Planar Linkage Synthesis for Coupler Point Path Guidance Using Poles and Rotation Angles

2014 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Analytical Solution ◽  
Nonlinear Equations ◽  
Design Problem ◽  
Graphical Solution ◽  
Design Time ◽  
Linkage Design ◽  
Pass Through ◽  
Solution Mechanism ◽  
Four Bar Linkage ◽  
Selection Of

Coupler point path guidance is a long standing linkage design problem. It is possible to design a four bar linkage with a coupler point that will pass through up to nine specified points. This paper discloses a new graphical solution to this problem. The approach is to consider the constraints imposed by the target points on the linkage through the poles and rotation angles. This approach enables the designer to explore the range of possible solutions when fewer than nine points are specified by dragging a fixed or moving pivot in the plane. The selection of free choices is made at the end of the process and the complete mechanism is visible when the choices are made. The constraints only need to be made once which eliminates the repetitive construction required by previous methods to consider multiple pivot locations. Since it is so easy to consider multiple pivot locations and the solution mechanism is always visible, the required design time is greatly reduced. A corresponding analytical solution is also developed and solved based on the same constraints. The analytical solution is defined by a system of 28 nonlinear equations with 28 unknowns.

Planar Linkage Synthesis for Function Generation Using Poles and Rotation Angles

2015 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Analytical Solution ◽  
Graphical Solution ◽  
Function Generation ◽  
Design Time ◽  
Input And Output ◽  
Linkage Design ◽  
Pass Through ◽  
Solution Mechanism ◽  
Four Bar Linkage ◽  
Selection Of

Function Generation is a long standing linkage design problem. It is possible to design a planar four bar linkage whose input and output links will pass through seven coordinated positions. This paper discloses the first graphical solution to this problem. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. This approach enables the designer to explore the range of possible solutions when fewer than seven positions are specified by dragging a fixed or moving pivot in the plane. The selection of free choices is made at the end of the process and the complete mechanism is visible when the choices are made. The constraints only need to be made once which eliminates the repetitive construction required by previous methods to consider multiple pivot locations. Since it is so easy to consider multiple pivot locations and the solution mechanism is visible, the required design time is greatly reduced. A corresponding analytical solution is also developed and solved based on the same constraints. This is a new analytical solution and is defined by a system of 20 nonlinear equations with 20 unknowns.

Synthesis of the four-bar linkage as path generation by choosing the shape of the connecting rod

2020 ◽  
Vol 234 (13) ◽  
pp. 2643-2652 ◽  
Author(s):  
SM Varedi-Koulaei ◽  
H Rezagholizadeh
Keyword(s):  
Analytical Solution ◽  
Nonlinear Equations ◽  
Linear Equations ◽  
Solution Process ◽  
Current Method ◽  
Path Generation ◽  
Connecting Rod ◽  
Complicated Process ◽  
Four Bar Linkage ◽  
Analytical Synthesis

This paper presents a method for path generation synthesis of a four-bar linkage that includes both graphical and analytical synthesis and both cases of with and without prescribed timing. The advantage of the proposed method over available techniques is that it is easier and does not need the complicated process (especially in graphical case). In an analytical solution, this method needs the solution of the linear equations, unlike the previous methods, in that they have required the solution of the nonlinear equations. Moreover, in the current method, one can choose the shape of the coupler, while, in other methods, the shape of the coupler is the result of the solution process. The proposed algorithm can be used for path generation synthesizing of a four-bar linkage for three precision points.

Four-Bar Linkages—Approximate Synthesis

1959 ◽  
Vol 81 (4) ◽  
pp. 293-296
Author(s):  
W. W. Worthley ◽  
R. T. Hinkle
Keyword(s):  
Analytical Method ◽  
Graphical Solution ◽  
Analytical Treatment ◽  
Function Generator ◽  
Approximate Synthesis ◽  
Four Bar Linkage ◽  
Arbitrary Selection ◽  
Selection Of

An analytical method for synthesizing a four-bar linkage as a function generator is presented. The method, which permits the arbitrary selection of four precision points and finite angular ranges, is based on a graphical solution. This permits a preliminary graphical investigation of the six possible linkages before selecting one for analytical treatment.

