Comprehensive approach for the dimensional synthesis of a four-bar linkage based on path assessment and reformulating the error function (original) (raw)
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Dimensional Synthesis of a Four-Bar Linkage Assessing the Path and Reformulating the Error Function
Mechanism Design for Robotics, 2021
The optimal dimensional synthesis approach presented in this paper aims to enhance one of the earliest and efficient methods-gradient methods. The process to achieve the optimal mechanism bases on characterizing the circuits and branches of the path traced by the coupler point, establishing the corresponding actuation mode according to some indices that avoid using penalty functions. The proposed optimal synthesis approach redefines the error function by including an additional characteristic: the slope of the tangent to each point of the trajectory. It will be demonstrated that incorporating the tangent characteristic permits better fitting to the desired curve than by defining additional points.
A new approach for the optimal synthesis of four-bar path generator linkages
SN Applied Sciences, 2019
In this paper, an optimal synthesis of four-bar path generator, using a robust mathematical formulation is presented. Natural coordinates are used in order to solve the four-bar mechanism kinematic position analytically and the Hermitian conjugate is used to build a goal function whose range is the real numbers' set. A Teaching Learning Based Optimization Algorithm is implemented to test the proposed formulation robustness, also the possibility of extending the method to another type of mechanism is described. The main advantages of the formulation are its simplicity and robustness due that the equations involved in the formulation are algebraic and the numerical field is the complex's set.
Inverse Problems in Engineering, 2002
Mechanism synthesis, the identification of the parameters of a mechanism, has been extensively studied especially for four-bar linkages using graphical and numerical optimization approaches. Graphical techniques follow a number of predefined steps and rely heavily on the user. Numerical optimization techniques that require the user to provide ''good initial guesses'' or bounds for the design variables have also been applied. In general, a linkage is synthesized for function generation, motion generation, and path generation. This article studies four-bar mechanism synthesis by combining Differential Evolution, an evolutionary optimization scheme that can search outside the initial defined bounds for the design variables, and a newly developed novel technique called the Geometric Centroid of Precision Points (GCPP) and the distant precision point in defining the initial bounds for the design variables. The developed methodology has been applied to the synthesis of four-bar linkages for path generation with prescribed timing, where the coupler point is required to pass through a number of precision points within a prescribed accuracy level and in the correct order, and for the generation of families of coupler curves. Two penalty functions were used, one for constraint violation and one for relative accuracy. The results of the application of this approach could also be used as ''good initial guesses'' for improving the desired accuracy level. Examples demonstrating the successful application of the developed methodology are presented.
Hybrid Optimization Based Mathematical Procedure for Dimensional Synthesis of Slider-Crank Linkage
Mathematics, 2021
In this paper, an optimization procedure for path generation synthesis of the slider-crank mechanism will be presented. The proposed approach is based on a hybrid strategy, mixing local and global optimization techniques. Regarding the local optimization scheme, based on the null gradient condition, a novel methodology to solve the resulting non-linear equations is developed. The solving procedure consists of decoupling two subsystems of equations which can be solved separately and following an iterative process. In relation to the global technique, a multi-start method based on a genetic algorithm is implemented. The fitness function incorporated in the genetic algorithm will take as arguments the set of dimensional parameters of the slider-crank mechanism. Several illustrative examples will prove the validity of the proposed optimization methodology, in some cases achieving an even better result compared to mechanisms with a higher number of dimensional parameters, such as the fou...
