Engineering Commons^™

A Personal Tribute To Professor Ashok Midha, Larry L. Howell

Faculty Publications

When I received the news that Professor Ashok Midha had passed away, I was grieved by the unexpected news. But I also felt another emotion: gratitude for having known him. I am grateful for him, for the opportunity I had to learn from him, and for the influence he has had on my life and career. I wanted to honor his memory in some way. This document is in response to that desire.

Some of my thoughts at his passing are summarized in the first chapter and the conclusion. The other writing is taken from a draft of my personal …

A Model For Multi-Input Mechanical Advantage In Origami-Based Mechanisms, Jared Butler, Adam Shrager, Timothy Simpson, Landen Bowen, Mary Frecker, Robert Lang, Eric Wilcox, Paris Von Lockette, Larry L. Howell, Spencer P. Magleby

Faculty Publications

Mechanical advantage is traditionally defined for single input and single-output rigid-body mechanisms. A generalized approach for identifying single-output mechanical advantage for a multiple-input compliant mechanism, such as many origami-based mechanisms, would prove useful in predicting complex mechanism behavior. While origami-based mechanisms are capable of offering unique solutions to engi neering problems, the design process of such mechanisms is complicated by the interaction of motion and forces. This paper presents a model of the mechanical advantage for multi input compliant mechanisms and explores how modifying the parameters of a model affects their behavior. The model is used to predict the force-deflection …

Large Deflection Analysis Of General Beams In Contact-Aided Compliant Mechanisms Using Chained Pseudo-Rigid-Body Model, Mohui Jin, Collin Ynchausti, Xianmin Zhang, Zhou Yang, Benliang Zhu, Larry L. Howell

Faculty Publications

The nonlinear analysis and design of contact-aided compliant mechanisms (CCMs) are challenging. This paper presents a nonlinear method for analyzing the deformation of general beams that contact rigid surfaces in CCMs. The large deflection of the general beam is modeled by using the chained pseudo-rigid-body model. A geometry constraint from the contact surface is developed to constrain the beam’s deformed configuration. The contact analysis problem is formulated based on the principle of minimum potential energy and solved using an optimization algorithm. Besides, a novel technique based on the principle of work and energy is proposed calculate the reaction force/moment of …

Deployable Convex Generalized Cylindrical Surfaces Using Torsional Joints, Todd G. Nelson, Jared T. Burton, Curtis G. Nelson, Luis M. Baldelomar Pinto, Zhicheng Deng, Larry L. Howell

Faculty Publications

The ability to deploy a planar surface to a desired convex profile with a simple actuation can enhance foldable or morphing airfoils, deployable antennae and reflectors, and other applications where a specific profile geometry is desired from a planar sheet. A model using a system of rigid links joined by torsional springs of tailorable stiffness is employed to create an approximate curved surface when two opposing tip loads are applied. A system of equations describing the shape of the surface during deployment is developed. The physical implementation of the model uses compliant torsion bars as the torsion springs. A multidimensional …

Rigidly Foldable Thick Origami Using Designed-Offset Linkages, Robert J. Lang, Nathan Brown, Brian Ignaut, Spencer P. Magleby, Larry L. Howell

Faculty Publications

We present new families of thick origami mechanisms that achieve rigid foldability and parallel stacking of panels in the flat-folded state using linkages for some or all of the hinges between panels. A degree-four vertex results in a multi-loop eight-bar spatial mechanism that can be analyzed as separate linkages. The individual linkages are designed so that they introduce offsets perpendicular to the panels that are mutually compatible around each vertex. This family of mechanisms offers the unique combination of a planar unfolded state, parallel-stacked panels in the flat folded state, and kinematic single-degree-of-freedom motion from the flat- unfolded to the …

Membrane-Enhanced Lamina Emergent Torsional Joints For Surrogate Folds, Guimin Chen, Spencer P. Magleby, Larry L. Howell

