Optimum Path Synthesis of a Geared Five-Bar Mechanism

Wen-Yi Lin

doi:10.1155/2013/757935

Abstract

Most studies on path synthesis problems are to trace simple or smooth trajectories. In this work, an optimum synthesis for several special trajectories generated by a geared five-bar mechanism is studied using the one-phase synthesis method. The synthesis problem for the special trajectories, which is originally studied using the two-phase synthesis method discussed in the literature, is a real challenge due to very few dimensionally proportioned mechanisms that can generate the special trajectories. The challenging special trajectories with up to 41 discrete points include a self-overlapping curve, nonsmooth curves with straight segments and vertices, and sophisticated shapes. The error function of the square deviation of positions is used as the objective function and the GA-DE evolutionary algorithm is used to solve the optimization problems. Findings show that the proposed method can obtain approximately matched trajectories at the cost of a tremendous number of evaluations of the objective function. Therefore, the challenging problems may serve as the benchmark problems to test the effectiveness and efficiency of synthesis methods and/or optimization algorithms. All the synthesized solutions have been validated using the animation of the SolidWorks assembly so that the obtained mechanisms are sound and usable.

Highlights

The problem of path synthesis is to generate a definite mechanism whose coupler point can trace a desired trajectory or target points
The challenging path synthesis problems for the special trajectories generating by the geared five-bar mechanism is studied using the one-phase synthesis method, where the error function of the square deviation of positions is used as the objective function and the genetic algorithm (GA)-differential evolution (DE) evolutionary algorithm [20, 28] is used to solve the optimization problem
The goal for the geared five-bar mechanism optimum synthesis problem is to minimize the error function of the square deviation of positions considered as the first part of the objective function, which may be expressed by fobj

Summary

Introduction

The problem of path synthesis is to generate a definite mechanism whose coupler point can trace a desired trajectory or target points. Roth and Freudenstein [1] proposed a numerical method for a path synthesis task with nine target points of a geared five-bar mechanism. Zhang et al [2] produced an atlas containing 732 coupler curves for the symmetric geared five-bar mechanism and used a nonlinear programming method in conjunction with the atlas as the initial guess for the optimal path synthesis of the mechanism. Nokleby and Podhorodeski [5] used a quasi-Newton optimization routine for the optimum path synthesis of a geared fivebar mechanism. These synthesis methods belong to the onephase synthesis method, which attempts to simultaneously satisfy the shape, size, location, and orientation information of the desired trajectories. Buskiewicz [8] proposed a two-phase synthesis method using the function of the distance of the curve from its centroid (DCC) to describe the curve shape in terms of its normalized Fourier coefficients

Methods

Results

Conclusion