Synthesis of Four-Bar Linkage Function Generators by Means of Equations of Motion

1965 ◽  
Vol 87 (2) ◽  
pp. 170-176 ◽  
Author(s):  
C. K. Wojcik
Keyword(s):  
Equations Of Motion ◽  
Angular Acceleration ◽  
Input Output ◽  
Connecting Rod ◽  
Function Generator ◽  
Function Generation ◽  
Function Generators ◽  
Two Parameters ◽  
Four Bar Linkage ◽  
Selection Of

The function generation method presented in this paper is based on consideration of the equations of motion of a four-bar linkage with an assumed input of θ˙1 = 1 rad/sec. For a specified input-output relationship, the task of synthesizing an appropriate four-bar linkage is reduced by this method to a problem of selecting two parameters: θ˙2—the angular velocity and θ¨2—the angular acceleration of the connecting rod. The selection of these parameters is governed by certain conditions imposed on the performance of the four-bar linkage function generator. Using this method, two specific problems are solved and discussed in detail.

Closed-Form Synthesis of Force-Generating Planar Four-Bar Linkages

1995 ◽  
Author(s):  
R. Randall Soper ◽  
Michael Scardina ◽  
Paul Tidwell ◽  
Charles Reinholtz ◽  
Michael A. Lo Presti
Keyword(s):  
Closed Form ◽  
The Other ◽  
Design Parameters ◽  
Synthesis Methods ◽  
Function Generator ◽  
Mechanical Advantage ◽  
Nonlinear Mechanical ◽  
Two Parameters ◽  
Selection Of ◽  
Weight Force

Abstract This paper presents a technique for synthesizing four-bar linkages to produce a specified resisting force or torque. The resisting energy is provided by a weight acting on the other grounded link. The linkage serves as a nonlinear mechanical advantage function generator. Force and velocity synthesis methods have been extensively discussed in the literature. The general approach, however, has been to assume that the specified force or velocity occurs at a prescribed position. This results in the loss of design parameters that are being used unnecessarily to control position. In this application, force input to the linkage is specified as a function of only the input link position and the magnitude and direction of the weight force. Mechanical advantage synthesis can be achieved at as many as seven precision points. The method presented in this paper allows free selection of two parameters and viewing one infinity of solutions.

Optimization of Planar, Spherical and Spatial Function Generators Using Input-Output Curve Planning

1994 ◽  
Vol 116 (3) ◽  
pp. 915-919 ◽  
Author(s):  
Zheng Liu ◽  
J. Angeles
Keyword(s):  
Performance Index ◽  
General Scheme ◽  
Optimization Procedure ◽  
Output Curve ◽  
Input Output ◽  
Function Generation ◽  
Spatial Function ◽  
Function Generators ◽  
Design Requirements ◽  
A Performance

A general scheme for the optimization of planar, spherical and spatial bimodal linkages for function generation is proposed. The problem is solved here following two basic steps: (i) planning input-output ((I/O) curves based on design requirements and selecting data from the planned curve; and (ii) setting up an optimization procedure to minimize a performance index.

Direct Analytic Synthesis of Four-Bar Function Generators With Optimal Structural Error

1973 ◽  
Vol 95 (2) ◽  
pp. 563-571 ◽  
Author(s):  
Richard S. Rose ◽  
George N. Sandor
Keyword(s):  
Conventional Method ◽  
Function Generator ◽  
Arbitrary Choice ◽  
Usual Procedure ◽  
Structural Error ◽  
Function Generators ◽  
Conventional Optimization ◽  
Four Bar Linkage ◽  
Additional Constraints

This paper is a departure from the usual procedure for obtaining the optimal dimensions of a four bar function generator by iteration. In the usual procedure, the accuracy points are first chosen by means of Chebishev spacing or some other means. Using these accuracy points, a four bar linkage is synthesized and the error calculated. Freudenstein’s respacing formula may then be used to respace the accuracy points so as to minimize the errors. After the respacing of the accuracy points is calculated, a new mechanism is synthesized. The process is repeated until the magnitudes of the extreme errors occurring between accuracy points are equalized. The procedure adopted in this paper is to immediately force the extreme errors between accuracy points to be equal in magnitude by imposing additional constraints upon the problem. These constraints eliminate the arbitrary choice of the first set of accuracy points. This procedure results in a more extensive set of equations to be solved than the conventional method. However, once the equations are solved, they lead directly to equalized (and thus minimized) extrema of the magnitude of structural errors between the precision points. Thus there is no need to perform the iterative steps of conventional optimization. The proposed method is illustrated with an example.