Faculty Publications

Lamina emergent compliant mechanisms (including origami-adapted compliant mechanisms) are mechanical devices that can be fabricated from a planar material (a lamina) and have motion that emerges out of the fabrication plane. Lamina emergent compliant mechanisms often exhibit undesirable parasitic motions due to the planar fabrication constraint. This work introduces a type of lamina emergent torsion (LET) joint that reduces parasitic motions of lamina emergent mechanisms (LEMs), and presents equations for modeling parasitic motion of LET joints. The membrane joint also makes possible one-way joints that can ensure origami-based mechanisms emerge from their flat state (a change point) into the desired …

Kinetostatic And Dynamic Modeling Of Flexure-Based Compliant Mechanisms: A Survey, Mingxiang Ling, Larry L. Howell, Junyi Cao, Guimin Chen

Faculty Publications

Flexure-based compliant mechanisms are becoming increasingly promising in precision engineering, robotics and other applications due to the excellent advantages of no friction, no backlash, no wear, and minimal requirement of assembly. Because compliant mechanisms have inherent coupling of kinematic- mechanical behaviors with large deflections and/or complex serial-parallel configurations, the kinetostatic and dynamic analyses are challenging in comparison to their rigid-body counterparts. To address these challenges, a variety of techniques have been reported in a growing stream of publications. This paper surveys and compares the conceptual ideas, key advances, applicable scopes and open problems of the state-of-the-art kinetostatic and dynamic modeling …

Load-Displacement Characterization In Three Degrees Of Freedom For General Let Arrays, Nathan A. Pehrson, Pietro Bilancia, Spencer P. Magleby, Larry L. Howell

Faculty Publications

Lamina emergent torsion (LET) joints for use in origami-based applications enables folding of panels. Placing LET joints in series and parallel (formulating LET arrays) opens the design space to provide for tunable stiffness characteristics in other directions while maintaining the ability to fold. Analytical equations characterizing the elastic load-displacement for general serial-parallel formulations of LET arrays for three degrees of freedom are presented: rotation about the desired axis, in-plane rotation, and extension/compression. These equations enable the design of LET arrays for a variety of applications, including origami-based mechanisms. These general equations are verified using finite element analysis and, to show …

Limits Of Extramobile And Intramobile Motion Of Cylindrical Developable Mechanisms, Jared Butler, Larry L. Howell, Spencer P. Magleby, Jacob Greenwood

Faculty Publications

Mechanisms that can both deploy and provide motions to perform desired tasks offer a multifunctional advantage over traditional mechanisms. Developable mechanisms (DMs) are devices capable of conforming to a predetermined developable surface and deploying from that surface to achieve specific motions. This paper builds on the previously identified behaviors of extramobility and intramobility by introducing the terminology of extramobile and intramobile motion, which define the motion of developable mechanisms while interior and exterior to a developable surface. The limits of motion are identified using defined conditions. It is shown that the more difficult of these conditions to kinematically predict may …

Analysis Of The Rigid Motion Of A Conical Developable Mechanism, Mckell Woodland, Michelle Hsiung, Erin L. Matheson, C Alex Safsten, Jacob Greenwood, Denise M. Halverson, Larry L. Howell

Faculty Publications

We demonstrate analytically that it is possible to construct a developable mechanism on a cone that has rigid motion. We solve for the paths of rigid motion and analyze the properties of this motion. In particular, we provide an analytical method for predicting the behavior of the mechanism with respect to the conical surface. Moreover, we observe that the conical developable mechanisms specified in this paper have motion paths that necessarily contain bifurcation points which lead to an unbounded array of motion paths in the parameterization plane.

Conceptualizing Stable States In Origami-Based Devices Using An Energy Visualization Approach, Jacob Greenwood, Larry L. Howell, Alex Avila, Spencer P. Magleby

Faculty Publications

In many origami-based applications, a device needs to be maintained in one or more fold states. The origami stability integration method (OSIM) presented in this paper pro- vides an approach for graphically combining various techniques to achieve stability. Existing stability techniques are also categorized into four groups based on whether they are intrinsic or extrinsic to the origami pattern and whether they exhibit gradual or non-gradual energy storage behaviors. These categorizations can help designers select appropriate techniques for their applications. The paper also contains de- sign considerations and resources for achieving stability. Finally, two case studies are presented that use …

