An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms

1999 ◽  
Vol 121 (2) ◽  
pp. 229-234 ◽  
Author(s):  
J. A. Hetrick ◽  
S. Kota
Keyword(s):  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Stress Constraints ◽  
Optimization Techniques ◽  
Mechanical Transmission ◽  
Dimensional Synthesis ◽  
Size And Shape ◽  
Mechanical Devices

Compliant mechanisms are jointless mechanical devices that take advantage of elastic deformation to achieve a force or motion transformation. An important step toward automated design of compliant mechanisms has been the development of topology optimization techniques. The next logical step is to incorporate size and shape optimization to perform dimensional synthesis of the mechanism while simultaneously considering practical design specifications such as kinematic and stress constraints. An improved objective formulation based on maximizing the energy throughput of a linear static compliant mechanism is developed considering specific force and displacement operational requirements. Parametric finite element beam models are used to perform the size and shape optimization. This technique allows stress constraints to limit the maximum stress in the mechanism. In addition, constraints which restrict the kinematics of the mechanism are successfully applied to the optimization problem. Resulting optimized mechanisms exhibit efficient mechanical transmission and meet kinematic and stress requirements. Several examples are given to demonstrate the effectiveness of the optimization procedure.

Size and Shape Optimization of Compliant Mechanisms: An Efficiency Formulation

1998 ◽  
Author(s):  
Joel A. Hetrick ◽  
Sridhar Kota
Keyword(s):  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Stress Constraints ◽  
Mechanical Efficiency ◽  
Optimization Techniques ◽  
Mechanical Transmission ◽  
Dimensional Synthesis ◽  
Size And Shape

Abstract Compliant mechanisms are jointless mechanical devices that take advantage of elastic deformation to achieve a force or motion transformation. A milestone toward systematic design of compliant mechanisms has been the development of topology optimization techniques. The next logical step is to incorporate size and shape optimization to identify the exact dimensional form of the mechanism. A new objective formulation based on maximizing the mechanical efficiency of a compliant mechanism is developed in order to perform the size and shape optimization. An advantage of this formulation is that precise control over the mechanism’s mechanical or geometric advantage can be enforced during optimization. Finite element beam models are used to perform dimensional synthesis of planar compliant mechanisms. This technique allows stress constraints to limit the maximum stress in the mechanism which improves the mechanism’s durability and flexibility. Resulting optimized mechanisms exhibit efficient mechanical transmission and meet kinematic and stress requirements. Several examples are given to demonstrate the effectiveness of the optimization procedure.

scholarly journals Hybrid Optimization Based Mathematical Procedure for Dimensional Synthesis of Slider-Crank Linkage

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1581
Author(s):  
Alfonso Hernández ◽  
Aitor Muñoyerro ◽  
Mónica Urízar ◽  
Enrique Amezua
Keyword(s):  
Genetic Algorithm ◽  
Fitness Function ◽  
Linear Equations ◽  
Optimization Procedure ◽  
Optimization Techniques ◽  
Dimensional Synthesis ◽  
Hybrid Strategy ◽  
Dimensional Parameters ◽  
Optimization Methodology ◽  
Crank Mechanism

In this paper, an optimization procedure for path generation synthesis of the slider-crank mechanism will be presented. The proposed approach is based on a hybrid strategy, mixing local and global optimization techniques. Regarding the local optimization scheme, based on the null gradient condition, a novel methodology to solve the resulting non-linear equations is developed. The solving procedure consists of decoupling two subsystems of equations which can be solved separately and following an iterative process. In relation to the global technique, a multi-start method based on a genetic algorithm is implemented. The fitness function incorporated in the genetic algorithm will take as arguments the set of dimensional parameters of the slider-crank mechanism. Several illustrative examples will prove the validity of the proposed optimization methodology, in some cases achieving an even better result compared to mechanisms with a higher number of dimensional parameters, such as the four-bar mechanism or the Watt’s mechanism.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

On the Extraction of Kinematic Behavior From Optimal Compliant Topologies With Application to Number Synthesis of Linkages

2001 ◽  
Author(s):  
Anupam Saxena ◽  
G. K. Ananthasuresh
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Method ◽  
Dimensional Synthesis ◽  
Kinematic Chains ◽  
Design Specifications ◽  
Kinematic Behavior ◽  
Added Benefit ◽  
Number Synthesis ◽  
Elastic Mechanics

Abstract This paper presents a number of systematically designed compliant topologies and discusses how the intrinsic kinematic behavior can be extracted from them. This is then applied to the number synthesis of linkages. Many techniques developed for number synthesis of linkages enumerate numerous possible kinematic chains, but few can select the best configuration among them. A systematic computational approach that can select the best configuration based on kinetostatic design specifications is presented here. This is a serendipitous result that transpired when two well-developed design techniques for compliant mechanisms were combined. A number of examples with non-intuitive design specifications are included to illustrate the new approach to number synthesis. The examples also illustrate that the kinematic behavior is aptly captured in the elastic mechanics-based topology optimization method to compliant mechanism design. Dimensional synthesis is also accomplished in the same procedure, which is an added benefit of this approach.

