Direct Displacement Synthesis Method for Shape Morphing Skins Using Compliant Mechanisms

2010 ◽  
Author(s):  
Luke A. Berglind ◽  
Joshua D. Summers
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Synthesis Method ◽  
Bending Stiffness ◽  
Optimization Techniques ◽  
Synthesis Methods ◽  
Specific Load ◽  
Shape Morphing ◽  
Continuum Structure

This paper presents a direct displacement synthesis method for the design of shape morphing skin structures using compliant mechanisms. The objective of this method is to design a skin structure that will deform to a desired final shape when acted on by a specific load. The method utilizes a ground structure geometry which can facilitate variable bending stiffness along the length of the skin using compliant spring members. Synthesis procedures involve the use of direct displacement to determine how the bending stiffness of the skin must vary to produce the desired shape change. The direct displacement synthesis method differs from other compliant mechanism synthesis methods found in literature, such as pseudo-rigid-body and continuum structure optimization, in the approach taken to solve for the unknown variables in the system. By using direct displacement to determine how the structure must respond to a specific load to achieve the desired shape change, the unknown variables within the system can be extracted directly without the use of optimization techniques.

A Conceptual Design Tool for Synthesis of Spatial Compliant and Shape Morphing Mechanisms

2018 ◽  
Author(s):  
Sreekalyan Patiballa ◽  
Kazuhiro Uchikata ◽  
Ramkumar Komanduri Ranganath ◽  
Girish Krishnan
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Design Guidelines ◽  
Design Tool ◽  
Three Dimensions ◽  
Shape Morphing ◽  
Compliant Surfaces ◽  
Flow Through ◽  
External Loads

Synthesis of spatial compliant mechanisms for morphing surfaces in three dimensions is challenging as it not only involves meeting the kinematic requirement for spatial shape change, but also providing support against external loads. In three dimensions, there are no existing insightful techniques for synthesis, and the computational approaches are rendered complex. This paper builds on a new insightful technique to synthesize compliant mechanism topologies by visualizing a kinetostatic field of forces that flow through the mechanism geometry. Such a framework when extended to three dimensions, enables a maximally decoupled synthesis framework of shape morphing compliant surfaces, where a primary mechanism meets the shape change requirement, and an auxiliary mechanism provides the required support under external loads. The preliminary design guidelines are implemented using an immersive Virtual Reality based design tool, and verified using finite element simulations for several spatial compliant mechanisms. This design framework is deemed useful for a larger class of shape morphing structures beyond the examples presented in the paper.

Spatial Concept Synthesis of Compliant Mechanisms Utilizing Non-Linear Eigentwist Characterization

2018 ◽  
Author(s):  
Joep P. A. Nijssen ◽  
Giuseppe Radaelli ◽  
Just L. Herder ◽  
J. B. Ring ◽  
Charles J. Kim
Keyword(s):  
Large Deformation ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
Planar Mechanisms ◽  
Spatial Concept ◽  
Spatial Design ◽  
Kinematic Behavior ◽  
Non Linear

Spatial compliant mechanism are challenging to design owing to their complex spatial kinetic and kinematic behavior. There are many synthesis methods to design compliant mechanisms, but they are often presented for planar mechanisms or have other limitations such as lack of designer input possibilities. In this paper a method based on the compliance ellipsoid is presented to create compliant mechanism topologies for spatial design cases. The result of this synthesis method is a qualitative concept which fundamentally creates the desired kinetic and kinematic profile. This concept can then be further refined using a large deformation eigentwist analysis, presented here. Lastly, these tools are used in a design example to show its potential.

Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation

1999 ◽  
Vol 123 (4) ◽  
pp. 535-541 ◽  
Author(s):  
L. Saggere ◽  
S. Kota
Keyword(s):  
Compliant Mechanisms ◽  
Shape Change ◽  
Synthesis Method ◽  
Elastic Equilibrium ◽  
Body Motion ◽  
Motion Generation ◽  
Generation Task ◽  
Potential Applications ◽  
Flexible Segment ◽  
Definition Of

Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.

Kinematic Synthesis of Planar, Shape-Changing Compliant Mechanisms Using Pseudo-Rigid-Body Models

2012 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Flexible Beam ◽  
Beam Model ◽  
Flexible Beams ◽  
Multi Objective Genetic Algorithm ◽  
Optimization Loop

This paper presents a procedure using Pseudo-Rigid-Body Models (PRBMs) to synthesize partially compliant mechanisms capable of approximating a shape change defined by a set of morphing curves in different positions. To generate a single-piece compliant mechanism, flexural pivots and flexible beams are both utilized in the mechanism. New topologies defined by compliant mechanism matrices are enumerated by modifying the components that make up a single degree-of-freedom (DOF) rigid-body mechanism. Because of the introduction of the PRBM for flexural pivots and the simplified PRBM for flexible beams, torsional springs are attached at the characteristic pivots of the 1-DOF rigid-body mechanism in order to generate a corresponding pseudo-rigid-body mechanism. A multi-objective genetic algorithm is employed to find a group of viable compliant mechanisms in the form of candidate pseudo-rigid-body mechanisms that tradeoff minimizing shape matching error with minimizing actuator energy. Since the simplified beam model is not accurate, an optimization loop is established to find the position and shape of the flexible beam using a finite link beam model. The optimal flexible beams together with the pseudo-rigid-body mechanism define the solution mechanism. The procedure is demonstrated with an example in which a partially compliant mechanism approximating two closed-curve profiles is synthesized.

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.

