Optimum Path Synthesis of a Geared Five-Bar Mechanism

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.

Discussion of Hwang and Chen's constraint equations to eliminate order, circuit and branch defects for the paper: Defect-free synthesis of Stephenson-III motion generators, published in Journal of Mechanical Engineering Science, 2008; 222: 2485–2494

“…In practice, some optimum synthesis results show that the obtained input angles do not satisfy θ2,1< θ2,2 <…<θ2,n, as shown in literature. 12,14,28–30 Therefore, the constraint equation for avoiding order defects proposed by Hwang and Chen 1 may lose better candidate solutions. In order to examine order defects, we can use a new coordinate system Ax 1 y 1 with the x 1 axis chosen to coincide with the input link at the orientation of θ2,1.…”

“…4–11 In fact, a lot of studies have checked whether the synthesis mechanism is free from the defects after the optimum synthesis is completed. 12–19 In 2008, in their pioneering work, Hwang and Chen 1 proposed using the constraints for freedom from the order, circuit and branch defects to solve the optimum synthesis problem of Stephenson III six-bar motion generators. In 2009, Hwang and Chen 20 proposed using the constraints for freedom from the order, circuit and branch defects to solve the optimum synthesis problem of Watt-I six-bar motion generators.…”

Optimum variable input speed for kinematic performance of Geneva mechanisms using teaching-learning-based optimization algorithm

“…This method has been successfully applied to solve some unique and difficult optimization tasks. [30][31][32][33] However, the GA-DE algorithms fail to extend the predetermined range of the value of the design variable to a larger range. Thus, a new evolutionary algorithm, known as teaching-learning-based optimization (TLBO), recently proposed by Rao, Savsani and Vakharia, 34,35 comprising two phases, i.e., a teacher phase and a learner phase, is used.…”

A novel five-bar mechanism driven by a cam mechanism

“…Some literatures discussed the specific path generated by the five-bar mechanism [3]. Lin [4] studied the optimum synthesis for several special trajectories generated by a GFBM using the one-phase synthesis method. Mundo et al [4] tried to use the noncircular gears as the input of a GFBM for the path generation when the lengths of links are given.…”

“…Lin [4] studied the optimum synthesis for several special trajectories generated by a GFBM using the one-phase synthesis method. Mundo et al [4] tried to use the noncircular gears as the input of a GFBM for the path generation when the lengths of links are given. When the five-bar mechanism merged with gear pair or noncircular gear pair, the input and out links have full rotation.…”