Design of Structures and Compliant Mechanisms by Evolutionary Optimization of Morphological Representations of Topology

1998 ◽  
Vol 122 (4) ◽  
pp. 560-566 ◽  
Author(s):  
K. Tai ◽  
T. H. Chee
Keyword(s):  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Evolutionary Process ◽  
Discrete Optimization Problem ◽  
Structural Geometry ◽  
Design Synthesis ◽  
Continuum Structures ◽  
Representation Scheme ◽  
Shape Characteristics

This paper demonstrates the automatic design synthesis of continuum structures by the process of topology/shape optimization. The problem is solved as a discrete optimization problem using the genetic algorithm (GA). Past efforts using this approach have not been very effective due to the lack of an appropriate structural geometric representation which is highly essential to the success of the evolutionary processes of the GA. Based on the morphology of living creatures, a representation scheme has been developed using arrangements of skeleton and ‘flesh’ to define structural geometry. This scheme facilitates the transmission of topological and shape characteristics across generations in the evolutionary process, and will not render any structurally invalid designs. Good results are illustrated using this scheme to design a compliant mechanism and a cantilever beam. [S1050-0472(00)02104-8]

Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape

2000 ◽  
Author(s):  
Kang Tai ◽  
Guang Yu Cui ◽  
Tapabrata Ray
Keyword(s):  
Evolutionary Algorithm ◽  
Compliant Mechanisms ◽  
Evolutionary Process ◽  
Shape Design ◽  
Discrete Optimization Problem ◽  
Design Synthesis ◽  
Optimization Methodology ◽  
Computationally Intensive ◽  
Representation Scheme ◽  
Shape Characteristics

Abstract This work demonstrates the successful synthesis of path generating compliant mechanisms by the process of topology and shape design optimization. As geometric topology variation of continuum structures is difficult to treat and analysis of the displacement path or trajectory of such structures is computationally intensive, a highly effective and efficient optimization methodology is needed. This paper describes the use of a recently developed morphological geometric representation scheme coupled with an evolutionary algorithm to synthesize the mechanism. The scheme uses arrangements of skeleton and ‘flesh’ to define structural geometry, which facilitates transmission of topological/shape characteristics across generations in the evolutionary process and will not render any geometrically invalid designs. The evolutionary algorithm solves the problem as a discrete optimization problem, with a proficient constraint handling capability.

Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape

2002 ◽  
Vol 124 (3) ◽  
pp. 492-500 ◽  
Author(s):  
Kang Tai ◽  
Guang Yu Cui ◽  
Tapabrata Ray
Keyword(s):  
Evolutionary Algorithm ◽  
Compliant Mechanisms ◽  
Design Procedure ◽  
Evolutionary Process ◽  
Shape Design ◽  
Discrete Optimization Problem ◽  
Design Synthesis ◽  
Computationally Intensive ◽  
Representation Scheme ◽  
Shape Characteristics

This work demonstrates the successful synthesis of path generating compliant mechanisms by the process of topology and shape design optimization. As geometric topology variation of continuum structures is difficult to treat and analysis of the displacement path or trajectory of such structures is computationally intensive, a highly effective and efficient optimal design procedure is needed. This paper describes the use of a recently developed morphological geometric representation scheme coupled with an evolutionary algorithm to synthesize the mechanism. The scheme uses arrangements of skeleton and “flesh” to define structural geometry, which facilitates transmission of topological/shape characteristics across generations in the evolutionary process and will not render any geometrically invalid designs. The evolutionary algorithm solves the problem as a discrete optimization problem, with a proficient constraint handling capability.

Load-Transmitter Constraint Sets: Part I—An Effective Tool for Visualizing Load Flow in Compliant Mechanisms and Structures

2010 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Deformation Behavior ◽  
Design Methodology ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Load Flow ◽  
Mathematical Framework ◽  
Design Synthesis ◽  
Fundamental Building Block ◽  
Block Based

Visualizing load flow aids in conceptual design synthesis of machine components. In this paper, we present a mathematical framework to visualize load flow in compliant mechanisms and structures. This framework uses the concept of transferred forces to quantify load flow from input to the output of a compliant mechanism. The key contribution of this paper is the identification a fundamental building block known as the Load-Transmitter Constraint (LTC) set, which enables load flow in a particular direction. The transferred force in each LTC set is shown to be independent of successive LTC sets that are attached to it. This enables a continuous visualization of load flow from the input to the output. Furthermore, we mathematically relate the load flow with the deformation behavior of the mechanism. We can thus explain the deformation behavior of a number of compliant mechanisms from literature by identifying its LTC sets to visualize load flow. This method can also be used to visualize load flow in optimal stiff structure topologies. The insight obtained from this visualization tool facilitates a systematic building block based design methodology for compliant mechanisms and structural topologies.

