign up

Export Citation Format

Share Document