Trade Space Exploration of Magnetically Actuated Origami Mechanisms

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Landen Bowen ◽  
Kara Springsteen ◽  
Mary Frecker ◽  
Timothy Simpson
Keyword(s):  
Magnetic Material ◽  
Dynamic Models ◽  
Active Material ◽  
Approximation Error ◽  
Joint Stiffness ◽  
Design Tool ◽  
Target Shape ◽  
Self Assembling ◽  
Magnetically Actuated ◽  
Trade Space Exploration

Self-folding origami has the potential to be utilized in novel areas such as self-assembling robots and shape-morphing structures. Important decisions in the development of such applications include the choice of active material and its placement on the origami model. With proper active material placement, the error between the actual and target shapes can be minimized along with cost, weight, and input energy requirements. A method for creating magnetically actuated dynamic models and experimentally verifying their results is briefly reviewed, after which the joint stiffness and magnetic material approximations used in the dynamic model are discussed in more detail. Through the incorporation of dynamic models of magnetically actuated origami mechanisms into the Applied Research Laboratory's trade space visualizer (atsv), the trade spaces of self-folding dynamic models of the waterbomb base and Shafer's frog tongue are explored. Finally, a design tradeoff is investigated between target shape approximation error and the placement of magnetic material needed to reach a target shape. These two examples demonstrate the potential use of this process as a design tool for other self-folding origami mechanisms.

Optimization of a Dynamic Model of Magnetic Actuation of an Origami Mechanism

2015 ◽  
Author(s):  
Landen Bowen ◽  
Kara Springsteen ◽  
Mary Frecker ◽  
Timothy Simpson
Keyword(s):  
Dynamic Models ◽  
Active Material ◽  
Joint Stiffness ◽  
Design Tool ◽  
Magnetic Actuation ◽  
Cost Weight ◽  
Shape Morphing ◽  
Self Assembling ◽  
Optimization Routine ◽  
Potential Use

Self-folding origami has the potential to be utilized in novel areas such as self-assembling robotics and shape-morphing structures. Important decisions in the development of such applications include the choice of active material and its placement on the origami model. With proper placement, the error between the actual and target shapes can be minimized along with cost, weight, and power requirements. Through the incorporation of dynamic models of self-folding origami mechanisms into an optimization routine, optimal orientations for magnetically-active material are identified that minimize error to specified target shapes. The dynamic models, created using Adams 2014, are refined by improvements to magnetic material simulation and more accurate joint stiffness characterization. Self-folding dynamic models of the waterbomb base and Shafer’s Frog Tongue are optimized, demonstrating the potential use of this process as a design tool for other self-folding origami mechanisms.

Mixed Mathematical and Physical Modeling for Nonlinear Systems

2005 ◽  
Author(s):  
Kiriakos Kiriakidis
Keyword(s):  
Linear Growth ◽  
Dynamic Models ◽  
Linear Models ◽  
Approximation Error ◽  
Basis Functions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Growth Bound ◽  
Nonlinear Dynamic Models ◽  
Mathematical And Physical Modeling

The paper proposes a finite series expansion to approximate general nonlinear dynamic models to arbitrary accuracy. The method produces an approximation of nonlinear dynamics in the form of an aggregation of linear models, weighted by unimodal basis functions, and results in a linear growth bound on the approximation error. Furthermore, the paper demonstrates that the proposed approximation satisfies the modeling assumptions for analysis based on linear matrix inequalities and hence widens the applicability of these techniques to the area of nonlinear control.

Magnetically Actuated Microplatform Scanners for Intravascular Ultrasound Imaging

2000 ◽  
Author(s):  
Carl W. Chang ◽  
Paul Lum ◽  
Richard S. Muller
Keyword(s):  
Magnetic Material ◽  
Silicon Nitride ◽  
Intravascular Ultrasound ◽  
Ultrasound Imaging ◽  
Present State ◽  
Lower Cost ◽  
State Of The Art ◽  
Deionized Water ◽  
Intravascular Ultrasound Imaging ◽  
Magnetically Actuated

Abstract We have fabricated a magnetically actuated microplatform scanner for use in a catheter-based intravascular ultrasound imaging (IVU) system. The torsional microplatform is fabricated from low stress silicon nitride with electroplated-Ni stripes for the magnetic material. Experiments with the microplatform have shown it capable of positioning an attached ultrasonic source (350 by 350 by 400 μm3 with a mass of 150 μg) through a total scan angle of 90°. The devices were evaluated in both air and immersed in deionized water. An IVU system based on this microplatform promises lower cost and greater flexibility than are provided by present state-of-the-art mechanically driven IVU systems.