Design of 2-DOF Compliant Mechanisms to Form Grip-and-Move Manipulators for 2D Workspace

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
N. F. Wang ◽  
K. Tai
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Nonlinear Finite Element ◽  
Optimal Designs ◽  
Structural Topology ◽  
Structural Geometry ◽  
Multiobjective Genetic Algorithm ◽  
Topology And Shape Optimization ◽  
Morphological Representation

This paper demonstrates the design of compliant grip-and-move manipulators by structural optimization using genetic algorithms. The manipulator is composed of two compliant mechanisms (each with two degrees of freedom) that work like two fingers so that the manipulator can grip an object and convey it from one point to another anywhere within a two-dimensional workspace. The synthesis of such compliant mechanisms is accomplished by formulating the problem as a structural topology and shape optimization problem with multiple objectives and constraints to achieve the desired behavior of the manipulator. A multiobjective genetic algorithm is then applied coupled with an enhanced morphological representation for defining and encoding the structural geometry variables. The solution framework is integrated with a nonlinear finite element code for large-displacement analyses of the compliant structures to compute the paths generated by these mechanisms, with the resulting optimal designs used to realize various manipulator configurations.

Runner Optimization for In-Mold Assembly of Multi-Material Compliant Mechanisms

2011 ◽  
Author(s):  
Wojciech Bejgerowski ◽  
Satyandra K. Gupta
Keyword(s):  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Polymer Melt ◽  
Injection Molding Process ◽  
Optimization Approach ◽  
Assembly Process ◽  
Molding Process ◽  
Design Variables

The runner system in injection molding process is used to supply the polymer melt from injection nozzle to the gates of final part cavities. Realizing complex multi-material mechanisms by in-mold assembly process requires special runner layout design considerations due to the existence of the first stage components. This paper presents the development of an optimization approach for runner systems in the in-mold assembly of multi-material compliant mechanisms. First, the issues specific to the in-mold assembly process are identified and analyzed. Second, the general optimization problem is formulated by identification of all parameters, design variables, objective functions and constraints. Third, the implementation of the optimization problem in Matlab® environment is described based on a case study of a runner system for an in-mold assembly of a MAV drive mechanism. This multi-material compliant mechanism consists of seven rigid links interconnected by six compliant hinges. Finally, several optimization approaches are analyzed to study their performance in solving the formulated problem. The most appropriate optimization approach is selected. The case study showed the applicability of the developed optimization approach to runner systems for complex in-mold assembled multi-material mechanism designs.

Design Synthesis of 2-D Compliant Mechanisms Utilizing Serial Concatenation of Building Blocks

2009 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Unique Point ◽  
Compliance Matrix ◽  
Design Synthesis ◽  
Parametric Variation ◽  
Point Of Interest

In this section we implement a characterization based on eigen-twists and eigen-wrenches for the deformation of a compliant mechanism at a given point of interest. For 2-D mechanisms, this involves characterizing the compliance matrix at a unique point called the center of elasticity. At the center of elasticity, the translation and rotational compliances are decoupled. We give an intuitive graphical understanding of compliance at this point by representing the translational compliance as an ellipse and the coupling between the translational and rotational parameters as vectors (Coupling vectors). This representation gives us an intuitive understanding of series and parallel combination of building blocks. We obtain a parametric variation of these quantities for a compliant dyad building block, and show with examples how a mechanism can be synthesized by a combination of building blocks to obtain desired deformation requirements. We also propose a combination of series and parallel concatenation to achieve more than one specification simultaneously. Such a characterization can be extended to synthesize involving multiple ports.

An Automated Design Synthesis Method for Compliant Mechanisms With Application to Morphing Wings

2006 ◽  
Author(s):  
Hongqing Vincent Wang ◽  
David W. Rosen
Keyword(s):  
Particle Swarm Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Method ◽  
Particle Swarm ◽  
Automated Design ◽  
Cellular Structures ◽  
Swarm Optimization ◽  
Design Synthesis ◽  
Axial Forces

An automated design synthesis method is developed to design an airfoil with a reconfigurable shape, which can change from one type of geometry to another. A design synthesis method using unit truss approach and particle swarm optimization is presented. In the unit truss approach, unit truss is used as a new unit cell for mechanics analysis of cellular structures, including lightweight structures and compliant mechanisms. Using unit truss approach, axial forces, bending, torsion, nonlinearity, and buckling in structures can be considered. It provides good analysis accuracy and computational efficiency. A synthesis method using unit truss approach integrated with particle swarm optimization is developed to systematically design adaptive cellular structures, in particular, compliant mechanisms discussed in this paper. As an example study, the authors realize the design synthesis of a compliant mechanism that enables an entire closed-loop airfoil profile to change shape from NACA 23015 to FX60-126 for the desired morphing wing. The nonlinear behavior of compliant mechanisms under large deformation is considered. The resulting design is validated by testing its robustness and considering nonlinearity.

