Topology optimization of planar linkage mechanisms

Abstract

SUMMARYIn spite of increasing interest in gradient‐based topology optimization of linkage mechanisms, it is still difficult to solve practical, realistic problems. Besides the apparent difficulty resulting from high nonlinearity, the optimization problem faces other major difficulties: difficulty to satisfy the discrete DOF condition with continuous design variables and lack of intrinsic mechanisms to generate distinct black‐and‐white layouts. To deal with the DOF issue, we propose a new formulation, which maximizes a single objective function, the energy transmittance efficiency. It is shown that the efficiency function maximization handles DOF redundancy and deficiency simultaneously. To obtain distinct linkage layouts, a common practice is to introduce an artificial mass constraint and/or to remove unnecessary links during optimization. However, we do not use any artificial mass constraint but post‐process the optimized result to obtain the final layout by a special post‐processing algorithm. In this study, the linkage design model consists of nonlinear ground bars and zero‐length springs. The springs are used to fix bar‐connecting nodes to the ground, generating pinned joints. After verifying the effectiveness of the proposed approach for four‐bar linkage synthesis, we synthesize an automobile steering mechanism satisfying the Ackermann condition. The steering mechanism problem is solved here for the first time. Copyright © 2014 John Wiley & Sons, Ltd.

Topology optimization of planar linkage systems involving general joint types

“…Although the model in [24] is different from the newly proposed D-SBM, the formulation in [24] should equally work with the D-SBM. For mechanism synthesis, the work transmittance efficiency function is used to define the objective function and the Euclidean distance between the desired target path and the current output path is used as a constraint equation.…”

“…As a means to synthesize a desired linkage mechanism using the D-SBM, we use a topology optimization-based approach developed for a nonlinear bar model [24]. Although the model in [24] is different from the newly proposed D-SBM, the formulation in [24] should equally work with the D-SBM.…”

“…Nevertheless, they did not succeed in designing ground pivots of large rotation linkage systems due to the high nonlinearity of their formulations. Alternately, Kim and Kim [24] have recently proposed another formulation using a work transmittance efficiency function and succeeded in designing even ground pivots for large rotation linkage mechanisms. So, this formulation is employed in this study and our investigation will be mainly focused on handling of several joint types for topology optimization of planar linkage systems.…”

“…An attempt for the simultaneous synthesis using a genetic algorithm was reported [12] but the synthesis of an arbitrary topology with dimensional synthesis was not performed. Thus, topology optimizations of linkage systems, which simultaneously determine the number and dimension of a desired linkage mechanism, have been previously studied [13][14][15][16][17][18][19][20][21][22][23][24][25]. Among them, gradient-based methodologies [13,15,16,[18][19][20]22,24,25] are promising because of their computational efficiency.…”

“…In Section 3, the optimization formulation and the sensitivity analysis will be presented. To synthesize a mechanism by an optimization formulation, the work transmittance efficiency function [24] is used as the objective function to ensure the correct DOF while the Euclidean distance between the desired target path and the current output path is used as a constraint equation to find a mechanism tracing the desired path. An additional constraint function can be considered if the complexity of the synthesized mechanism is to be controlled.…”