Comparing model-based control methods for simultaneous stiffness and position control of inflatable soft robots

2020 ◽  
pp. 027836492091196
Author(s):  
Charles M. Best ◽  
Levi Rupert ◽  
Marc D. Killpack
Keyword(s):  
Dynamic Models ◽  
Position Control ◽  
Sliding Mode ◽  
Joint Stiffness ◽  
Variable Stiffness ◽  
Soft Robots ◽  
End Effector ◽  
Simultaneous Control ◽  
Stiffness Model ◽  
Stiffness Control

Inflatable robots are naturally lightweight and compliant, which may make them well suited for operating in unstructured environments or in close proximity to people. The inflatable joints used in this article consist of a strong fabric exterior that constrains two opposing compliant air bladders that generate torque (unlike McKibben actuators where pressure changes cause translation). This antagonistic structure allows the simultaneous control of position and stiffness. However, dynamic models of soft robots that allow variable stiffness control have not been well developed. In this work, a model that includes stiffness as a state variable is developed and validated. Using the stiffness model, a sliding mode controller and model predictive controller are developed to control stiffness and position simultaneously. For sliding mode control (SMC), the joint stiffness was controlled to within 0.07 Nm/rad of a 45 Nm/rad command. For model predictive control (MPC) the joint stiffness was controlled to within 0.045 Nm/rad of the same stiffness command. Both SMC and MPC were able to control to within 0.5° of a desired position at steady state. Stiffness control was extended to a multiple-degree-of-freedom soft robot using MPC. Controlling stiffness of a 4-DOF arm reduced the end-effector deflection by approximately 50% (from 17.9 to 12.2cm) with a 4 lb (1.8 kg) step input applied at the end effector when higher joint stiffness (40 Nm/rad) was used compared with low stiffness (30 Nm/rad). This work shows that the derived stiffness model can enable effective position and stiffness control.

Manufacturability-Oriented Ground Beam-Joint Topology Optimization for Multi-Piece Frame Structure Design

2007 ◽  
Author(s):  
Myung-Jin Kim ◽  
Gang-Won Jang ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Structural Modification ◽  
Joint Stiffness ◽  
Structure Design ◽  
Design Tool ◽  
Frame Structure ◽  
Structural Performance ◽  
Beam Model ◽  
Optimal Layout ◽  
Design Variables

Topology optimization is a useful design tool, but it often yields layouts difficult to manufacture without considerable post structural modification. As a result, its structural performance can be significantly deteriorated. To minimize the undesirable postprocessing, we aim to develop a manufacturability-oriented compliance-minimizing topology optimization using a ground beam model incorporating additional zero-length elastic joint elements. In the present formulation, design variables control the stiffness of zero-length elastic joints, not the stiffness of beams. Because joint stiffness values at the converged state can be utilized to select candidate assembly locations, the technique is extremely useful to design multi-piece frame structures. An optimal layout is also extracted based on the stiffness values. Because structural properties of ground beams can take only on discretely available values or remain unchanged for optimization process, no post structural modification is required in an actual manufacturing step.

Dynamic Modeling and Analysis of an Origami-Inspired Optical Shield for the Starshade Spacecraft

2016 ◽  
Author(s):  
Landen Bowen ◽  
Brian Trease ◽  
Mary Frecker ◽  
Timothy Simpson
Keyword(s):  
Dynamic Model ◽  
Dynamic Models ◽  
Joint Stiffness ◽  
Design Requirement ◽  
Deployable Structures ◽  
Design Decisions ◽  
Modeling And Analysis ◽  
Critical Design ◽  
Joint Forces ◽  
Shield Design

