Computerized Synthesis of Straight-Line Four-Bar Linkages From Inflection Circle Properties

1977 ◽  
Vol 99 (3) ◽  
pp. 610-614
Author(s):  
J. M. Simo´n
Keyword(s):  
Digital Computer ◽  
Selection Method ◽  
Interest Points ◽  
Straight Line ◽  
Four Bar Linkage

The instantaneous property of the inflection circle corresponding to a four-bar linkage is used in the present paper to obtain points of the coupler with significant straight-line paths. These points are the interest points (IP) of the coupler, the existence and properties of which are demonstrated here using a digital computer to solve the developed equations that define the IP’s. This led us to propose a computerized trial and selection method of synthesizing straight-line four-bar linkages with new steps—the determination of IP’s and their paths—which will, we hope, shorten considerably the time it used to take to obtain the desired results of a particular problem.

The Determination of Maximum Range for an Unpowered Atmospheric Vehicle

1964 ◽  
Vol 68 (638) ◽  
pp. 111-116 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Calculus Of Variations ◽  
Lagrange Multipliers ◽  
Digital Computer ◽  
Necessary Conditions ◽  
Lagrange Equations ◽  
Initial Portion ◽  
End Conditions ◽  
Maximum Range ◽  
Isothermal Atmosphere

SummaryThe problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.

Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface

1998 ◽  
Vol 120 (3) ◽  
pp. 441-447 ◽  
Author(s):  
K. Kawasaki ◽  
H. Tamura
Keyword(s):  
Cutting Edge ◽  
Tooth Surface ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Ring Gear ◽  
Circular Arc ◽  
Hypoid Gears ◽  
Manufacturing Method ◽  
Straight Line

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.

Solutions to the Vector Tetrahedron Equation

1965 ◽  
Vol 87 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Milton A. Chace
Keyword(s):  
Closed Form ◽  
Digital Computer ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Spherical Coordinates ◽  
Tetrahedron Equation ◽  
Position Determination ◽  
Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

scholarly journals Simple and Exact Closed-Form Expression for Determination of a Penetrated Ray Path in a Ray Tracing

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hyun Wook Moon ◽  
Woojoong Kim ◽  
Sewoong Kwon ◽  
Jaeheung Kim ◽  
Young Joong Yoon
Keyword(s):  
Closed Form ◽  
Approximate Method ◽  
Ray Tracing ◽  
Conventional Method ◽  
Closed Form Expression ◽  
Indoor Environments ◽  
Straight Line ◽  
Ray Path ◽  
Ray Tracing Simulation

A simple and exact closed-form equation to determine a penetrated ray path in a ray tracing is proposed for an accurate channel prediction in indoor environments. Whereas the penetrated ray path in a conventional ray tracing is treated as a straight line without refraction, the proposed method is able to consider refraction through the wall in the penetrated ray path. Hence, it improves the accuracy in ray tracing simulation. To verify the validation of the proposed method, the simulated results of conventional method, approximate method, and proposed method are compared with the measured results. The comparison shows that the proposed method is in better agreement with the measured results than the conventional method and approximate method, especially in high frequency bands.

scholarly journals A New Method for the Extraction of Diode Parameters Using a Single Exponential Model

2000 ◽  
Vol 22 (3) ◽  
pp. 157-163 ◽  
Author(s):  
S. Dib ◽  
M. De La Bardonnie ◽  
A. Khoury ◽  
F. Pelanchon ◽  
P. Mialhe
Keyword(s):  
Least Squares Method ◽  
Exponential Model ◽  
New Method ◽  
Ordinate Axis ◽  
Straight Line ◽  
Current Voltage ◽  
Method Approach ◽  
Single Exponential

A new method for extracting junction parameters of the single diode model is presented. A least squares method approach considers the deviation ∆V=f(I) between the experimental current-voltage (I-V) characteristic and a theoretical arbitrary characteristic. A specific case- the ∆V graph reducing to a straight line–is identified and the knowledge of the slope and of the intercept with the ordinate axis leads to the determination of the junction parameters. The method is applied to the characterization of the emitter-base junction of transistors and the results are discussed.

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.

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