The Displacement Synthesis of Four-Bar Straight-Line Mechanisms

1975 ◽  
Vol 97 (1) ◽  
pp. 322-326 ◽  
Author(s):  
R. G. Mitchiner ◽  
H. H. Mabie
Keyword(s):  
Analytical Method ◽  
Functional Relationship ◽  
Straight Line ◽  
Crank Angle ◽  
Four Bar Linkage ◽  
Crank Mechanism

This paper presents an analytical method for synthesizing a four-bar linkage from a slider-crank mechanism using the cubic of stationary curvature of the slider crank. A coupler point on the resulting linkage will generate an approximate straight line, and the functional relationship between the displacement of the coupler point and the crank angle will be the same as the relation of slider displacement to crank angle of the original slider crank.

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.

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. .

Synthesis of a Large Oscillation Four-Bar Mechanism

1997 ◽  
Author(s):  
Gloria K. Starns ◽  
Donald R. Flugrad
Keyword(s):  
Reduced Gradient Method ◽  
Large Oscillation ◽  
Oscillation Mechanism ◽  
Straight Line ◽  
Transmission Angle ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Angular Oscillations ◽  
Four Bar Linkage ◽  
Effective Transmission

Abstract This paper demonstrates procedures implemented for the synthesis of a four-bar mechanism that produces large angular oscillations of the output member while maintaining effective transmission angles. The mechanisms are modeled as being driven by a force applied at the coupler link. Additionally this force’s line of action is constrained to occur along an approximate straight line. This research was conducted out of the need for a device that is capable of retraction of the horizontal tool bar housed on the back of a tractor. The tool bars accommodate the implements required to accomplish the numerous tasks of the farmer, i.e. row markers, sprayer arms, planters, etc. Upon retraction of the tool bar so that it is parallel to ground, the appropriate tools are lowered to their working position. As the length of these bars increases, a savings of time and increased productivity is realized. Kurt Hain makes the following observation regarding large oscillation mechanisms in [1]: “It would be very difficult to solve this problem with one four-bar linkage, because it is difficult to design a four-bar linkage having such a large oscillation of a crank without running into problems of poor transmission angle characteristics; it might be possible to use linkages in combinations with gears, but this would make the mechanism more expensive, less efficient, and probably noisier.” In this study simulated annealing, a genetic algorithm and the generalized reduced gradient method are used to produce mechanisms with large angular oscillations of the output member and transmission angles that vary by as little as 20° from 90°. A comparative analysis of each of the optimization procedures is presented with observations regarding the efficacy of each method in the solution of the large oscillation mechanism.

A quantitative measure of nonlinearity

1993 ◽  
Vol 39 (5) ◽  
pp. 766-772 ◽  
Author(s):  
K Emancipator ◽  
M H Kroll
Keyword(s):  
Analytical Method ◽  
Response Curve ◽  
Polynomial Regression ◽  
Quantitative Measure ◽  
Square Root ◽  
Straight Line ◽  
The Mean ◽  
The Difference ◽  
Definition Of ◽  
Fitting In

Abstract Quantitative measures of the nonlinearity of an analytical method are defined as follows: the "(dimensional) nonlinearity" of a method is the square root of the mean of the square of the deviation of the response curve from a straight line, where the straight line is chosen to minimize the nonlinearity. The "relative nonlinearity" is defined as the dimensional nonlinearity divided by the difference between the maximum and minimum assayed values. These definitions may be used to develop practical criteria for linearity that are still objective. Calculation of the nonlinearity requires a method of curve-fitting. In this article, we use polynomial regression to demonstrate calculations, but the definition of nonlinearity also accommodates alternative nonlinear regression procedures.

A New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Flowing-Pressure Boundary Condition

2012 ◽  
Vol 15 (03) ◽  
pp. 370-384 ◽  
Author(s):  
Morteza Nobakht ◽  
C.R.. R. Clarkson
Keyword(s):  
Shale Gas ◽  
Analytical Method ◽  
Flow Analysis ◽  
Initial Pressure ◽  
Reliable Estimate ◽  
Square Root ◽  
Linear Flow ◽  
Straight Line ◽  
Half Length ◽  
Time Plot

Summary Many tight/shale gas wells exhibit linear flow, which can last for several years. Linear flow can be analyzed using a square-root-of-time plot, a plot of rate-normalized pressure vs. the square root of time. Linear flow appears as a straight line on this plot, and the slope of this line can be used to calculate the product of fracture half-length and the square root of permeability. In this paper, linear flow from a fractured well in a tight/shale gas reservoir under a constant-flowing-pressure constraint is studied. It is shown that the slope of the square-root-of-time plot results in an overestimation of fracture half-length, if permeability is known. The degree of this overestimation is influenced by initial pressure, flowing pressure, and formation compressibility. An analytical method is presented to correct the slope of the square-root-of-time plot to improve the overestimation of fracture halflength. The method is validated using a number of numerically simulated cases. As expected, the square-root-of-time plots for these simulated cases appear as a straight line during linear flow for constant flowing pressure. It is found that the newly developed analytical method results in a more reliable estimate of fracture half-length, if permeability is known. Our approach, which is fully analytical, results in an improvement in linear-flow analysis over previously presented methods. Finally, the application of this method to multifractured horizontal wells is discussed and the method is applied to three field examples.

Equations for Four-Bar Line-Envelopes

1981 ◽  
Vol 103 (4) ◽  
pp. 743-749 ◽  
Author(s):  
K. H. Hunt ◽  
E. F. Fichter
Keyword(s):  
The Other ◽  
Straight Line ◽  
Sliding Joint ◽  
Line Equation ◽  
Four Bar Linkage ◽  
Sliding Joints

A line-equation (in tangential coordinates) is derived for the envelope of a general straight line attached to the coupler of a planar hinged four-bar linkage. Since a line can be identified with an axis of relative translation parallel to a sliding joint, the study of how lines move in a mechanism has practical potential. Nevertheless the emphasis here is on the geometry of the line-envelopes, and some envelopes are plotted both as samples of what can be obtained and to exemplify some of the properties which they possess. Towards the end of the paper all the other forms of planar four-bar linkage, namely those in which one or two sliding joints replace hinges, are examined, and their envelope-equations are presented.

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