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Responding to an increasing demand for mechanism synthesis tools that are both efficient and
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accurate, this paper presents a novel approach to themulti-objective optimal design of four-bar
linkages for path-generation purposes. Three, often conflicting criteria including the
mechanism's tracking error, deviation of its transmission angle from 90° and its maximum
angular velocity ratio are considered as objectives of the optimization problem. To accelerate
the search in the highly multimodal solution space, a hybrid Pareto genetic algorithm with a
built-in adaptive local search is employed which extends its exploration to an adaptively
adjusted neighborhood of promising points. The efficiency of the proposed algorithm is
demonstrated by applying it to a classical design problem for one, two and three objective
functions and comparing the results with those reported in the literature. The comparison
shows that the proposed algorithmdistinctly outperforms other algorithms both quantitatively
and qualitatively (from a practical point of view).5019
© 2011 Elsevier Ltd. All rights reserved.1. Introduction
Due to their topological simplicity and functional versatility, four-bar mechanisms are widely used for path (trajectory)
generation in practical engineering applications. The path generation task is most conveniently represented by a number of
“precision points” to be tracked by the coupler point of the mechanism. The problem would then be to determine the topology/
dimensions of the linkage so that its coupler point tracks a set of given precision points as precisely as possible. This could be
achieved by various analytical, numerical and graphical methods, collectively referred to as “synthesis” methods [1–4].Itis
generally believed that the complexity and computational cost of traditional synthesis methods increase with an increase in the
number of precision points [5]. The recent emergence of efficient global search/optimization techniques has provided researchers
with an alternative approach to mechanism synthesis, that is to formulate the problem as an optimization problem with some
measure(s) of the tracking precision as the objective and the linkage defining parameters as design variables [6–8]. The problemso
defined would then be a constrained one, with such conditions as the sequence of input angles, the Grashof conditions and the
variables' upper and lower bounds [8].
Various search/optimization techniques have been employed to solve the problem at hand [7–20]. However, with a few
exceptions, they have all been used as single-objective optimizers. That is, the objective has been to design mechanisms for
minimum Tracking Errors, TEs, only, regardless of other possible performance measures [8,17,18,20]. This is somewhat simplistic;
as there are other performance measures that contribute to the desirability of a mechanism, including the transmission angle,
whose deviation from90○ is an indication of the torque and energy transfer in themechanismand a decisive factor in determining
the actuator size [6].A more realistic, and practically viable, approach to the design of a mechanism for various purposes, including path generation
would then be to consider the problem, a multi-objective one, if in fact all aspects of the mechanism's lifecycle, including energy
consumption, endurance andmanufacturing considerations are to be taken into account. This approach has been recently adopted
by some researchers who have included a second objective, namely the transmission angle's deviation from 90°, TA, in their
treatment of the problem [16,19]. However, they have overlooked a third, equally important, objective, the Maximum Angular
Velocity Ratio, MAVR, whose minimization would improve the kinetic performance and practical usability of the mechanism.