Optimal Synthesis of Crank Rocker Mechanism for Point to Point Path Generation
2012
The Present Work Introduces The Concept Of Orientation Structure Error Of The Fixed Link And Present A New Optimal Synthesis Method Of Crank Rocker Linkages For Path Generation. The Orientation Structure Error Of The Fixed Link Effectively Reflects The Overall Difference Between The Desired And Generated Path. Avoid By Making Point By Point Comparisons Between The Two Paths And Requires No Prescription Of Timing. In The Kinematic Synthesis Of Four Bar Path Generating Linkages, It Is Required To Determine The Linkage Dimensions' So That A Point On The Coupler Link Traces Out The Desired Curve. There Are Two Types Of Task For Path Generation. One Of Them Specified Only Small Number Of Points On The Path, And The Trajectory Between Any Two Specified Point Is Not Prescribed. The Concept Of Orientation Structure Error Of The Fixed Link Is Introduced. A Simple And Effective Optimal Synthesis Method Of Crank -Rocker Path Generating Linkages Is Presented.
Synthesis of Four-Bar Linkage with Adjustable Crank Length for Multi-Path Generation
International Journal of Mechanical Engineering and Robotics Research, 2020
Synthesis of planar mechanism with adjustable crank length for generating multiple paths is presented. Least-square approximation problem is considered which allows carrying out approximate synthesis with unlimited number of desired coupler point positions and with unlimited number of prescribed trajectories. By reducing the task to synthesis of two-element link with variable binary link length, which is called RPR-module, the analytical solution is obtained to determine not only constant design parameters (mechanism link lengths) but the adjusting parameter values as well. Thus the number of design variables for non-linear optimization (applied to find the remaining parameters) will be decreased significantly. The applied method is exemplified by synthesis of the mechanism for variable straight line generation, where the required height of the end-effector is adjusted by adjusting the crank length. Combined with random search technique the method allows to find all local minimums of the optimized goal function and thus allows to take full advantage from the considered mechanism structure during design.
This paper deals with an optimization based method for synthesis of adjustable planar fourbar, crank-rocker mechanisms. For multiple different and desired paths to be traced by a point on the coupler, a two stage method first determines the parameters of the possible driving dyads. Then the remaining mechanism parameters are determined in the second stage where a least-squares based circle-fitting procedure is used. Compared to existing formulations, the optimization method uses less number of design variables. Two numerical examples demonstrate the effectiveness of the proposed synthesis method.
OPTIMAL SYNTHESIS OF EIGHT BAR MECHANISM FOR SPECIFIED PATH GENERATION WITH VARIABLE TOPOLOGY.doc
This paper proposes an analytical synthesis method for optimal synthesis of planar eight bar mechanism for path generation with variable topology. The eight bar planar mechanism has been considered to be made of three phases where each of the phases is a four bar mechanism of RRRR type. The method of kinematic synthesis involves the use of Cheybeychev's spacing for locating precision points and Freudenstein's equations for determining link lengths. For any given function, link lengths of the mechanism are determined by assuming the range of input and output angular rotations. Optimized length of rocker link and output angle of the first phase is used as input values for the second phase and same procedure is continued to find the dimensions of the third phase. The combined objective function is established for optimization with transmission angle and link length ratios as design variables. The optimized values of lengths of links of the resulting mechanism satisfy Grashof's condition and have controlled transmission angle. The coupler connected to third phase generates the coupler curve for obtained optimized link lengths. The method developed herein is illustrated with a numerical example.
Integrated Type and Dimensional Synthesis of Planar Four-Bar Mechanisms
Latest Advances in Robot Kinematics, 2012
A novel approach to integrated type and approximate dimensional synthesis of planar four-bar mechanisms (i.e. linkages comprised of any two of RR, PR, RP, and PP dyads) for rigid-body guidance is proposed. The essence is to correlate coordinates of the coupler attachment points in two different coordinate frames, thereby reducing the number of independent variables defining a suitable dyad for the desired rigid-body motion from five to two. After applying these geometric constraints, numerical methods are used to size link lengths, locate joint axes, and decide between RR, PR, RP and PP dyads that, when combined, guide a rigid body through the best approximation, in a least-squares sense, of n specified positions and orientations, where n ≥ 5. No initial guesses of type or dimension are required. An example is presented illustrating the effectiveness and robustness of this new approach.
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.