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Microsoft Word ThesisMorteza A Thesis entitled Design and Simulation of a Single Hinge and Adaptive Ankle Foot Orthoses Based on Superelasticity of Shape Memory Alloys by Morteza Gorzin Mataee Submitt[.]
A Thesis entitled Design and Simulation of a Single-Hinge and Adaptive Ankle Foot Orthoses Based on Superelasticity of Shape Memory Alloys by Morteza Gorzin Mataee Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering _ Dr Mohammad Elahinia, Committee Chair _ Dr Lesley Berhan, Committee Member _ Dr Mohamed Samir Hefzy, Committee Member _ Dr Patricia R Komuniecki, Dean College of Graduate Studies The University of Toledo December 2013 Copyright 2013, Morteza Gorzin Mataee This document is copyrighted material Under copyright law, no parts of this document may be reproduced without the expressed permission of the author An Abstract of Design and Simulation of a Single-Hinge and Adaptive Ankle Foot Orthoses Based on Superelasticity of Shape Memory Alloys by Morteza Gorzin Mataee Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering The University of Toledo December 2013 The goal of this thesis is to propose and develop new designs of Ankle Foot Orthosis (AFO) based on superelastic characteristics of shape memory alloys (SMAs) The problem investigated in this research is a human gait abnormality called drop foot caused by the paralysis of the muscles which allow the ankle to dorsiflex This neuromuscular disorder results in foot slap after heel strike and toe drag during leg swing As the most common solution, drop foot patients use an orthotic device called AFO add support and improve their gait However, development of a more compact assistive device, which could passively or actively secure the normal gait requirements, is still a need by both patients and clinicians Based on investigations and experimentations performed in Dynamic and Smart Systems Laboratory at University of Toledo, SMA is a potential solution due to its unique stiffness behavior and hysteretic characteristics In this work superelastic characteristics of SMAs is considered as an enabler in the development of new generation of AFOs iii Within this work a passive AFO design is proposed which employs a superelastic SMA element as the hinge of the device This SMA hinge controls the ankle motion by storing and releasing energy during walking The superelastic element enables the AFO to provide sufficient torque during dorsiflexion to raise the foot in the swing phase of the gait In order to evaluate the design performance a comprehensive gait analysis study is performed to extract the requirements of motion, understand the critical loads, and calibrate the desired stiffness profiles for the ankle and the superelastic element A Finite Element Analysis is performed to realize an optimum design for the SMA hinge Preliminary simulations are carried out in the sagittal plane of the body to verify the functionality of the design in providing the motion requirements Unlike existing AFOs with two hinges, the proposed design uses only one hinge The multi-axial loading of the ground reaction in 3D is then simulated to estimate lateral response of the hinge in preventing hypermobility and securing the walking stability. To maintain stability the hinge should limit the motion in directions other than rotation in the sagittal plane In addition to this passive hinge, superelastic SMA is also envisioned to realize an active AFO To this end, an active superelastic SMA element which is adjusted structurally and dynamically is used to reproduce the stiffness variation of a healthy ankle This concept could produce a controlled stiffness profile desired for different walking conditions such as various speeds Actuation mechanism design for this concept is also discussed iv Although, the major contribution of this study is developing a reliable passive AFO design, experimental and numerical analyses confirm the functionality of both passive and active SMA AFOs v Acknowledgements I would like to express my gratitude to my advisor, Dr Mohammad Elahinia, for his understanding, encouraging and personal guidance in this research and throughout my studies at University of Toledo Without his guidance and persistent help this research would not have been possible. In addition, I would like to thank my committee members Dr Berhan and Dr Hefzy, for the useful comments, directions and engagement to complete this master thesis I also thank to all my lab mates at the Dynamic and Smart System Lab, who provided me support, motivation and wishes for the successful completion of this project I would like to thank especially to Reza Mehrabi for his incredible help to me and sharing the knowledge during this work Finally, I would like to express my heartfelt thanks to my parents for their blessings and emotional support throughout my life vi Table of Contents Abstract iii Acknowledgements vi Table of Contents vii List of Tables x List of Figures xi List of Abbreviations xv List of Symbols xvi Introduction 1.1 Ankle foot orthosis 2 1.1.1 Passive