Shannon Zirbel

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Papers by Shannon Zirbel

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

Journal of Mechanical Design, Jun 1, 2011

An underactuated or underconstrained compliant mechanism may have a determined equilibrium positi... more 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 mechanism’s 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 mechanism’s behavior is not adequately modeled using a 1-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.

Intervertebral disc degeneration alters lumbar spine segmental stiffness in all modes of loading under a compressive follower load

The Spine Journal, Sep 1, 2013

BACKGROUND CONTEXT: Previous studies have investigated the relationship between the degeneration ... more BACKGROUND CONTEXT: Previous studies have investigated the relationship between the degeneration grade of the intervertebral disc (IVD) and the flexibility of the functional spinal unit (FSU) but were completed at room temperature without the presence of a compressive follower load. This study builds on previous work by performing the testing under more physiological conditions of a compressive follower load at body temperature and at near 100% humidity. PURPOSE: The present work evaluates the effects of IVD degeneration on segmental stiffness, range of motion (ROM), hysteresis area, and normalized hysteresis (hysteresis area/ROM). This study also briefly evaluates the effect of the segment level, temperature, and follower load on the same parameters. STUDY DESIGN: In vitro human cadaveric biomechanical investigation. METHODS: Twenty-one FSUs were tested in the three primary modes of loading at both body temperature and room temperature in a near 100% humidity environment. A compressive follower load of 440 N was applied to simulate the physiological conditions. Fifteen of the 21 segments were also tested without the follower load to determine the effects of the follower load on segmental biomechanics. The grade of degeneration for each segment was determined using the Thompson scale, and the torque-rotation curves were fit with the Dual-Inflection-Point Boltzmann sigmoid curve. RESULTS: Intervertebral disc degeneration resulted in statistically significant changes in segmental stiffness, ROM, and hysteresis area in axial rotation (AR) and lateral bending (LB) and statistically significant changes in ROM and normalized hysteresis in flexion-extension (FE). The progression of these changes with increased degeneration is nonlinear, with changes in the FE and LB tending to respond in concert and opposite to the changes in AR. The lumbosacral joint was significantly stiffer and demonstrated a decreased ROM and hysteresis area as compared with other lumbar segments in AR and LB. Temperature had a significant effect on the stiffness and hysteresis area in AR and on the hysteresis area in LB. Application of a compressive follower load increased the stiffness in all three modes of loading but was significant only in AR and LB. It also reduced the ROM and increased normalized hysteresis in all three modes of loading. CONCLUSIONS: The results from this testing quantify the effects of degeneration on spinal biomechanics. Because the testing was conducted under physiological conditions (including a compressive follower load and at body temperature), we expect the measured response to closely match the in vivo response. The testing results can be used to guide the selection of appropriate surgical treatments in the context of IVD degeneration and to validate the mathematical and engineering models of the lumbar spine, including finite element models.

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Deployment Methods for an Origami-Inspired Rigid-Foldable Array

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

This paper describes a fully compliant constant-force micro-mechanism that enables dual-stage mot... more 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.

A Tristable Mechanism Configuration Employing Orthogonal Compliant Mechanisms

Journal of Mechanisms and Robotics, Nov 19, 2009

Tristable mechanisms, or devices with three distinct stable equilibrium positions, have promise f... more Tristable mechanisms, or devices with three distinct stable equilibrium positions, have promise for future applications, but the complexities of the tristable behavior have made it difficult to identify configurations that can achieve tristable behavior while meeting practical stress and fabrication constraints. This paper describes a new tristable configuration that employs orthogonally oriented compliant mechanisms that result in tristable mechanics that are readily visualized. The functional principles are described and design models are derived. Feasibility is conclusively demonstrated by the successful operation of four embodiments covering a range of size regimes, materials, and fabrication processes. Tested devices include an in-plane tristable macroscale mechanism, a tristable lamina emergent mechanism, a tristable micromechanism made using a carbon nanotube-based fabrication process, and a polycrystalline silicon micromechanism.

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A standardized representation of spinal quality of motion

Proceedings Of The Institution Of Mechanical Engineers, Part H: Journal Of Engineering In Medicine, Nov 1, 2014

The experimentally determined torque-rotation curve of the lumbar spine is mathematically describ... more 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, m1 and m2 indicate the inflection points of the curve where the stiffness changes markedly, and α1 and α2 are associated with the rates of change of the curve at m1 and m2, 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.

Ensemble repliable de panneaux tridimensionnels comprenant des composants électriques fonctionnels

Des modes de realisation de l'invention concernent un ensemble repliable de panneaux tridimen... more Des modes de realisation de l'invention concernent un ensemble repliable de panneaux tridimensionnels, qui peuvent comprendre un ou plusieurs composants electriques fonctionnels. Par exemple, l'ensemble a multiples panneaux tridimensionnels peut etre reconfigure d'une configuration sensiblement plane a une configuration tridimensionnelle.

Deployment Methods for an Origami-Inspired Rigid-Foldable Array

The design for the array was inspired by the origami flasher model (Lang, 1997; Shafer, 2001). Fi... more The design for the array was inspired by the origami flasher model (Lang, 1997; Shafer, 2001). Figure 1 shows the array prototyped from Garolite and Kapton film at the CubeSat scale. Prior work demonstrated that rigid panels like solar cells could successfully be folded into the final stowed configuration without requiring the panels to flex (Zirbel, Lang, Thomson, & al., 2013). The design of the array is novel and enables efficient use of space. The array can be wrapped around the central bus of the spacecraft in the case of the large array, or can accommodate storage of a small instrument payload in the case of the CubeSat array. The radial symmetry of this array around the spacecraft is ideally suited for spacecraft that need to spin.

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Characterization of the Mechanical Response of the Lumbar Spine

Characterization of the Mechanical Response of the Lumbar Spine Shannon A. Zirbel Department of M... more Characterization of the Mechanical Response of the Lumbar Spine Shannon A. Zirbel Department of Mechanical Engineering, BYU Master of Science The primary objective of this research is to associate lumbar segmental mechanical response with intervertebral disc degeneration under physiologic testing conditions. Because no mathematical model exists for lumbar spine segmental rotations, a portion of this thesis evaluates potential methods for curve fitting the torque-rotation curves. The Dual Inflection Point (DIP) Boltzmann equation was developed during the course of this research and is presented here as a method for fitting spinal motion data wherein a physical meaning can be assigned to each of the model coefficients. This model can tell us more about the effects of degeneration, testing conditions, and other factors that are expressed in the change in spinal motion. Previous studies have investigated the relationship between the degeneration grade and flexibility of the intervertebr...

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