Linkage Synthesis Using Algebraic Curves

1986 ◽  
Vol 108 (4) ◽  
pp. 543-548 ◽  
Author(s):  
J. L. Blechschmidt ◽  
J. J. Uicker
Keyword(s):  
Nonlinear Equations ◽  
Algebraic Polynomial ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Optimization Techniques ◽  
Synthesis Methods ◽  
Nonlinear Functions ◽  
Pass Through ◽  
Four Bar Linkage ◽  
Set Of Points

A method to snythesize four-bar linkages using the algebraic curve of the motion of the coupler point on the coupler link of the four-bar linkage is developed. This method is a departure from modern synthesis methods, most of which are based upon Burmester theory. This curve, which is a planar algebraic polynomial in two variables for the four-bar linkage, is a trinodal tricircular sextic (sixth order). These properties are used to determine the coefficients of the curve given a set of points that the coupler point of the coupler link is to pass through. The coefficients of this curve are nonlinear functions of the linkage parameters. The resulting set of nonlinear equations are solved using iterative/optimization techniques for the linkage parameters.

scholarly journals Optimal synthesis of a four-bar linkage by method of controlled deviation

2004 ◽  
Vol 31 (3-4) ◽  
pp. 265-280 ◽  
Author(s):  
Radovan Bulatovic ◽  
Stevan Djordjevic
Keyword(s):  
Objective Function ◽  
Optimal Synthesis ◽  
Straight Line ◽  
Individual Comparison ◽  
Four Bar Linkage ◽  
The Given ◽  
Initial Selection ◽  
Selection Of ◽  
Process Calculation ◽  
Made In

This paper considers optimal synthesis of a four-bar linkage by method of controlled deviations. The advantage of this approximate method is that it allows control of motion of the coupler in the four-bar linkage so that the path of the coupler is in the prescribed environment around the given path on the segment observed. The Hooke-Jeeves?s optimization algorithm has been used in the optimization process. Calculation expressions are not used as the method of direct searching, i.e. individual comparison of the calculated value of the objective function is made in each iteration and the moving is done in the direction of decreasing the value of the objective function. This algorithm does not depend on the initial selection of the projected variables. All this is illustrated on an example of synthesis of a four-bar linkage whose coupler point traces a straight line, i.e. passes through sixteen prescribed points lying on one straight line. .

scholarly journals A Transit Route Network Design Problem Considering Equity

2019 ◽  
Vol 11 (13) ◽  
pp. 3527 ◽  
Author(s):  
Myeonghyeon Kim ◽  
Seung-Young Kho ◽  
Dong-Kyu Kim
Keyword(s):  
Network Design ◽  
Public Transportation ◽  
Design Problem ◽  
Network Design Problem ◽  
Modal Split ◽  
Route Network ◽  
Line Selection ◽  
Transit Route ◽  
Selection Of

As concerns about environmental quality, social equity, and economic efficiency are increasing, efforts on improving the sustainability of public transportation are being made all over the world. This study aims to propose a transit route network design problem that considers modal and spatial equities. The equities are accommodated by using two indexes that can simultaneously reflect mobility and accessibility. A decision-making process for designing a transit route network consists of the selection of the target line, selection of the target node, the determination of an alternative line, and the implementation of a procedure for setting frequency. The model is configured through bi-level modeling based on an iterative process to calculate the modal split and the traffic and transit assignments with changes in the transit route network. While the frequency of each line is determined by a genetic algorithm in the upper model, the modal split and traffic and transit assignments are implemented in the lower model. This transit route network design model and the associated algorithms are applied to a sample network. As a result, an improved solution with equity and the lower total cost is identified based on a comparison with the existing transit route network.

Synthesis of Planar Four-Bar for Generating Path with Prescribed Arc

2014 ◽  
Vol 541-542 ◽  
pp. 808-812
Author(s):  
Wen Yeuan Chung
Keyword(s):  
Nonlinear Equations ◽  
Path Generation ◽  
Pass Through

This paper demonstrates the synthesis of planar four-bar for path generation. The feature is that the path includes an arc segment. The users can prescribe coordinates of arc center, a precision point on the arc, and the corresponding pole. The four-bar is synthesized mainly with the aid of the Bobillier theorem. The tasks that the paths or coupler curves pass through at most two additional precision points are also considered. Several nonlinear equations thus have to be derived and combined to find the coordinates of the pivots in synthesizing the four-bar.

The Selection of the Optimal Load Matching Parameter Based on MATLAB

2014 ◽  
Vol 945-949 ◽  
pp. 972-975
Author(s):  
Jun Xia Gao
Keyword(s):  
Servo System ◽  
Selection Method ◽  
Analytic Method ◽  
Load Matching ◽  
Design Time ◽  
Optimal Load ◽  
Hydraulic Servo ◽  
Hydraulic Servo System ◽  
Selection Of

During design the electro-hydraulic servo system, usually choose components based on load matching principle. This paper introduces a selection method of power element parameters based on MATLAB. Compared with the previous analytic method, it greatly save the design time and improve the accuracy.

An Intriguing Exponential Inequality

2009 ◽  
Vol 103 (1) ◽  
pp. 50-55
Author(s):  
John Robert Perrin
Keyword(s):  
Analytical Solution ◽  
Exponential Inequality ◽  
Graphical Solution ◽  
Calculus Students

An algebra problem with a graphical solution challenges precalculus and calculus students to determine an analytical solution.

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