ankle foot orthosis 3 1.1.2 Active ankle foot orthosis 1.2 Problem statement 10 1.3 Objective 11 1.4 Approach 12 1.5 Contributions 13 vii 1.6 Outline 14 1.7 Publications 15 Shape memory alloys 16 2.1 SMA phase diagram and transformation 17 2.2 Shape memory effect 18 2.3 Superelasticity 20 2.4 Stiffness variation property 22 Gait analysis 25 3.1 Gait cycle and its phases 25 3.2 Gait parameters and analysis techniques 27 3.3 Ankle stiffness behavior 30 3.4 Ankle range of motion 36 3.5 Multi-axial loading of ankle-foot complex during the gait 40 Design of a passive AFO with a one-sided SMA hinge 47 4.1 Concept development 47 4.2 SMA hinge desing 49 4.3 Sagittal plane simulation 51 4.4 Multi-axial loading simulation 55 4.5 Design optimization 61 4.6 Mesh study 63 Investigations of active AFO concepts based on an adaptive SMA element 65 viii 5.1 Adjustable compliance concept 65 5.2 Actuation mechanism 67 5.3 Mechanical adjustment design 68 5.4 Structural adjustment design 70 5.5 Modeling and simulation 76 Results and discussion 79 6.1 Finite element analysis for the passive one-sided hinge 79 6.2 Stiffness behavior evaluation for active SMA element 88 Conclusions and future works 95 6.1 Conclusions 95 6.2 Future works 96 References 98 ix List of Tables 2.1: Summary of austenite elastic modulus EA and martensite elastic modulus EM reported in literatures [41, 48] 23 4.1: Material properties for the superelastic SMA hinge [41] 51 4.2: Four-step loading-unloading rotation of the ankle 53 4.3: Simplified resultant rotation of two phases 53 4.4: Critical conditions in the 3D loading 58 5.1: Dimensions of tubes in telescopic tube configuration 73 5.2: Optimized dimension of the adjustable SMA hinge 75 6.1: Material properties for the SMA rod [41] 89 6.2: Parameters to control uni-axial loading 90 x stiffer behavior desired for slow walking speed is achievable by simultaneously decreasing the portion of axial recovery and pre-tension Multi‐Axial Loading of Superelastic SMA Rod with Adjustment of Axial Loading Parameters 23000 Torque (N.m) 18000 13000 Element Stiffness (Slow) Element Stiffness (Normal) Element Stiffness (Fast) Ankle Stiffness (Slow) Ankle Stiffness (Normal) Ankle Stiffness (Fast) 8000 3000 ‐2000 10 Rotation (degree) 12 14 16 Figure 6-9: Element stiffness from simulation results for SMA rod undergoing of multiaxial loading in comparison with experimental ankle in normal, slow and fast walking Simulation for structurally controlling stiffness approach (engaging and disengaging the tubes in the telescopic concept): Three different SMA tubes with the aforementioned dimensions are connected to each other As was discussed in Section 5.4 regarding the design, a linear actuator engages and disengages the tubes while changing the active length and thickness of the whole system This provides different stiffness profiles The material properties are the same as the superelastic rod presented in Table 6.1 The simulation was performed at a temperature of 293 K Simulation results are presented in Figure 6-10, which are compared to the experimental ankle stiffness data in swing From this investigation, it is 91 observed that by engaging only tube 1, stiffness of the system is very close to the ankle stiffness in slow walking Engaging both tube and produces a stiffness profile very similar to the ankle stiffness in the normal speed of the gait as shown in the graph below To mimic the ankle stiffness for fast walking, all three tubes should be engaged The optimized dimensions of all three tubes were presented in Table 5.1 of Section 5.4 Stiffness Adjustment for Telescopic Superelastic SMA Tubes 23000 Torque (N.m) 18000 13000 Element Stiffness (Tube 1) Element Stiffness (Combination of Tube 1 & 2) Element Stiffness (Combination of Tube 1 & 2 & 3) Ankle Stiffness (Slow) Ankle Stiffness (Normal) Ankle Stiffness (Fast) 8000 3000 ‐2000 10 Rotation (Degree) 12 14 16 Figure 6-10: Element stiffness from simulation results for SMA telescopic tubes in comparison with experimental ankle in normal, slow, and fast walking Simulation of structurally controlling stiffness approach (adjusting active length of the SMA hinge): For the adjustable hinge concept as discussed previously in Section 5.4, the fixed end of the element along its main length is controlled by the provided movement of the slider through a linear actuator This modulates the active length of the element and 92 determines the stiffness profile of the element For three different lengths, dimensions of the hinge are optimized to provide the desired stiffness profile for these three various speeds of walking Optimized dimensions were previously presented in Table 5.2 Figure 6-11 shows the simulation results compared to the real stiffness profiles of the ankle To follow the ankle stiffness in slow walking, the length of the hinge is fixed at the end of 55 mm, so that the element exhibits stiff behavior In order to mimic the stiffness profile of normal walking, it is fixed to a length of 35 mm Finally, for fast speed, the element is fixed at 20 mm in order to show a soft behavior This