Synthesis of Compliant Mechanisms for Path Generation using Genetic Algorithm

2004 ◽  
Vol 127 (4) ◽  
pp. 745-752 ◽  
Author(s):  
Anupam Saxena
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Analysis ◽  
Compliant Mechanisms ◽  
Topology Design ◽  
Optimal Topology ◽  
Path Generation ◽  
Geometrically Nonlinear Analysis ◽  
Design Variables ◽  
Gradient Based ◽  
Shape And Size

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.

On Optimal Design of Compliant Mechanisms for Specified Nonlinear Path Using Curved Frame Elements and Genetic Algorithm

2006 ◽  
Author(s):  
Ashok Rai ◽  
Anupam Saxena ◽  
Nilesh D. Mankame ◽  
Chandra Shekhar Upadhyay
Keyword(s):  
Genetic Algorithm ◽  
Compliant Mechanisms ◽  
Beam Theory ◽  
Topology Design ◽  
Size Optimization ◽  
Discrete Topology ◽  
Topology Optimization Problem ◽  
Young’S Moduli ◽  
Design Variables ◽  
Out Of Plane

This paper discusses topology, shape and size optimization of fully compliant mechanisms for path generation applications using curved frame elements and genetic algorithm. The topology optimization problem is treated as a discrete ‘0-1’ problem wherein the elastic modulus is chosen as 0 or some pre-specified value, and no intermediate value in between. As the Young’s moduli are discrete topology design variables, function based genetic algorithm is employed for optimization. The size optimization variables are the lengths, in-plane widths and out-of-plane thicknesses of frame elements. Shape optimization is performed using the end slopes. Kirchhoff’s shallow arch beam theory is employed along with co-rotational geometrically nonlinear formulation. Synthesis examples are presented to demonstrate the applicability of min-max criterion proposed to achieve a curved path specified using precision points.

scholarly journals A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization

2008 ◽  
pp. 103-126
Author(s):  
David W. Zingg ◽  
Marian Nemec ◽  
Thomas H. Pulliam
Keyword(s):  
Genetic Algorithm ◽  
Shape Optimization ◽  
Comparative Evaluation ◽  
Pareto Front ◽  
Optimization Problems ◽  
Aerodynamic Optimization ◽  
Design Variables ◽  
Gradient Based ◽  
Degree Of Convergence ◽  
Multipoint Optimization

A genetic algorithm is compared with a gradient-based (adjoint) algorithm in the context of several aerodynamic shape optimization problems. The examples include singlepoint and multipoint optimization problems, as well as the computation of a Pareto front. The results demonstrate that both algorithms converge reliably to the same optimum. Depending on the nature of the problem, the number of design variables, and the degree of convergence, the genetic algorithm requires from 5 to 200 times as many function evaluations as the gradientbased algorithm.

scholarly journals Evaluation of a Particle Swarm Algorithm For Biomechanical Optimization

2005 ◽  
Vol 127 (3) ◽  
pp. 465-474 ◽  
Author(s):  
Jaco F. Schutte ◽  
Byung-Il Koh ◽  
Jeffrey A. Reinbolt ◽  
Raphael T. Haftka ◽  
Alan D. George ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Test Problem ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Test Problems ◽  
Biomechanical Test ◽  
Length Scales ◽  
Design Variables ◽  
Analytical Test ◽  
Gradient Based

