Circuit Rectification for Four Precision Position Synthesis of Four-Bar and Watt Six-Bar Linkages

1995 ◽  
Vol 117 (4) ◽  
pp. 612-619 ◽  
Author(s):  
J. A. Mirth ◽  
T. R. Chase
Keyword(s):  
Solution Space ◽  
Potential Solution ◽  
Position Synthesis ◽  
Linkage Synthesis

The circuit defect arises in precision position based linkage synthesis when a potential solution linkage cannot be moved between all precision positions without disassembly. Circuit rectification consists of reducing the potential solution space to include only those linkages that are free of the circuit defect. Circuit rectification for four precision position synthesis of Watt six-bar linkages is developed here. Circuit rectification of four-bar linkages is refined in the process. An example demonstrates the synthesis of a new Watt I sofa bed linkage free of the circuit defect.

A Generalized Performance Sensitivity Synthesis Methodology for Four-Bar Mechanisms

1992 ◽  
Author(s):  
Ming-Yih Lee ◽  
Arthur G. Erdman ◽  
Salaheddine Faik
Keyword(s):  
Solution Space ◽  
Design Solution ◽  
Link Length ◽  
Performance Sensitivity ◽  
Closed Chain ◽  
Synthesis Methodology ◽  
Position Synthesis ◽  
The Relationship ◽  
Accuracy Performance ◽  
Sensitivity Maps

Abstract A generalized accuracy performance synthesis methodology for planar closed chain mechanisms is proposed. The relationship between the sensitivity to variations of link lengths and the location of the moving pivots of four-link mechanisms is investigated for the particular objective of three and four position synthesis. In the three design positions case, sensitivity maps with isosensitivity curves plotted in the design solution space allow the designer to synthesize a planar mechanism with desired sensitivity value or to optimize sensitivity from a set of acceptable design solutions. In the case of four design positions, segments of the Burmester design curves that exhibit specified sensitivity to link length tolerance are identified. A performance sensitivity criterion is used as a convenient and a useful way of discriminating between many possible solutions to a given synthesis problem.

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.

Using Your Fingers to Think: Enabling Subjective Routing with a Rubber Band Metaphor

2015 ◽  
Vol 25 (02) ◽  
pp. 397-413
Author(s):  
Andrew Bennett ◽  
Matthew D'Orazio ◽  
Christopher Lueg
Keyword(s):  
Elastic Properties ◽  
Route Planning ◽  
Solution Space ◽  
Experimental System ◽  
Rubber Band ◽  
Potential Solution ◽  
Complex Problems ◽  
Transit Times

There is a class of complex problems where solutions must satisfy multiple subjective criteria, while meeting specific quantifiable constraints. Route planning for leisurely travel is an example of a problem in this class. Constraints including total available time, transit times, and one's budget and subjective interests determine whether a potential solution is acceptable to a prospective traveler. In this paper we present a route planning (routing) interface that metaphorically leverages various elastic properties of a rubber band to allow for playful interaction with the relevant constraints. Each of these properties — attenuation, tension, and color — were integrated into an experimental system and then investigated in a series of task-based evaluations. Our research shows this playful interaction enables potential travelers to explore the solution space in order to find a route that meets, not only the easily quantifiable constraints, but also their own subjective preferences.

Determination of the Shortest Crank in Four Position Synthesis: A Numerical Apporach

1992 ◽  
Author(s):  
Shin-Min Song ◽  
Fu-Hung Lu ◽  
Ning-Xin Chen ◽  
Kenneth J. Waldron
Keyword(s):  
Numerical Stability ◽  
Search Algorithm ◽  
Solution Space ◽  
Numerical Approach ◽  
Parameter Perturbation ◽  
Spurious Solutions ◽  
Automatic Search ◽  
Position Synthesis ◽  
Parameter Perturbation Method

Abstract The shortest crank of a four position synthesis can be determined by solving a statically determinate five-bar structure and a set of seven nonlinear equations have been proposed for this purpose. In this paper a numerical method which can directly solve the shortest crank is presented. It is found that a direct implementation of the original seven equations has two problems: many spurious solutions and poor numerical stability. And the spurious solutions are of the following two types: solutions with incorrect signs of angles and solutions with incorrect geometry. In order to solve the problems, a set of ten equations is developed and parameter perturbation method is applied. Furthermore, a set of eight equations is developed for better numerical stability. Both the ten and eight equations can eliminate the spurious solutions with incorrect geometry. Yet the spurious solutions with incorrect signs of angles can only be rectified after convergence. An automatic search algorithm is included to automatically search the shortest crank in the solution space. Many examples are given to illustrate this numerical approach.

Branch Identification of Geared Five-Bar Chains

1996 ◽  
Vol 118 (3) ◽  
pp. 384-389 ◽  
Author(s):  
Xiaohong Dou ◽  
Kwun-Long Ting
Keyword(s):  
Synthesis Problem ◽  
Input Condition ◽  
Computer Aided ◽  
Position Synthesis ◽  
Linkage Synthesis

This paper presents the method to identify the rotatability and branch condition in linkages containing simple geared five-bar chains. The method is subsequently extended to identify the existence of dead positions. When used in the computer aided linkage synthesis, the algorithm may effectively reduce the complexity of the finite position synthesis of geared five-bar linkages to the level similar to that of four-bar linkages. The algorithm is effective for any linkage inversion, any type of synthesis problem, any input condition, and any number of discrete positions. The method can be generalized to other serially connected multiloop linkages.

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.

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]

Moving Pivot Specification for Three Precision Position Planar Linkage Synthesis

2008 ◽  
Author(s):  
John T. Wanner ◽  
Andrew E. Sherman ◽  
Benjamin J. Fisher ◽  
Thomas R. Chase
Keyword(s):  
Analytical Solution ◽  
Complex Number ◽  
Vehicle Suspension ◽  
Graphical Construction ◽  
Position Synthesis ◽  
Linkage Synthesis

An analytical solution to moving pivot specification of motion generating dyads at three precision positions is derived using the complex number formulation. This solution enables replicating the functionality of a well-known graphical construction for three position synthesis. It complements an existing complex number based solution for ground pivot specification. The solution is demonstrated by a practical example of designing a vehicle suspension linkage. The example also demonstrates how moving pivot specification can be applied to synthesize multiloop linkages.

Software for Investigating the Kinematics, Statics and Dynamics of Coupler-Driven Four-Bars for Two Position Synthesis

2007 ◽  
Author(s):  
Michael L. Turner ◽  
Eric M. Grimm ◽  
Daniel Debrosse ◽  
Kevin Kosmac ◽  
Andrew P. Murray
Keyword(s):  
Solution Space ◽  
Branch Points ◽  
Joint Force ◽  
Statics And Dynamics ◽  
Position Synthesis ◽  
Four Bar Linkage

The synthesis of a planar four-bar in which a point on the coupler reaches two specified points and orientations generates a six-fold space of solutions. The solution space increases if additional links are added to drive the mechanism, such as the Stephenson III. This paper presents an investigation of a coupler driven four-bar linkage, a Stephenson III six-bar with an RPR chain driving the four-bar sub-chain instead of the classically defined 3R chain. The software allows the designer to specify the problem and quickly scan the solution space. A comparison is constructed between a four-bar driven through a torque at the input link and a coupler-driven four-bar. Changes in branch points, the joint force index and the dynamics are observed.

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.

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