investigation indicates that the lower stiffness curves cover fast gait speeds occurring within the higher percentile of element length, and that higher stiffness curves cover slow gait speeds occurring within the lower percentile of element length Stiffness Adjustment for the Superelastic SMA Hinge Controlling the Active Lenght of the Element 23000 Torque (N.m) 18000 Element Stiffness (Fixed End of 55mm) Element Stiffness (Fixed End of 35mm) Element Stiffness (Fixed End of 20mm) Ankle Stiffness (Slow) Ankle Stiffness (Normal) Ankle Stiffness (Fast) 13000 8000 3000 ‐2000 10 Rotation (degree) 15 Figure 6-11: Element stiffness from simulation results for SMA telescopic tubes in comparison with experimental ankle in normal, slow, and fast walking 93 The variable stiffness behavior of the superelastic hinge is extended for a wider range of active length to obtain a profile in order to determine the stiffness as a function of slider position, indicating the element active length This profile is shown in Figure 612 Stiffness vs. Slider Position (Element Active Lenght) 80000 57 70000 60000 50000 55 40000 50 30000 20000 40 10000 30 20 10 0 10 20 30 40 50 60 Figure 6-12: Hinge stiffness vs slider position (active length of the hinge) From the curve-fitting of the stiffness profile of the hinge with degree polynomial and degree polynomial, the following functions are achieved Equations 6.1 and 6.2 define a numerical relationship between stiffness and active length of the element Curve fitted with degree polynomial: F s, 2s3 140s2 3455s 17745 (6.1) Curve fitted with degree polynomial: F s, s5 21s4 461s3 5023s2 21289s 94 (6.2) Chapter Conclusions and future work 7.1 Conclusions The capability of shape memory alloys as passive or active controllable elements implemented in ankle foot orthoses is investigated in this thesis It is demonstrated that the superelastic characteristic of SMAs provides a promising actuation technique for a new generation of lightweight and portable orthoses A novel design of an articulated passive AFO with one-sided superelastic SMA hinge is proposed in this work Based on the detailed gait analysis study in both regular plane of motion (sagittal plane) and lateral planes (fontal and transverse planes), a 3D loading pattern is extracted for the SMA hinge during the whole gait cycle For the SMA hinge, a FEA was carried out in ABAQUS for different loading conditions By performing a uni-axial loading simulation in the plane of motion, stiffness and torque requirements of the ankle joint were satisfied as the main design parameters of the application Lateral behavior was also evaluated by finding lateral components of the ground reaction forces and moments, and exerting these multi-axial loads to the element Numerical simulations showed that the one-sided hinge design, besides providing flexibility for the desired motion, prevents deflections and hypermobility, and therefore 95 secure the stability of walking Based on critical point evaluation during an optimization process, the hinge dimensions and position were tuned Within the scope of this research, an investigation for active mechanism of AFO based on superelastic characteristics of SMA was carried out Three potential techniques were introduced based on mechanically and structurally stiffness control of SMA element as the active component Mechanical adjustment was achieved through applying specific arrangements of axial-torsional loads to a SMA rod Two variables (pre-tension and portion of axial recovery) are defined in the model for controlling the axial load input exerted by a linear actuator To control the stiffness by structural adjustment, two different designs were developed In the first design, a telescopic concept consisting of three adjustable tubes was investigated, in which the stiffness of the configuration is subjected to change via a linear actuator by engaging and disengaging the tubes In the second design, an adjustable hinge was presented By modulating the active length of the hinge, resultant bending stiffness was controlled After designing the active element, a numerical study was performed for investigation of the stiffness behavior according to the ankle experimental data in three different speeds Simulations confirmed that the desired stiffness profile of the ankle in various walking conditions are achievable through intended designs 7.2 Future work In continuing this work the next step could be fabrication of the designed passive hinge based on proposed geometry and material properties However, further material properties study is recommended before the fabrication process Afterwards, testing 96 operation on the fabricated element for both uni-axial and multi-axial loading, according to the calculated loading conditions in the context of this thesis, is suggested After establishing the test setup, available commercial hinges may be tested and compared to the SMA hinge For this, a particular test procedure needs to be developed based on specific requirements of the application Implementation 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