Optimization is frequently employed in biomechanics research to solve system identification problems, predict human movement, or estimate muscle or other internal forces that cannot be measured directly. Unfortunately, biomechanical optimization problems often possess multiple local minima, making it difficult to find the best solution. Furthermore, convergence in gradient-based algorithms can be affected by scaling to account for design variables with different length scales or units. In this study we evaluate a recently- developed version of the particle swarm optimization (PSO) algorithm to address these problems. The algorithm’s global search capabilities were investigated using a suite of difficult analytical test problems, while its scale-independent nature was proven mathematically and verified using a biomechanical test problem. For comparison, all test problems were also solved with three off-the-shelf optimization algorithms—a global genetic algorithm (GA) and multistart gradient-based sequential quadratic programming (SQP) and quasi-Newton (BFGS) algorithms. For the analytical test problems, only the PSO algorithm was successful on the majority of the problems. When compared to previously published results for the same problems, PSO was more robust than a global simulated annealing algorithm but less robust than a different, more complex genetic algorithm. For the biomechanical test problem, only the PSO algorithm was insensitive to design variable scaling, with the GA algorithm being mildly sensitive and the SQP and BFGS algorithms being highly sensitive. The proposed PSO algorithm provides a new off-the-shelf global optimization option for difficult biomechanical problems, especially those utilizing design variables with different length scales or units.

Using Rigid-Body Mechanism Topologies to Design Path Generating Compliant Mechanisms

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mesh Network ◽  
Optimal Topology ◽  
Optimal Size ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Straight Line ◽  
Rigid Body Transformation

For a path generation problem, this paper uses the base topology of a single degree-of-freedom (DOF) rigid-body mechanism solution to synthesize fully distributed compliant mechanisms that can trace the same path. Two different strategies are proposed to employ the base topology in the structural optimization so that its design space size can be intelligently reduced from an arbitrary complexity. In the first strategy, dimensional synthesis directly determines the optimal size and shape of the compliant mechanism solution while maintaining the exact base topology. In the second, the base topology establishes an initial mesh network to determine the optimal topology and dimensions simultaneously. To increase the possibility of converging to an optimal design, the objective metrics to evaluate the path generation ability are computed in a novel manner. A section-by-section analysis with a rigid-body transformation is implemented to examine the full path of each candidate mechanism. A two-objective genetic algorithm (GA) is employed to find a group of viable designs that tradeoff minimizing the average Euclidean distance between the desired and actual paths with minimizing the peak distance between corresponding points on those paths. Two synthesis examples generating straight-line and curved paths are presented to demonstrate the procedure's utility.

Optimal fiber orientation and topology design for compliant mechanisms with fiber-reinforced composites

2016 ◽  
Vol 231 (12) ◽  
pp. 2302-2312 ◽  
Author(s):  
Xinxing Tong ◽  
Wenjie Ge ◽  
Yonghong Zhang
Keyword(s):  
Fiber Orientation ◽  
Strain Energy ◽  
Compliant Mechanisms ◽  
Linear Optimization ◽  
Topology Design ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
And Topology ◽  
Glass Fiber Reinforced ◽  
Design Variables

An approach for designing compliant mechanisms with glass fiber-reinforced epoxy materials is presented to obtain the optimum fiber orientation and topology structure simultaneously in this paper. Four-node hybrid stress elements and nodal design variables are adopted to suppress the islands and checkerboard phenomenon without additive filter technology and constraint. Taking fiber orientation and relative density as design variables, minimizing the weighted linear combination of the mutual strain energy and the strain energy is considered as objective function to achieve the desired deformation and enough load-carrying capacity of compliant mechanisms with the volume constraint. The displacement field of structure is obtained by the finite element analysis, and the non-linear optimization problem is solved via the well-known method of moving asymptotes. The numerical examples of designing compliant inverters and grippers with different weighted factors are investigated to demonstrate the effectiveness of the proposed method.

