In this paper is described a procedure to synthesize the optimal topology, shape, and size of compliant continua for a given nonlinear output path. The path is prescribed using a finite number of distinct precision points much in accordance with the synthesis for path generation in traditional kinematics. Geometrically nonlinear analysis is employed to model large displacements of the constituent members. It is also essential to employ nonlinear analysis to allow the output port to negotiate the prescribed path accurately. The topology synthesis problem is addressed in its original binary form in that the corresponding design variables are only allowed to assume values of “0” for no material and “1” for the material present at a site in the design region. Shape and size design variables are modeled using continuous functions. Owing to the discrete nature of topology design variables, since gradient based optimization methods cannot be employed, a genetic algorithm is used that utilizes only the objective values to approach an optimum solution. A notable advantage of a genetic algorithm over its gradient based counterparts is the implicit circumvention of nonconvergence in the large displacement analysis, which is another reason why a genetic algorithm is chosen for optimization. The least squared objective is used to compare the design and desired output responses. To allow a user to specify preference for a precision point, individual multiple least squared objectives, same in number as the precision points are used. The multiple objectives are solved using Nondominated Sorting in Genetic Algorithm (NSGA-II) to yield a set of pareto optimal solutions. Thus, multiple solutions for compliant mechanisms can be obtained such that a mechanism can traverse one or some precision points among those specified more precisely. To traverse the entire path, a solution that minimizes the sum of individual least square objectives may be chosen. Synthesis examples are presented to demonstrate the usefulness of the proposed method that is capable of generating a solution that can be manufactured as is without requiring any interpretation.

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July 2005

Technical Papers

# Synthesis of Compliant Mechanisms for Path Generation using Genetic Algorithm

Anupam Saxena

Anupam Saxena

Mechanical Engineering,

Indian Institute of Technology

, Kanpur 208016, India
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Anupam Saxena

Mechanical Engineering,

Indian Institute of Technology

, Kanpur 208016, India*J. Mech. Des*. Jul 2005, 127(4): 745-752 (8 pages)

**Published Online:**September 29, 2004

Article history

Received:

April 29, 2004

Revised:

September 29, 2004

Citation

Saxena, A. (September 29, 2004). "Synthesis of Compliant Mechanisms for Path Generation using Genetic Algorithm." ASME. *J. Mech. Des*. July 2005; 127(4): 745–752. https://doi.org/10.1115/1.1899178

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