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.
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. vi Table of Contents. vii List of Tables. x List of Figures.
xi List of Abbreviations. xv List of Symbols. Ankle foot orthosis. Passive ankle foot orthosis.
Active ankle foot orthosis. Shape memory alloys. SMA phase diagram and transformation. Shape memory effect.
Stiffness variation property. Gait cycle and its phases. Gait parameters and analysis techniques. Ankle stiffness behavior.
Ankle range of motion. Multi-axial loading of ankle-foot complex during the gait. Design of a passive AFO with a one-sided SMA hinge. SMA hinge desing.
Sagittal plane simulation. Multi-axial loading simulation. Investigations of active AFO concepts based on an adaptive SMA element. Adjustable compliance concept.
Mechanical adjustment design. Structural adjustment design. Modeling and simulation. Results and discussion.
Finite element analysis for the passive one-sided hinge. Stiffness behavior evaluation for active SMA element. Conclusions and future works. 98 ix List of Tables 2.1: Summary of austenite elastic modulus EA and martensite elastic modulus EM reported in literatures [41, 48] .1: Material properties for the superelastic SMA hinge [41].2: Four-step loading-unloading rotation of the ankle.3: Simplified resultant rotation of two phases.4: Critical conditions in the 3D loading.1: Dimensions of tubes in telescopic tube configuration.2: Optimized dimension of the adjustable SMA hinge.1: Material properties for the SMA rod [41] .2: Parameters to control uni-axial loading.
90 x List of Figures 1-1: Passive thermoplastic AFOs [17]. 4 1-2: Tamarack Flexure Joint for thermoplastic and carbon laminate bracing [18]. 5 1-3: Passive hybrid AFOs [19, 20]. 6 1-4: University of Toledo SMA AFO device with superelastic wires [10, 21].
9 2-1: Stress-temperature-transformation plot of a shape memory material [41]. 18 2-2: Shape memory effect temperature-load phase diagram [43, 44]. 19 2-3: Shape memory effect in 3D stress–strain-temperature space [42]. 20 2-4: Stress-temperature diagram for pseudo-elastic effect [42].
21 2-5: Peudoelastic effect stress-strain diagram [45]. 22 2-6: Stress-strain diagram shows stiffness variation. 24 3-1: Human gait cycle and phases [49]. 25 3-2: Segmented cycle diagram of human gait main events and phases [50].
27 3-3: Reference planes of the human body in the standard anatomical position [50]. 28 3-4: Step length and stride length in the walking. 29 3-5: Ankle stiffness behavior for slow, normal and fast speeds of gait [55]. 31 3-6: Rotation-moment ankle behavior for a healthy foot in normal condition.
32 3-7: Ankle stiffness variation both dorsi-flexion (DF) and plantar-flexion (PF) during stance phase [57]. 33 xi 3-8: Ankle torque vs. rotation for fast walking speed in swing phase of the gait. 34 3-9: Ankle torque vs.
rotation for normal walking speed in swing phase. 35 3-10: Ankle torque vs. rotation for slow walking speed in swing phase. 35 3-11: Comparisons of the 2nd order polynomial ankle stiffness in various speeds.
36 3-12: Body advancement due to the heel, ankle and forefoot rockers used [59]. 37 3-13: Ankle range of motion during a gait cycle. 39 3-14: Ankle rotation for a drop foot subject with hinged/non-hinged AFOs [10]. 40 3-15: Foot subjected to the mlti-axial loading [50].
41 3-16: The 3D ground reaction forces as a function of time [50]. 42 3-17: Foot pressure patterns and CoP path for left and right side foots [65]. 43 3-18: Center of pressure pattern for normal and neuropathic subjects [66]. 44 3-19: The GRF components over the entire stance phase for a representative subject walking at normal speed [67].