Optimal Thin-Film Topology Design for Specified Temperature Profiles in Resistive Heaters

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
François Mathieu-Potvin ◽  
Louis Gosselin
Keyword(s):  
Thin Film ◽  
Genetic Algorithm ◽  
Film Thickness ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Electrical Potential ◽  
Topology Design ◽  
Temperature Profiles ◽  
Thin Film Thickness ◽  
Design Variables

In this paper, we optimized the topology of a thin-film resistive heater as well as the electrical potential of the electrodes on the boundaries. The objective was to minimize the difference between the actual and prescribed temperature profiles. The thin-film thickness was represented by 100 design variables, and the electrical potential at each electrode were also design variables. The topology optimization problem (inverse problem) has been solved with two methods, i.e., with a genetic algorithm (GA) and with a conjugate gradient method using adjoint and sensitivity problems (CGA). The genetic algorithm used here was modified in order to prevent nonconvergence due to the nonuniqueness of topology representation. The conjugate gradient method used in inverse conduction was extended to cope with our electrothermal problem. The GA and CGA methods started with random topologies and random electrical potential values at electrodes. Both the CGA and GA succeeded in finding optimal thin-film thickness distributions and electrode potential values, even with 100 topology design variables. For most cases, the maximum discrepancy between the optimized and prescribed temperature profiles was under 0.5°C, relative to temperature profiles of the order of 70°C. The CGA method was faster to converge, but was more complex to implement and sometimes led to local minima. The GA was easier to implement and was more unlikely to lead to a local minimum, but was much slower to converge.

Intelligent Genetic Algorithm with a Gradient-Based Local Search Applied to Supersonic Wing Planform Optimization

2007 ◽  
Vol 23 (4) ◽  
pp. 285-294 ◽  
Author(s):  
J.-L. Liu ◽  
J.-L. Chen
Keyword(s):  
Genetic Algorithm ◽  
Local Search ◽  
Objective Function ◽  
Initial Conditions ◽  
Fractional Factorial ◽  
Optimization Approach ◽  
Design Variables ◽  
Gradient Based ◽  
Global Optima ◽  
Intelligent Genetic Algorithm

AbstractThis study proposes an efficiently evolutionary algorithm, termed IGA-LS, which combines an intelligent genetic algorithm (IGA) with a gradient-based local search (LS). The IGA performs a crossover operation and uses a fractional factorial design to determine the optimal combination of design variables. That is, in the proposed IGA, the chromosomes of children are generated via an intelligent crossover process with factorial experiments after the execution of the selection operation of the GA. This gene mating process differs from that of the traditional GA, in which each chromosome of child exchange genes randomly. The gradient-based optimization approach seeks feasible and usable directions in which to minimize a specified objective function. The initial conditions are provided by the IGA in each generation. Therefore, the IGA-LS offers fast convergence and high numerical accuracy. Several multi-modal test functions are introduced herein to examine the algorithmic capacity and efficiency of finding the global optima. Moreover, the proposed IGA-LS algorithm is applied to optimize the design of a supersonic wing planform for supersonic airplane. The objective function is to minimize the drag during supersonic cruising. From the numerical results, the presented algorithm outperforms the traditional GA, the micro-GA and the intelligent GA in terms of convergence rate and value of the optimal function.

scholarly journals Hybrid Seven-bar Press Mechanism

2018 ◽  
Vol 12 (3) ◽  
pp. 181-187
Author(s):  
M. Erkan Kütük ◽  
L. Canan Dülger
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Design Optimization ◽  
Hybrid System ◽  
Degrees Of Freedom ◽  
Dimensional Synthesis ◽  
Design Variables ◽  
Optimization Study ◽  
Metal Stamping

An optimization study with kinetostatic analysis is performed on hybrid seven-bar press mechanism. This study is based on previous studies performed on planar hybrid seven-bar linkage. Dimensional synthesis is performed, and optimum link lengths for the mechanism are found. Optimization study is performed by using genetic algorithm (GA). Genetic Algorithm Toolbox is used with Optimization Toolbox in MATLAB®. The design variables and the constraints are used during design optimization. The objective function is determined and eight precision points are used. A seven-bar linkage system with two degrees of freedom is chosen as an example. Metal stamping operation with a dwell is taken as the case study. Having completed optimization, the kinetostatic analysis is performed. All forces on the links and the crank torques are calculated on the hybrid system with the optimized link lengths

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