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.

Multiple-Segment-Pseudo-Rigid-Body Model Concept in Compliant Mechanism Design and Analysis

2000 ◽  
Author(s):  
Gregory A. Mettlach ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Methods ◽  
Model Concept ◽  
Displacement Boundary ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Beam Type

Abstract The concept of a pseudo-rigid-body model for a flexible member proven very instrumental in the design and analysis of compliant mechanisms. It provides a means by which a compliant mechanism may be modeled as an equivalent pseudo-rigid-body mechanism. This makes it possible for compliant mechanisms to be analyzed and designed using a wealth of existing methods for rigid-body mechanisms. Oftentimes, however, it is not possible to model a compliant member with a typical pseudo-rigid-body model. This may be due to a force or displacement boundary condition applied to a compliant member at a point other than the beam end. For situations such as these, a planar, multiple-segment pseudo-rigid-body model concept is introduced which allows arbitrary beam type compliant members, regardless of geometry, loading, or boundary conditions, to be modeled as an assemblage of rigid members with torsional springs at characteristic pivots. This methodology enables existing analysis and synthesis methods to be applied in the design of complex compliant mechanisms.

Geometric Synthesis of Spatial Compliant Mechanisms Using Three-Dimensional Wide Curves

2008 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Method ◽  
Three Dimensional ◽  
Programming Algorithm ◽  
Variable Cross ◽  
Finite Element Procedure ◽  
And Performance ◽  
Selection Of

A three-dimensional wide curve is a spatial curve with variable cross sections. This paper introduces a geometric synthesis method for spatial compliant mechanisms by using three-dimensional wide curves. In this paper, every connection in a spatial compliant mechanism is represented by a three-dimensional wide curve and the whole spatial compliant mechanism is modeled as a set of connected three-dimensional wide curves. The geometric synthesis of a spatial compliant mechanism is considered as the generation and optimal selection of control parameters of the corresponding three-dimensional parametric wide curves. The deformation and performance of spatial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm. The effectiveness of the proposed geometric procedures is verified by the demonstrated examples.

Constraint-Based Synthesis of Shape-Morphing Structures in Virtual Reality

2010 ◽  
Author(s):  
Judy M. Vance ◽  
Denis Dorozhkin
Keyword(s):  
Virtual Reality ◽  
Rigid Body ◽  
Method Development ◽  
Compliant Mechanisms ◽  
Design Method ◽  
Shape Change ◽  
The Body ◽  
Motion Path ◽  
Primary Methods ◽  
Shape Morphing

This manuscript outlines a novel approach to the design of compliant shape-morphing structures using constraint-based design method. Development of robust methods for designing shape-morphing structures is the focus of multiple current research projects, since the ability to modify geometric shapes of the individual system components, such as aircraft wings and antenna reflectors, provides the means to affect the performance of the corresponding mechanical systems. Of particular interest is the utilization of compliant mechanisms to achieve the desired adaptive shape change characteristics. Compliant mechanisms, as opposed to the traditional rigid link mechanisms, achieve motion guidance via the compliance and deformation of the mechanism’s members. The goal is to design a single-piece flexible structure capable of morphing a given curve or profile into a target curve or profile while utilizing the minimum number of actuators. The two primary methods prevalent in the design community at this time are the pseudo-rigid body method (PRBM) and the topological synthesis. Unfortunately these methods either tend to suffer from a poor ability to generate potential solutions (being more suitable for the analysis of existing structures) or are susceptible to overly-complex solutions. By utilizing the constraint-based design method (CBDM) we aim to address those shortcomings. The concept of CBDM has generally been confined to the Precision Engineering community and is based on the fundamental premise that all motions of a rigid body are determined by the position and orientation of the constraints (constraint topology) which are placed upon the body. Any mechanism motion path may then be defined by the proper combination of constraints. In order to apply the CBDM concepts to the design and analysis of shape-morphing compliant structures we propose a tiered design method that relies on kinematics, finite element analysis, and optimization. By discretizing the flexible element that comprises the active shape surface at multiple points in both the initial and the target configurations and treating the resulting individual elements as rigid bodies that undergo a planar or general spatial displacement we are able to apply the traditional kinematics theory to rapidly generate sets of potential solutions. The final design is then established via an FEA-augmented optimization sequence. Coupled with a virtual reality interface and a force-feedback device this approach provides the ability to quickly specify and evaluate multiple design problems in order to arrive at the desired solution.

Optimal Synthesis of Compliant Mechanisms to Satisfy Kinematic and Structural Requirements: Preliminary Results

1996 ◽  
Author(s):  
Mary I. Frecker ◽  
Noboru Kikuchi ◽  
Sridhar Kota
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Method ◽  
Design Procedure ◽  
Problem Formulation ◽  
Mechanism Synthesis ◽  
Ground Structure ◽  
Design Problems ◽  
Structural Requirements ◽  
External Loads

Abstract Compliant mechanism synthesis is an automated design procedure which allows the designer to systematically generate the optimal structural form for a particular set of loading and motion requirements. The synthesis method presented here solves a particular class of design problems, where the compliant mechanism is required to be both flexible to meet motion requirements, and stiff to withstand external loads. A two-part problem formulation is proposed using mutual and strain energies, whereby the conflicting design objectives of required flexibility and stiffness are handled via multi-criteria optimization. The resulting compliant mechanism topologies satisfy both kinematic and structural requirements. The problem formulation is implemented using a truss ground structure and SLP algorithm. Several design examples are presented to illustrate this method.

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