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.

Geometric Characteristics of the Center-Point Curve Based on the Kinematics of the Compatibility Linkage

1992 ◽  
Author(s):  
J. A. Schaaf ◽  
J. A. Lammers
Keyword(s):  
Complex Number ◽  
Change Point ◽  
Double Point ◽  
Classification Scheme ◽  
Center Point ◽  
Degenerate Form ◽  
Point Curve ◽  
Position Synthesis ◽  
Point Form

Abstract In this paper we develop a method of characterizing the center-point curves for planar four-position synthesis. We predict the five characteristic shapes of the center-point curve using the kinematic classification of the compatibility linkage obtained from a complex number formulation for planar four-position synthesis. This classification scheme is more extensive than the conventional Grashof and non-Grashof classifications in that the separate classes of change point compatibility linkages are also included. A non-Grashof compatibility linkage generates a unicursal form of the center-point curve; a Grashof compatibility linkage generates a bicursal form; a single change point compatibility linkage generates a double point form; and a double or triple change point compatibility linkage generates a circular-degenerate or a hyperbolic-degenerate form.

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.

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

1992 ◽  
Author(s):  
John A. Mirth ◽  
Thomas R. Chase
Keyword(s):  
Complex Number ◽  
Sequential Analysis ◽  
Design Space ◽  
Circuit Defects ◽  
Position Synthesis

Abstract The circuit defect arises when a linkage can not be moved between all precision positions without disassembly. The synthesis of linkages by precision position methods is simplified by reducing the design space to include only those linkages that are free of the circuit defect. Solutions for four-bar and Watt six-bar mechanisms are developed here. Multiple circuits in the Watt six-bar chain arise from circuits within a four-bar chain of the linkage or from the limits of motion that are imposed on the entire linkage by the two four-bar subchains. The circuit defects that are introduced by these conditions are eliminated through the sequential analysis of the Burmester curves for four-position synthesis. The points on the Burmester curves where the circuit attributes change are found. The curve segments yielding mechanisms that exhibit the circuit defect are then eliminated from consideration. The process is numerical and based on the complex number formulation of Burmester theory.

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.

Improved Centerpoint Curve Generation Techniques for Four-Precision Position Synthesis Using the Complex Number Approach

1985 ◽  
Vol 107 (3) ◽  
pp. 370-376 ◽  
Author(s):  
T. R. Chase ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Complex Number ◽  
Independent Parameter ◽  
Trial And Error ◽  
Sequential Order ◽  
Automatic Computation ◽  
Theory Result ◽  
Generate Solution ◽  
Position Synthesis

A method for predetermining the properties of a centerpoint curve of the Burmester curve pair which will result from an arbitrary set of four precision positions is introduced. The method is based on the discovery that the shape of any Burmester curve is dependent on the Grashof type of the associated compatibility linkage. Three improvements over the existing theory result. First, the exact range of the independent parameter which will generate solution dyads may be determined, eliminating the need to search for solutions on a trial-and-error basis. Second, the composition of the centerpoint curve may be predicted in advance, enabling improved plotting techniques. Third, the points comprising the centerpoint curve can be generated in their natural sequential order. These techniques may be readily programmed for automatic computation.

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.

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 Complex Number Approach for Absolute Precision Position Synthesis for Three Precision Positions

1992 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Closed Form ◽  
Complex Number ◽  
Closed Form Solution ◽  
Form Solution ◽  
Path Generation ◽  
Motion Generation ◽  
The Absolute ◽  
Position Problem ◽  
Position Synthesis

Abstract Dyads can be synthesized by prescribing the precision point coordinates and the absolute planar orientations of one dyad vector at each of three precision positions. This differs from traditional complex number methods wherein the vector orientations are described relative to one another. Absolute precision position synthesis can be performed for both motion generation, and path generation with prescribed timing. The method presented uses vector loop equations and complex number notation to produce a closed form solution for the three absolute precision position problem. Absolute precision position synthesis is applicable to cases that require specific coupler geometries. The synthesis of flat-folding mechanisms is an example of one such application.

Solution region synthesis methodology of planar eight-bar linkage for four specified positions of a 4R chain

2020 ◽  
Vol 234 (24) ◽  
pp. 4813-4826
Author(s):  
Guangzhen Cui ◽  
Jianyou Han ◽  
Yanqiu Xiao ◽  
Caidong Wang
Keyword(s):  
Feasible Solution ◽  
Solution Curve ◽  
Defect Identification ◽  
Different Types ◽  
Practical Engineering ◽  
Solution Region ◽  
Synthesis Methodology ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

The solution region methodology for solving the problem of four-bar linkage synthesis with four specified positions was extended to solve the problem of eight-bar linkage synthesis. The processes to build solution regions for synthesizing different types of eight-bar linkages are described, and the methods of building solution regions are divided into five types. First, the synthesis equation is derived, and the curve expressed by the synthesis equation is called the solution curve. Second, the process to build the spatial solution regions from the solution curves is detailed, and a new defect identification method is developed for building the spatial feasible solution region, which is a set of linkage solutions meeting four positions and excluding defects. Finally, linkage solutions that do not meet practical engineering requirements are eliminated from the spatial feasible solution region to obtain the useful spatial solution region. The examples demonstrate the feasibility of the proposed method. The proposed synthesis methodology is simple and easy to program, and provides reference for four specified position synthesis of other multi-bar linkages.

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