The Starshade is a future exoplanet discovery mission consisting of a satellite and a 34 meter diameter starshade used to block the light of a star of interest, enhancing visualization of the orbiting planets. The starshade itself is composed of a number of 7 meter long petals surrounding a 20 meter diameter optical shield. A critical design requirement of the optical shield is stowage in a 3 meter diameter area during launch. Origami has been investigated as a means of collapsing the optical shield, specifically a family of action origami models known as “flashers.” In this paper a dynamic model of an optical shield design candidate based on a flasher pattern is created in Adams 2014. As these patterns can have many parts and joints, a method for the automatic creation of dynamic models using information about the geometry of the crease pattern is utilized. As the fabricated optical shield panels will be somewhat flexible, each quadrilateral panel is modeled as two rigid triangles connected with a joint. The effect of joint stiffness on the forces and torques developed during deployment is investigated. It is found that the optical shield design is rigid foldable if the panel flexibility is taken into account by additional joints, which are found to bend from 10° – 40°. Joint forces are predicted over the deployment, and maximum and average joint forces are tabulated. These and other insights gained from the dynamic model can help guide future Starshade design decisions, and similar analyses can be performed for other origami-inspired deployable structures.

scholarly journals The discretization filter: A simple way to estimate nonlinear state space models

2021 ◽  
Vol 12 (1) ◽  
pp. 41-76 ◽  
Author(s):  
Leland E. Farmer
Keyword(s):  
Lower Bound ◽  
Interest Rates ◽  
State Space ◽  
Phillips Curve ◽  
Dynamic Models ◽  
Nonlinear Models ◽  
Approximation Error ◽  
State Space Models ◽  
Gaussian State ◽  
Zero Lower Bound

Existing methods for estimating nonlinear dynamic models are either highly computationally costly or rely on local approximations which often fail adequately to capture the nonlinear features of interest. I develop a new method, the discretization filter, for approximating the likelihood of nonlinear, non‐Gaussian state space models. I establish that the associated maximum likelihood estimator is strongly consistent, asymptotically normal, and asymptotically efficient. Through simulations, I show that the discretization filter is orders of magnitude faster than alternative nonlinear techniques for the same level of approximation error in low‐dimensional settings and I provide practical guidelines for applied researchers. It is my hope that the method's simplicity will make the quantitative study of nonlinear models easier for and more accessible to applied researchers. I apply my approach to estimate a New Keynesian model with a zero lower bound on the nominal interest rate. After accounting for the zero lower bound, I find that the slope of the Phillips Curve is 0.076, which is less than 1/3 of typical estimates from linearized models. This suggests a strong decoupling of inflation from the output gap and larger real effects of unanticipated changes in interest rates in post Great Recession.

A Framework for the Design and Optimization of Self-Folding Structures

2017 ◽  
Author(s):  
Landen Bowen ◽  
Mary Frecker ◽  
Timothy W. Simpson ◽  
Rebecca Strzelec
Keyword(s):  
Active Material ◽  
Optimization Methods ◽  
Design And Optimization ◽  
Simulation And Optimization ◽  
Optimization Framework ◽  
Simulation Based ◽  
Trade Space Exploration ◽  
Specific Implementation ◽  
Passive Materials ◽  
Novel Design

Due to the multidisciplinary nature and complexity of self folding structures, it can be difficult to know where to start when designing for a new application. Decisions about the active and passive materials to be used and the functionality of the design are very interrelated and can create problems if not considered holistically. There is a need to formalize the steps necessary to move from an origami-inspired shape to a full self-folding concept. In this paper, an optimization framework is proposed to help designers create self-folding, origami-inspired structures that can accommodate any type of active material. The optimization framework formalizes the design steps needed to move from a target shape/application to a self-folding design. The method is simulation-based, allowing a self-folding design candidate to be identified quickly prior to costly trial-and-error physical prototyping. A general version of the framework is presented that can accommodate a variety of simulation and optimization methods, after which a specific implementation of the framework utilizing a dynamic model and trade space exploration tools is discussed and then used to design a multi-field self-folding carton. By using the framework, a novel design was identified that both significantly decreased the folding error as well as the amount of active material used when compared to designs that would typically be attempted in a trial-by-error design approach. The demonstrated self-folding design optimization framework has the potential to streamline the design of self-folding structures, resulting in better designs with less time, effort, and cost.

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