Comparative study of four-bar hyperbolic function generation mechanism with four and five accuracy points (original) (raw)
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Synthesis of Four Bar Mechanisms as Function Generators by Freudenstein -Cebyshev
This paper describes new method for the synthesis of four-bar linkages for generating a required input-to-output motion. The synthesis method is based on the direct application of Chebyshev’s Alternation Theorem for the Equation of Freudenstein. By this approach the maximum structural error which corresponds to the best approximation can be estimated in advance. Two comparative examples are herewith used to illustrate some of the main features of the method. The innovation in this paper is the presentation of the target function as exact satisfied equation. On substituting the solution of this equation in the Equation of Freudenstein a generalized polynomial of Chebyshev is obtained. This polynomial is minimized by the Chebyshev’s alternation theorem. This method does not require Chebyshev’s spacing of the structural error of the mechanisms. One of the advantages of the so proposed approach is the possibility to predict the peculiarities of the mechanism with respect to the synthesis problem in the beginning of the solution. The so proposed method combines the power of the Freudenstein’s equation and the Chebyshev’s theorem comprehensiveness. The method of Freudenstein-Chebyshev presented here shows that for every structural error which could be presented as generalized polynomial of Chebyshev can be found the best approximation.
IEEE Access
In this paper, the dimensional synthesis of the four-bar mechanism for path generation is formulated using the relative angle motion analysis and the link geometry parameterization with Cartesian coordinates. The Optimum Dimensional Synthesis using Relative Angles and the Cartesian space link Parameterization (ODSRA+CP) is stated as an optimization problem, and the solution is given by the differential evolution variant DE/best/1/bin. This study investigates the behavior and performance of such formulation and performs a comparative empirical study with the well-known synthesis method based on vector-loop equation motion analysis where different modifications in the metaheuristic algorithms are established in the literature to improve the obtained solution. Five study cases of dimensional synthesis for path generation with and without prescribed timing are solved and analyzed. The empirical results show that the way of stating the optimization problem in the ODSRA+CP significantly improves the search process for finding promising solutions in the optimizer without requiring algorithm modifications. Therefore, it is confirmed that the optimizer search process in the optimal synthesis of mechanisms is not the only way of improving the obtained solutions, but also the optimization problem formulation has a significant influence on the search for better solutions. INDEX TERMS Mechanism synthesis, four-bar mechanism, optimization, differential evolution.
International review of applied engineering research, 2013
An analytical method is developed for the synthesis of planar eight bar mechanism with variable topology. The method uses Freudenstein’s equation for three point function generation. The synthesis of eight bar mechanism involves three phases. Each phase comprises of a four bar mechanism. The output angular positions of the first phase are taken as the input angular positions of the second phase and the output angular positions of the second phase are taken as the input angular positions of the third phase. The transmission angle is maintained within the optimum limit. Also, the method is illustrated with an example.
ALGORITHM ON SYNTHESIS OF FOUR BAR MECHANISM USING THREE PRECISION POINTS
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & MANAGEMENT , 2015
This paper deals with solution methods of optimal synthesis of planar mechanisms. A searching procedure is defined which applies genetic algorithms based on three precision points. Problems of synthesis of fourbar planar mechanisms are used to test the method, showing that solutions are accurate and valid for all cases. The possibility of extending the method to other mechanism type is outlined. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution. This paper deals with algorithm on synthesis of four bar mechanism using three precision points Key word-Synthesis of mechanism, three precision points
The problem of optimum synthesising of a mechanism to best approximate a function, while simultaneously ensuring good motion transmission characteristics is discussed. Distinction is made between the design variables that determine the shape of the input-output (I/O) function of the mechanism, and the design variables that affect the degree of overlap between this I/O function and the function to be mechanised, through scaling, mirroring and rotations in 90º increments. Examples are given of designing the planar four-bar and slider-crank linkages of a logarithmic scale, and that of a tangent-function generator. These are performed on modified mechanisms with an added degree-of-freedom, which substantially simplify the synthesis problem.
On a technique for higher order synthesis of four-bar function generators
Mechanism and Machine Theory, 1989
The aim of the present paper is to introduce a synthesis technique developed 17 years ago. As this technique has been finding frequent applications, and the previous works are not accessible for most kinematicians, we have therefore completed this paper, giving all information in a concise manner, and also listing the computer programs so that a designer can quickly synthesize a function generator without a thorough understanding of kinematics. Two special cases are investigated, and examples are given.
Mechanisms and Machine Science, 2014
Double-spherical six-bar linkage is one of the Bennett over-constrained 6R linkages. Kinematic synthesis of such linkages can be tedious and impossible to solve for analytically. In order to cope with higher number of unknowns in these types of linkages, decomposition method is a valuable tool. This paper focuses on the function generation synthesis of double-spherical six-bar linkage. Two procedures for applying decomposition method are explained. Two numerical studies are conducted for both procedures to evaluate the performance of each procedure.
A new approach to the synthesis of 4-bar function generators
Mechanism and Machine Theory, 1979
In the present work a new approach to the synthesis of 4-bar function generators has been presented. Using this graphical method quick and at the same time sufficiently accurate synthesis is possible in a large number of cases, The method is based on the principle of coordinating two positions and the corresponding velocities of the input and the output links. Thus four conditions are satisfied and better accuracy than that with three point synthesis may be expected. Positions of the proper accuracy points have been discussed and some guidance to the selection of the initial data has been presented in this paper. One problem has been solved as an example.
Function generation with two loop mechanisms using decomposition and correction method
Mechanism and Machine Theory, 2017
Method of decomposition has been successfully applied to function generation with multi-loop mechanisms. For a two-loop mechanism, a function y = f(x) can be decomposed into two as w = g(x) and y = h(w) = h(g(x)) = f(x). This study makes use of the method of decomposition for two-loop mechanisms, where the errors from each loop are forced to match each other. In the first loop, which includes the input of the mechanism, the decomposed function (g) is generated and the resulting structural error is determined. Then, for the second loop, the desired output of the function (f) is considered as an input and the structural error of the decomposed function (g) is determined. By matching the obtained structural errors, the final error in the output of the mechanism is reduced. Three different correction methods are proposed. The first method has three precision points per loop, while the second method has four. In the third method, the extrema of the errors from both loops are matched. The methods are applied to a Watt II type planar six-bar linkage for demonstration. Several numerical examples are worked out and the results are compared with the results in the literature.
Kinematic design and analysis of the rack-and-gear mechanism for function generation
Mechanism and Machine Theory, 1984
The complex number method is applied to the kinematic design and analysis of the rack-and-gear function generating mechanism for three finely separated positions. The rack-and-gear mechanism is a useful planar mechanism that can be used to generate many functions that the four-bar mechanism can generate plus a great deal more. Due to the extra complexity of the rack-and-gear both monotonic and non-monotonic functions, as well as non-linear amplified motions, can be generated. A major advantage of the rack-and-gear mechanism is that the transmission angle always remains at its optimal value since the rack is always tangential to the gear. Both the design and analysis have been programmed for use on the PDP 11/70 and are available to interested readers.