An Optimization-based approach for the synthesis of practical mechanisms
Date
1994
Authors
Fang, Xiaoqi
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Abstract
This thesis presents an optimization-based approach for the synthesis of planar mechanisms. The approach is practical since it can be applied to several mechanism types and a variety of mechanism synthesis problems. The mechanisms synthesized are practical since convergence to certain categories of mechanisms within specific types is ensured and the consideration of arbitrary performance objectives in the optimization is allowed.
A least p-th algorithm with tasks specified by upper and lower limit constraints on output displacement components is used to generate initial feasible mechanisms. A sequentially unconstrained minimization technique (SUMT) is used to ensure motion feasibility during mechanism optimization for specified objectives. The concept of using relative displacements for specifying upper and lower displacement limits is introduced. Basing the motion specification on relative displacements is effective since it eliminates the global location of the mechanism from the search parameters. Furthermore it is effective since it allows initial input displacements to be considered as search parameters.
A direct search method 1s used with the least p-th and SUMT optimizations. While slower to converge than gradient based methods, direct search methods allow the consideration of arbitrary objective functions. Transformations of unconstrained search variables to constrained mechanism parameters are utilized to allow unconstrained searching. Transforms based on redefining link length limits, incorporating "Grashof-Criteria" considerations concurrently with transformation of unconstrained search variable set values, are introduced for link length parameters. The transforms facilitate effective optimization allowing searching and convergence within a preferred mechanism sub-type.
Two example problems , one path generation and the other motion generation, and a case study for a digger mechanism (motion generation) are presented demonstrating the effectiveness of the developed approach.