Shannon A. Zirbel

Accommodating Thickness in Origami-Based Deployable Arrays

The purpose of this work is to create deployment systems with a large ratio of stowed-to-deployed diameter. Deployment from a compact form to a final flat state can be achieved through origami-inspired folding of panels. There are many models capable of this motion when folded in a material with negligible thickness; however, when the application requires the folding of thick, rigid panels, attention must be paid to the effect of material thickness not only on the final folded state, but also during the folding motion (i.e., the panels must not be required to flex to attain the final folded form). The objective is to develop new methods for deployment from a compact folded form to a large circular array (or other final form). This paper describes a mathematical model for modifying the pattern to accommodate material thickness in the context of the design, modeling, and testing of a deployable system inspired by an origami six-sided flasher model. The model is demonstrated in hardware as a 1/20th scale prototype of a deployable solar array for space applications. The resulting prototype has a ratio of stowed-to-deployed diameter of 9.2 (or 1.25 m deployed outer diameter to 0.136 m stowed outer diameter). INTRODUCTION The purpose of this work is to develop deployment systems that unfold from a compact form to a large array. This work ∗Corresponding author: lhowell@byu.edu is motivated by the need for compactly folded solar arrays for space applications. A large ratio of stowed-to-deployed diameter enables large solar arrays to be launched in their compact, folded configuration and then deployed in space to a much larger surface area. For our objectives, a design with synchronous deployment was desired to simplify actuation and deployment. Deployment from a compact form to a final flat state can be achieved through origami-inspired folding of panels. There are many models capable of this motion when folded in paper or other materials with negligible thickness; however, when the application requires the folding of thick, rigid panels, material thickness can inhibit the folding motion. To be rigid-foldable, the panels must not be required to flex to attain the final folded form. This paper describes the approach for modifying the design of an origami six-sided flasher model to accommodate material thickness. This work builds on existing models to present a unique design that is rigid-foldable through two different methods. In the first method, the panels are allowed to flex along their diagonals. In the second method, the panels are affixed to a flexible membrane with discrete gap spacing between the panels. Both folding solutions enable the model to be rigid-foldable.

A Tristable Mechanism Configuration Employing Orthogonal Compliant Mechanisms

ristable mechanisms, or devices with three distinct stable equiibrium positions, have promise for future applications, but the omplexities of the tristable behavior have made it difficult to dentify configurations that can achieve tristable behavior while eeting practical stress and fabrication constraints. This paper escribes a new tristable configuration that employs orthogonally riented compliant mechanisms that result in tristable mechanics hat are readily visualized. The functional principles are described nd design models are derived. Feasibility is conclusively demontrated by the successful operation of four embodiments covering range of size regimes, materials, and fabrication processes. ested devices include an in-plane tristable macroscale mechaism, a tristable lamina emergent mechanism, a tristable microechanism made using a carbon nanotube-based fabrication proess, and a polycrystalline silicon micromechanism. DOI: 10.1115/1.4000529

A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

An underactuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudorigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanisms vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for underactuated 1-DOF and 2-DOF pseudorigid-body models. Experimental force-deflection data are presented for a fully compliant constant-force mechanism. Because the mechanisms behavior is not adequately modeled using a I-DOF pseudorigid-body model, a 13-DOF pseudorigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with nonlinear finite element analysis and experimental force-displacement data.

Characterization and prediction of rate-dependent flexibility in lumbar spine biomechanics at room and body temperature

BACKGROUND CONTEXT The soft tissues of the spine exhibit sensitivity to strain-rate and temperature, yet current knowledge of spine biomechanics is derived from cadaveric testing conducted at room temperature at very slow, quasi-static rates. PURPOSE The primary objective of this study was to characterize the change in segmental flexibility of cadaveric lumbar spine segments with respect to multiple loading rates within the range of physiologic motion by using specimens at body or room temperature. The secondary objective was to develop a predictive model of spine flexibility across the voluntary range of loading rates. STUDY DESIGN This in vitro study examines rate- and temperature-dependent viscoelasticity of the human lumbar cadaveric spine. METHODS Repeated flexibility tests were performed on 21 lumbar function spinal units (FSUs) in flexion-extension with the use of 11 distinct voluntary loading rates at body or room temperature. Furthermore, six lumbar FSUs were loaded in axial rotation, flexion-extension, and lateral bending at both body and room temperature via a stepwise, quasi-static loading protocol. All FSUs were also loaded using a control loading test with a continuous-speed loading-rate of 1-deg/sec. The viscoelastic torque-rotation response for each spinal segment was recorded. A predictive model was developed to accurately estimate spine segment flexibility at any voluntary loading rate based on measured flexibility at a single loading rate. RESULTS Stepwise loading exhibited the greatest segmental range of motion (ROM) in all loading directions. As loading rate increased, segmental ROM decreased, whereas segmental stiffness and hysteresis both increased; however, the neutral zone remained constant. Continuous-speed tests showed that segmental stiffness and hysteresis are dependent variables to ROM at voluntary loading rates in flexion-extension. To predict the torque-rotation response at different loading rates, the model requires knowledge of the segmental flexibility at a single rate and specified temperature, and a scaling parameter. A Bland-Altman analysis showed high coefficients of determination for the predictive model. CONCLUSIONS The present work demonstrates significant changes in spine segment flexibility as a result of loading rate and testing temperature. Loading rate effects can be accounted for using the predictive model, which accurately estimated ROM, neutral zone, stiffness, and hysteresis within the range of voluntary motion.