45 3-20: The cop displacements in anterior-posterior direction and medial-lateral direction over the entire stance phase for a representative subject walking at normal speed [67]. 46 4-1: The superelastic hinge stores and releases energy during the gait. 48 4-2: CAD image of the one-sided SMA hinge AFO. 49 4-3: SolidWorks CAD image of the hinge element.
50 4-4: Main ankle rotation happens in sagittal plane [50, 68]. 52 4-5: Ankle rotation profile for four-step and two-step loading-unloading behavior. 53 4-6: Stiffness profile of the ankle for the normal condition in swing phase. 54 4-7: The hinge deformation shape in uni-axial loading in the sagittal plane.
55 4-8: 3D Ground reaction forces at the hinge position. 56 xii 4-9: CoP distance variations with respect to the hinge position. 56 4-10: Resultant applied moments in the transverse plane. 57 4-11: Resultant applied moments in the frontal plane.
57 4-12: Loading condition and CoP location at the 1st critical point. 59 4-13: Loading and CoP at the 2nd and 3rd critical points. 59 4-14: Loading and CoP at the 4th critical point. 60 4-15: The hinge deflections in frontal and transverse planes after deformation.
60 4-16: Optimized dimensions of the SMA hinge element. 62 4-17: Appointed position of the hinge after optimization [68]. 63 4-18: Hinge element meshing with two different qualities. 64 5-1: Actuation mechanism embodiment.
67 5-2: 4-Step multi-axial loading conditions. 69 5-3: Modeled 4-link transmission mechanism in ADAMS. 70 5-4: Bending moment for the deflection of the beam [74]. 70 5-5: Torsional moment for the tube element [75].
71 5-6: Telescopic concept actuation mechanism. 72 5-7: Telescopic tubes configuration. 73 5-8: Tubes engagement/disengagement mechanism. 74 5-9: Adjustable hinge activation concept.
75 5-10: Adjustable hinge CAD design. 76 6-1: Rotation-Moment profile for SMA hinge simulation in sagittal plane for 2-step loading in comparison with experimental ankle stiffness in the swing. 80 xiii 6-2: Rotation-Moment profile for SMA hinge simulation in sagittal plane for 4-step loading in comparison with experimental ankle stiffness in the swing. 81 6-3: Stress and strain distribution for the deformed shape of the hinge.
82 6-4: Stress and strain profile for four nodes at a critical element of the hinge (element in the edge of the sides) in 2-step loading. 83 6-5: Stress and strain profile for four nodes at a critical element of the hinge (element in the edge of the sides) in 4-step loading. 84 6-6: The 3D deflection profiles at four critical points during stance phase of the gait. 86 6-7: Stress distributions and strain vector plot for the deformed shape of the hinge.
88 6-8: Actuator loading parameters: pre-tension vs. steps and PAR. 90 6-9: Element stiffness from simulation results for SMA rod underlying of multi-axial loading in comparison with experimental ankle in normal, slow and fast walking. 91 6-10: Element stiffness from simulation results for SMA telescopic tubes in comparison with experimental ankle in normal, slow and fast walking.
92 6-11: Element stiffness from simulation results for SMA telescopic tubes in comparison with experimental ankle in normal, slow and fast walking. 93 6-12: Hinge stiffness vs. 94 xiv List of Abbreviations 2D .Three dimensional AFO. Ankle foot orthosis CoP.
Center of pressure DACS. Dorsiflexion assist controlled by spring DF. Dorsi-flexion EMG .Finite Element Analysis GRF. Ground reaction force NiTi .Nickel-Titanium PAR.
Portion of axial recovery PF.Plantar-flexion PPAFO. Portable powered ankle foot orthosis SEA .Series elastic actuator SMA. Shape memory alloy UMAT .User Material xv List of Symbols .Cauchy stress tensor Ms .Martensite start transformation stress Mf .Martensite finish transformation stress As. Austenite start transformation stress Af .Austenite finish transformation stress ε .Total strain tensor T.
Martensitic volume fraction EM .