Wide Curve Based Geometric Optimization of Compliant Mechanisms

2005 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Geometric Optimization ◽  
Programming Algorithm ◽  
Free Form ◽  
Control Parameters ◽  
Practical Constraints

A wide curve is a curve with width or cross-section. This paper presents a geometric optimization method of compliant mechanisms based on the free form wide curve theory. With the proposed method, geometric optimization can be performed to further improve the performance of a compliant mechanism after its topology is selected. Every connection in the topology is represented as a parametric wide curve in which variable shape and size are fully described and conveniently controlled by the limited number of parameters. The geometric optimization is formulated on the control parameters of the 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 programming algorithm in Matlab Optimization Toolbox. An example is presented to verify the effectiveness of the proposed optimization procedure.

Estimating Optimized Stress Bounds in Early Stage Design of Compliant Mechanisms

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Sree Kalyan Patiballa ◽  
Girish Krishnan
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Early Stage ◽  
Functional Characterization ◽  
Stress Constraints ◽  
Design Synthesis ◽  
Stage Design ◽  
Computationally Intensive ◽  
Early Stage Design ◽  
Selection Of

Design synthesis of distributed compliant mechanisms is often a two-stage process involving (a) conceptual topology synthesis and a subsequent (b) refinement stage to meet strength and manufacturing specifications. The usefulness of a solution is ascertained only after the sequential completion of these two steps that are, in general, computationally intensive. This paper presents a strategy to rapidly estimate final operating stresses even before the actual refinement process. This strategy is based on the uniform stress distribution metric, and a functional characterization of the different members that constitute the compliant mechanism topology. Furthermore, this paper uses the underlying mechanics of stress bound estimation to propose two rule of thumb guidelines for insightful selection of topologies and systematically modifying them for an application. The selection of the best conceptual solution in the early stage design avoids refinement of topologies that inherently may not meet the stress constraints. This paper presents two examples that illustrate these guidelines through the selection and refinement of topologies for a planar compliant gripper application.

Design and Optimization of a Bend-and-Sweep Compliant Mechanism

2013 ◽  
Author(s):  
Yashwanth Tummala ◽  
Mary Frecker ◽  
Aimy Wissa ◽  
James E. Hubbard
Keyword(s):  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Leading Edge ◽  
Von Mises Stress ◽  
Nsga Ii ◽  
Design And Optimization ◽  
Compliant Joint ◽  
Von Mises ◽  
Wing Morphing

A novel contact aided compliant mechanism called a bend-and-sweep compliant mechanism is presented. This mechanism has tailorable nonlinear stiffness properties in two orthogonal directions. The fundamental element of this compliant mechanism is the Angled Compliant Joint (ACJ), and the geometric parameters determine the stiffness. This paper presents the design and optimization of such a compliant mechanism. A multi-objective optimization problem was formulated for design optimization of the bend-and-sweep compliant mechanism. The objectives of the optimization problem were to maximize the bending and sweep displacements while minimizing the von Mises stress and mass of each mechanism. This optimization problem was solved using NSGA-II (a genetic algorithm). The results of this optimization for a single ACJ during upstroke and downstroke are presented. Results of two different loading conditions used during optimization of a single ACJ for upstroke are presented. Finally, optimization results comparing the performance of compliant mechanisms with one and two ACJs are also presented. It can be inferred from these results that the number of ACJs and the design of each ACJ determines the stiffness of the bend-and-sweep compliant mechanism. These mechanisms can be used in various applications. Ornithopters or flapping wing unmanned aerial vehicles have unique potential to revolutionize both civil and military applications. The overall goal of this research is to improve the performance of such ornithopters by passively morphing their wings. Passive wing morphing of ornithopters can be achieved by inserting contact-aided compliant mechanisms in the leading edge wing spar. Previously the authors have shown that bending of ornithopter wings can be achieved by integrating a one degree of freedom contact aided compliant mechanism called a compliant spine. The spine was inserted into the leading edge spar and successful flight testing has shown that passive wing bending in ornithopters is feasible and results in significant improvements in lift and thrust. In order to achieve a bio-inspired wing gait called continuous vortex gait, the wings of the ornithopter need to bend, sweep, and twist simultaneously. This can be achieved by using the bend-and-sweep compliant presented in this paper.

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