A unified approach to topology and dimensional synthesis of compliant mechanisms is presented in this paper as a discrete optimization problem employing both discrete (topology) and continuous (size) variables. The synthesis scheme features a design parameterization method that treats load paths as discrete design variables to represent various topologies, thereby ensuring structural connectivity among the input, output, and ground supports. The load path synthesis approach overcomes certain design issues, such as "gray areas" and disconnected structures, inherent in previous design schemes. Additionally, multiple gradations of structural resolution and a variety of configurations can be generated without increasing the number of design variables. By treating topology synthesis as a discrete optimization problem, the synthesis approach is incorporated in a genetic algorithm to search for feasible topologies for single-input single-output compliant mechanisms. Two design examples, commonly seen in the compliant mechanisms literature, are included to illustrate the synthesis procedure and to benchmark the performance. The results show that the load path synthesis approach can effectively generate well-connected compliant mechanism designs that are free of gray areas.

Topology and dimensional synthesis of compliant mechanisms using discrete optimization

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.

Synthesis of Compliant Mechanisms for Path Generation using Genetic Algorithm

Topology optimization of compliant mechanisms is presented in this paper wherein the layout design problem is addressed in its original binary or discrete (0-1) form. Design variables are modeled as discrete variables and allowed to assume values pertaining only to their void (0) or solid (1) states. Due to this discrete nature, a genetic algorithm is employed as an optimization routine. Using the barrier assignment approach, the search algorithm is extended to use with multiple materials. The layout design of compliant mechanisms is performed wherein displacements at multiple points (ports) in the design region are maximized along the respective prescribed directions. With multiple output ports and multiple materials, additional freedom in motion and force transduction can be achieved with compliant mechanisms. Geometrically large deformation analysis is employed to compute the displacement-based multiple objectives that are extremized using Nondominated Sorting in Genetic Algorithms (or NSGA). With genetic algorithms, buckling or snap through like issues with nonconvergent solutions in the population when computing nonlinear deformations can be implicitly circumvented.

Topology design of large displacement compliant mechanisms with multiple materials and multiple output ports

This paper describes a versatile methodology for solving topology design optimization problems using a genetic algorithm (GA). The key to its effectiveness is a geometric representation scheme that works by specifying a skeleton which defines the underlying topology/connectivity of a structural continuum together with segments of material surrounding the skeleton. The required design variables are encoded in a chromosome which is in the form of a directed graph that embodies this underlying topology so that appropriate crossover and mutation operators can be devised to recombine and help preserve any desirable geometry characteristics of the design through succeeding generations in the evolutionary process. The overall methodology is first tested by solving ‘target matching’ problems—simulated topology optimization problems in each of which a ‘target’ geometry is first created and predefined as the optimum solution, and the objective of the optimization problem is to evolve design solutions to converge towards this target shape. The methodology is then applied to design two path-generating compliant mechanisms—large-displacement flexural structures that undergo some desired displacement paths at some point when given a straight line input displacement at some other point—by an actual process of topology/shape optimization.

Structural topology optimization using a genetic algorithm with a morphological geometric representation scheme

A wide curve is a curve with width or cross section. This paper introduces a shape and size synthesis method for compliant mechanisms based on free-form wide curve theory. With the proposed method, detailed dimensions synthesis can be performed to further improve the performance after the topology is selected. Every connection in the topology is represented by a parametric wide curve in which variable shape and size are fully described and conveniently controlled by the limited number of parameters. The shape and size synthesis is formulated as the optimization of the control parameters of wide curves corresponding to all connections in the topology. Problem-dependent objectives are optimized and practical constraints are imposed during the optimization process. The optimization problem is solved by the constrained nonlinear programing algorithm in the MATLAB Optimization Toolbox. Two examples are included to demonstrate the effectiveness of the proposed synthesis procedure.

Shape and Size Synthesis of Compliant Mechanisms Using Wide Curve Theory

Compliant mechanisms achieve desired force and displacement characteristics through elastic deformation of their structure Current research in the synthesis of compliant mechanism topology has pursued multiobjective optimization using gradient-based search methods This paper will explore the use of a random-guided search method for multiobjective optimization of compliant mechanisms through genetic programming techniques The combination of genetic algorithms and compliant mechanisms is an effective and interesting combination of two biologically inspired engineering design areas This paper will describe and demonstrate the successful use of genetic programming to create a general design tool for topological synthesis of compliant mechanisms Features that exploit the implementation of genetic algorithms to compliant mechanism design, such as multiple criteria specification, multiple-design parameter variation, and final selections from a family of solutions will be presented and discussed Finally, the use of this design tool will be demonstrated on several familiar examples for validation and discussion

S.L. Canfield

Papers

Developing genetic programming techniques for the design of compliant mechanisms