Large Deformation Behavior of Compliant Mechanisms

2001 ◽  
Author(s):  
Jinyong Joo ◽  
Sridhar Kota ◽  
Noboru Kikuchi
Keyword(s):  
Shape Optimization ◽  
Large Deformation ◽  
Deformation Behavior ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Linear Formulation ◽  
Scaling Effect ◽  
Beam Elements ◽  
Linear And Nonlinear ◽  
Amplification Mechanism

Abstract This paper presents a non-linear formulation for size and shape optimization of compliant mechanisms using tapered beam elements. Designs based on linear and nonlinear formulations are compared using a stroke amplification mechanism example. Also, the scaling effect of the compliant mechanism is investigated.

Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Mesh Network ◽  
Adaptive Antenna ◽  
Optimal Size ◽  
Dimensional Synthesis ◽  
Element Analysis

This paper uses rigid-body mechanism topologies to synthesize fully distributed compliant mechanisms that approximate a shape change defined by a set of morphing curves in different positions. For a shape-change problem, a rigid-body mechanism solution is generated first to provide the base topology. This base topology defines a preselected design space for the structural optimization in one of two ways so as to obtain a compliant mechanism solution that is typically superior to the local minimum solutions obtained from searching more expansive design spaces. In the first strategy, the dimensional synthesis directly determines the optimal size and shape of the distributed compliant mechanism having exactly the base topology. In the second strategy, an initial mesh network established from the base topology is used to generate different topologies (in addition to the base), and an improved design domain parameterization scheme ensures that only topologies with well-connected structures are evaluated. The deformation of each generated compliant mechanism is evaluated using geometrically nonlinear finite element analysis (FEA). A two-objective genetic algorithm (GA) is employed to find a group of viable designs that trade off minimizing shape matching error with minimizing maximum stress. The procedure's utility is demonstrated with three practical examples—the first two approximating open-curve profiles of an adaptive antenna and the third approximating closed-curve profiles of a morphing wing.

Size and Shape Optimization of a 1.0mm Multifunctional Forceps-Scissors Instrument for Minimally Invasive Surgery

2007 ◽  
Author(s):  
Milton E. Aguirre ◽  
Mary Frecker
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Shape Optimization ◽  
Invasive Surgery ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Linear Deformation ◽  
Cross Sectional ◽  
Size And Shape ◽  
Grasping Forces

A size and shape optimization routine is developed and implemented on a 1 mm multifunctional instrument for minimally invasive surgery. The instrument is a compliant mechanism, without hinges, capable of both grasping and cutting. Multifunctional instruments have proven to be beneficial in the operating room because of their ability to perform multiple tasks, thereby decreasing the total number of instrument exchanges in a single procedure. In addition, with fewer exchanges the risk of inadvertent tissue trauma as well as overall surgical time and costs are reduced. The focus of the paper is to investigate the performance effects of allowing the cross-sectional area along the length of the device to vary. This is accomplished by defining various cross-sectional segments along the device in terms of parametric variables (Wi) and optimizing the dimensions to provide a sufficient forceps jaw opening while maintaining adequate cutting and grasping forces. Two optimization problems are considered. First, all parametric segments are set equal to one another permitting all cross-sections to vary uniformly and achieving size optimization. Second, each segment is defined as a separate design variable to allow segments to vary independently and thereby achieving shape optimization. Due to the device’s symmetry, one-half of the mechanism is modeled as a cantilever beam undergoing large deformation. ANSYS’ optimization module is employed using the first order method because it is capable of performing optimization considering non-linear deformation and multiple loading conditions. Finally, prototypes are fabricated using wire EDM and prototype evaluations are conducted to compare size versus shape optimization, and to validate ANSYS as the solution method.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Stress Constraint ◽  
Cell Problem ◽  
Design Variables ◽  
Design Cell

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical, or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary, and every design cell is either solid or void to prevent gray cell problem that is usually caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum. No postprocessing is required for topology uncertainty caused by either point connection or gray cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

A Two-Stage Design Method for Compliant Mechanisms Having Specified Non-Linear Output Paths

2006 ◽  
Author(s):  
Masakazu Kobayashi ◽  
Hiroshi Yamakawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Two Stage ◽  
Traditional Methods ◽  
Stage Design ◽  
Second Stage ◽  
Additional Constraints

Compliant mechanisms generated by traditional topology optimization methods have linear output response, and it is difficult for traditional methods to implement mechanisms having non-linear output responses, such as nonlinear deformation or path. To design a compliant mechanism having a specified nonlinear output path, a two-stage design method based on topology and shape optimization is constructed here. In the first stage, topology optimization generates an initial and conceptual compliant mechanism based on ordinary design conditions, with “additional” constraints that are used to control the output path at the second stage. In the second stage, an initial model for the shape optimization is created, based on the result of the topology optimization, and the additional constraints are replaced by spring elements. The shape optimization is then executed, to generate a detailed shape of the compliant mechanism having the desired output path. In this stage, parameters that represent the outer shape of the compliant mechanism and the properties of spring elements are used as design variables in the shape optimization. In addition to configuration of the specified output path, executing the shape optimization after the topology optimization also makes it possible to consider the stress concentration and large displacement effects. This is an advantage offered by the proposed method, since it is difficult for traditional methods to consider these aspects, due to inherent limitations of topology optimization.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Conduct Sensitivity Analysis

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is usually caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and avoid the need to select the initial guess solution and conduct sensitivity analysis. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

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