Compliant Constant-Force Micro-Mechanism for Enabling Dual-Stage Motion

This paper describes a fully compliant constant-force micro-mechanism that enables dual-stage motion for nanoinjection. Nanoinjection is a recently developed process for delivering DNA into mouse zygotes via electrostatic accumulation and release of the DNA onto a microelectromechanical system (MEMS) lance.The fully compliant constant-force nanoinjector is a concatenation of two separate mechanisms: a six-bar mechanism with compliant lamina-emergent torsional (LET) joints to raise the lance, and a pair of constant-force crank-sliders with LET joints positioned on either side of the six-bar mechanism to drive the lance forward.The fully compliant nanoinjector exhibits self-reconfiguring metamorphic motion to first raise the lance to the midline of the zygote and then translate the lance forward with a controlled motion. This dual-stage motion is necessary for the lance to pierce the zygote without causing damage to the cell membrane.The device achieves two sequential displacement behaviors in a compliant mechanism fabricated from a single, continuous piece of material.Copyright

An Origami-Inspired Self-Deployable Array

The objective of this paper is to show the development of a compact, self-deploying array based on the tapered map fold. The tapered map fold was modified by applying an elastic membrane to one side of the array and adequately spacing the panels adjacent to valley folds. Through this approach, the array can be folded into a fully dense volume when stowed. The panels are dimensioned to account for the panel thickness when folded, which otherwise would prevent the model from reaching a fully dense form.The folding motion is achieved by creating a rigid-foldable model of the origami-inspired crease pattern. The paper discusses a variety of approaches for creating rigid origami from the map fold, including pleat hinges and spacer panels. The tapered map fold is rigid-foldable through the incorporation of tapered spacer panels. By choosing appropriate values for the angles and tapered spacer panel dimensions, the tapered map fold is fully dense when stowed. The tapered spacer panels also enable the model to have a single degree of freedom of actuation. Stored strain energy in the elastic membrane enables self-actuation of the model. Applying a membrane also simplifies fabrication of the array.Potential applications for the array include a collapsible solar array, or other military or backpacking applications.Copyright

Bistable Mechanisms for Space Applications

Compliant bistable mechanisms are monolithic devices with two stable equilibrium positions separated by an unstable equilibrium position. They show promise in space applications as nonexplosive release mechanisms in deployment systems, thereby eliminating friction and improving the reliability and precision of those mechanical devices. This paper presents both analytical and numerical models that are used to predict bistable behavior and can be used to create bistable mechanisms in materials not previously feasible for compliant mechanisms. Materials compatible with space applications are evaluated for use as bistable mechanisms and prototypes are fabricated in three different materials. Pin-puller and cutter release mechanisms are proposed as potential space applications.

HanaFlex: a large solar array for space applications

HanaFlex is a new method for deployment from a compact folded form to a large array derived from the origami flasher folding pattern. One of the unique features of this model is that the height constraints of the stowed array do not limit the deployed diameter. Additional rings can be added to increase the deployed diameter while only minimally increasing the stowed diameter. Larger solar arrays may enable longer missions in space, manned missions to distant destinations, or clean energy sources for Earth. The novel folding design of the HanaFlex array introduces many new possibilities for space exploration. This paper demonstrates the performance of the HanaFlex array in four areas: deployed stiffness, deployed strength, stowed volume specific power, and mass specific power.

A standardized representation of spinal quality of motion

The experimentally determined torque–rotation curve of the lumbar spine is mathematically described with a proposed dual-inflection point Boltzmann equation. The result is a method for describing functional spinal unit motion data. The benefit of the model is that each of the coefficients has a specific meaning in relation to the torque–rotation curve: the points A and B identify the respective minimum and maximum rotations of the functional spinal unit, m 1 and m 2 indicate the inflection points of the curve where the stiffness changes markedly, and α 1 and α 2 are associated with the rates of change of the curve at m 1 and m 2 , respectively. The dual-inflection point Boltzmann captures the full quality of motion of the spinal segment and can also be used to derive relevant parameters such as range of motion, midrange stiffness, and hysteresis.

Bi-Behavioral Prosthetic Knee Enabled by a Metamorphic Compliant Mechanism

Metamorphic mechanisms with two distinct behaviors were designed using compliant mechanism theory with a potential application as a prosthetic knee. The mechanism has discrete “locking” points to restrict rotation when under a compressive load. The designs use cross-axis flexural pivots, either in inversion or isolation, with engaging teeth to carry loads at distinct angles. Inverted compliant mechanisms function by inverting the mechanism so the compliant members are in tension when a compressive load is applied. Compliant mechanisms in isolation provide an alternative loading pattern which redirects the load to a passive rest. The mechanism incorporates teeth which engage during weight-bearing in flexion at up to 60° of flexion to lock the mechanism. When tension is applied to the device, the teeth are disengaged and the mechanism is allowed to rotate freely. The purpose of this design is to hold compressive loads both when un-flexed and flexed. The concept is applied in the preliminary design of a prosthetic knee joint. Proof-of-concept prototypes successfully demonstrate the metamorphic behavior.