Planar Linkage Synthesis for Mixed Motion, Path and Function Generation Using Poles and Rotation Angles

2017 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Sufficient Conditions ◽  
Motion Path ◽  
Engineering Practice ◽  
Function Generation ◽  
Problem Types ◽  
The Family ◽  
And Function ◽  
Necessary And Sufficient ◽  
Four Bar Linkage ◽  
Selection Of

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not over constrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

Multiply Separated Position Design of the Geared Five-Bar Function Generator

1971 ◽  
Vol 93 (1) ◽  
pp. 74-84 ◽  
Author(s):  
S. A. Oleksa ◽  
D. Tesar
Keyword(s):  
Design Parameters ◽  
Function Generator ◽  
Function Generation ◽  
Four Bar Linkage ◽  
Generation Problem ◽  
Made In

The geared five-bar linkage is the foundation for a function generation problem meeting specifications for 5 multiply separated positions and containing 4 free design parameters. The four-bar linkage is shown to be a member of this class of mechanisms. Design examples of rarely treated functions are given with the quality of the generated approximation. Suggestions are made in terms of the 4 design parameters to assist the designer in obtaining good results.

Planar Linkage Synthesis for Mixed Motion, Path, and Function Generation Using Poles and Rotation Angles1

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Sufficient Conditions ◽  
Motion Path ◽  
Engineering Practice ◽  
Function Generation ◽  
Problem Types ◽  
The Family ◽  
And Function ◽  
Necessary And Sufficient ◽  
Four Bar Linkage ◽  
Selection Of

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path, and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not overconstrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints (PRCs) are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot, or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

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.

Link-Centre and Indexes of a Kinematic Chain

1992 ◽  
Author(s):  
V. P. Agrawal ◽  
J. N. Yadav ◽  
C. R. Pratap
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Input Output ◽  
Function Generator ◽  
Kinematic Chains ◽  
Graph Theoretic ◽  
Optimum Selection ◽  
Theoretic Concept ◽  
Selection Of

Abstract A new graph theoretic concept of link-centre of a kinematic chain is introduced. The link-centre of a kinematic chain is defined as a subset of set of links of the kinematic chain using a hierarchy of criteria based on distance concept. A number of structural invariants are defined for a kinematic chain which may be used for identification and classification of kinematic chains and mechanisms. An algorithm is developed on the basis of the concept of distance and the link-centre for optimum selection of input, output and fixed links in a multi-degree-of-freedom function generator.

scholarly journals DEVELOPMENT AND APPLICATION OF A COMPUTER PROGRAM FOR FOUR-BAR LINKAGE AND SLIDER-CRANK MECHANISMS

2020 ◽  
Vol 26 (3) ◽  
pp. 28-38
Author(s):  
OLADEJO KOLAWOLE ADESOLA ◽  
ADEKUNLE NURUDEEN OLATUNDE ◽  
ADETAN DARE ◽  
ABU RAHAMAN ◽  
ORIOLOWO KOLAWOLE TAOFIK
Keyword(s):  
Angular Acceleration ◽  
Visual Basic ◽  
Linear Displacement ◽  
Connecting Rod ◽  
Software Application ◽  
Crank Angle ◽  
Mathematical Problems ◽  
Angular Velocities ◽  
Four Bar Linkage ◽  
Crank Mechanism

Complex mathematical problems have been solved with the aid of software application to obtain reliable results. The positional kinematic analysis of a slider crank mechanism involves computation of the motion parameters: linear displacement, velocity and acceleration of the slider; and angular velocity and angular acceleration of the connecting rod for every 300 variation of the crank angle. This study aimed to develop a customized software which can be used to efficiently analyse a given design of a four-bar and a slider-crank mechanisms. A program was written using VB (Visual Basic) programming language for the equations of angular velocities and angular acceleration of the coupler and follower for the four-bar linkage and the linear velocity and acceleration of the piston for the slider crank mechanism. The program was tested with different parameters for the mechanisms and the solutions compared with the results from manual calculations. The findings revealed that there were no differences (p ≤ 0.05) between the results using the program and manual calculations, which imply the accuracy of the program. It can be concluded that the program could be used to solve problems of four- bar linkage and slider-crank mechanisms.

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.

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