Membrane-Enhanced Lamina Emergent Torsional Joints For Surrogate Folds, Guimin Chen, Spencer P. Magleby, Larry L. Howell

Faculty Publications

Lamina emergent compliant mechanisms (including origami-adapted compliant mechanisms) are me- chanical devices that can be fabricated from a planar material (a lamina) and have motion that emerges out of the fabrication plane. Lamina emergent compliant mechanisms often exhibit undesirable para- sitic motions due to the planar fabrication constraint. This work introduces a type of lamina emergent torsion (LET) joint that reduces parasitic motions of lamina emergent mechanisms (LEMs), and presents equations for modeling parasitic motion of LET joints. The membrane joint also makes possible one-way joints that can ensure origami-based mechanisms emerge from their flat state (a change point) into …

Regional Stiffness Reduction Using Lamina Emergent Torsional Joints For Flexible Printed Circuit Board Design, Bryce P. Defigueiredo, Brian Dale Russell, Trent K. Zimmerman, Larry L. Howell

Faculty Publications

Flexible printed circuit boards (PCBs) make it possi- ble for engineers to design devices that use space efficiently

and can undergo changes in shape and configuration. How- ever, they also suffer from trade-offs due to non-ideal mate- rial properties. Here, a method is presented that allows en- gineers to introduce regions of flexibility in otherwise rigid

PCB substrates. This method employs geometric features to reduce local stiffness in the PCB, rather than reducing

the global stiffness by material selection. Analytical and fi- nite element models are presented to calculate the maximum

stresses caused by deflection. An example device is produced …

Origami-Based Design Of Conceal-And-Reveal Systems, Bryce P. Defigueiredo, Kyler A. Tolman, Spencer P. Magleby, Nathan A. Pehrson, Erica Crampton, Larry L. Howell

Faculty Publications

This work introduces a type of motion termed “conceal-and-reveal” which is characterized by a state that protects a payload, a state that exposes the payload, and coupled motions between these two states. As techniques for thick, rigid origami-based engineering designs are being developed, origami is becoming increasingly more

attractive as inspiration for complex systems. This paper proposes a process for designing origami-based conceal- and-reveal systems, which can be generalized to design similar thick, rigid origami-based systems. The process

is demonstrated through the development of three conceal-and-reveal systems that present a luxury product to the consumer. The three designs also confirm …

Origami-Inspired Sacrificial Joints For Folding Compliant Mechanisms, Todd G. Nelson, Alex Avila, Larry L. Howell, Just L. Herder, Davood Farhadi Machekposhtic

Faculty Publications

Folding is a manufacturing method which can create complex 3D geometries from flat materi- als and can be particularly useful in cost-sensitive or planar-limited fabrication applications.

This paper introduces compliant mechanisms that employ folding techniques from origami to evolve from a flat material to deployed state. We present origami-inspired sacrificial joints, joints which have mobility during assembly of the mechanism but are rigid in their final position, to create regions of high and low stiffness and the proper alignment of compliant flexures in folded mechanisms. To demonstrate the method we fold steel sheet to create some well-known and complex compliant …

Normalized Coordinate Equations And Energy Method For Predicting Natural Curved-Fold Configurations, Jacob Badger, Todd G. Nelson, Rober J. Lang, Denise M. Halverson, Larry L. Howell

Faculty Publications

Of the many valid configurations that a curved fold may assume, it is of particular interest to identify natural—or lowest energy—configurations that physical models will preferentially assume. We present normalized coordinate equations—equations that relate fold surface properties

to their edge of regression—to simplify curved-fold rela- tionships. An energy method based on these normalized

coordinate equations is developed to identify natural con- figurations of general curved folds. While it has been noted

that natural configurations have nearly planar creases for curved folds, we show that non-planar behavior near the crease ends substantially reduces the energy of a fold.

A Pseudo-Static Model For Dynamic Analysis On Frequency Domain Of Distributed Compliant Mechanisms, Mingxiang Ling, Larry L. Howell, June Cao, Zhou Jiang

Faculty Publications

This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency-dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo- static model. The superiority of the proposed method is that when it is used for the dynamic modeling …