今對於單腳膝上截肢者，腿義肢之設計需求，為能夠模仿人類健康腿走路，以及，行走速度可自然隨著截肢者進行改變。故本文目的將使用特定方法為磁流變流之膝義肢，利用電壓的輸入進行控制，研究中將使用RecurDyn進行膝上義肢腿之動態模擬分析，並搭配Matlab/Simulink進行控制器設計，當中縮短開發時間並取得有效的控制器與參數分析。本文使用半主動控制器，可使膝上義肢腿行走時，有效的使其操作響應時間短、耗能低、流變效果顯著，且在行走中可改善膝上義肢系統之性能並達到省力之目的。

For the above knee amputee, the demand to design prosthetic leg, that can imitate walking to the sound legs and its walking speed can be changed naturally base on the amputee's walking speed. The purpose is to use the voltage to control magnetorheological fluid (MRF) damper of the Above-Knee (AK) prosthesis. In this thesis, RecurDyn is used to carry out the dynamic simulation analysis of the knee prosthesis and the controller is designed by MATLAB/Simulink. They reduce the period of time of developing a satisfactory controller and make the effective parameter analysis in this thesis.Using semi-active controller can get the fast response time, low energy dissipation, outstanding rheological effect,
and improve the performance of AK prosthesis system when AK prosthesis is walking.It can achieve the purpose that make the amputee walking easily.

Contents
Acknowledgement                                                             i
Chinese Abstract                                                           ii
Abstract                                                                  iii
Nomenclature                                                               iv
1 Introduction                                                              1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . .   2
2 The Above Knee Prosthesis System Using Magnetorheological
   Damper                                                                   4
2.1 The AK Prosthesis Model . . . . . . . . . . . . . . . . . . . . . . .   4
2.1.1 Simplified Model of Human Lower Limb by Fixed Ankle . . . . . . . .   4
2.1.2 The Artificial Knee Joint Type of the AK Prosthesis . . . . . . . .   7
2.2 MR Fluids and Dampers . . . . . . . . . . . . . . . . . . . . . . . .   8
2.2.1 MR Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   8
2.2.2 MR Dampers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  9
2.2.3 Mechanical Model Formulation of MR Damper . . . . . . . . . . . . .  10
2.3 Human Walk . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   12
2.3.1 Terminology Used in Gait Analysis . . . . . . . . . . . . . . . . .  13
2.3.2 Hip Trajectory of Progression . . . . . . . . . . . . . . . . . . .  15
2.3.3 Thigh Motion . . . . . . . . . . . . . . . . . . . . . . . . . . .   16
2.3.4 Knee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Dynamic Model of the Above Knee Prosthesis System Using
  Magnetorheological Damper                                                18
3.1 The AK Prosthesis System in RecurDyn . . . . . . . . . . . . . . . .   18
3.2 MR Damper Subsystem in RecurDyn . . . . . . . . . . . . . . . . . . .  21
3.2.1 The Position of MR Damper in AK Prosthesis . . . . . . . . . . . .   22
4 Semi-active Control Algorithm for the MR Dampers  . . . . . . . . . . .  25
4.1 Heaviside Function Method . . . . . . . . . . . . . . . . . . . . . .  26
4.2 The Modified Version of Heaviside Function Method . . . . . . . . . .  27
5 Numerical Examples                                                       29
6 Conclusion                                                               39
A Equations of System Model                                                40
Bibliography                                                               47

List of Tables
2.1 Typical properties of MR fluids, [11, 13] . . . . . . . . . . . . . .  8
3.1 MR damper specification . . . . . . . . . . . . . . . . . . . . . . .  23
5.1 Data used for simulation in RecurDyn, [6] . . . . . . . . . . . . . .  30
5.2 Parameters for the MR damper (RD-1005-1) [29] . . . . . . . . . . . .  30
5.3 RMS analysis with four cases . . . . . . . . . . . . . . . . . . . . . 35
5.4 RMS analysis at three different walking speeds . . . . . . . . . . . . 38

List of Figures
2.1 A simplified model of human lower limb . . . . . . . . . . . . . . . .  5
2.2 Basic operating models of MR fluids, [14]. . . . . . . . . . . . . . .  9
2.3 Commercial linear MR fluid-based damper [14]. . . . . . . . . . . . .  10
2.4 Modified Bouc-Wen model . . . . . . . . . . . . . . . . . . . . . . .  11
2.5 The eight main phases of the walking cycle [17]. . . . . . . . . . . . 13
2.6 Terms used to describe foot placement on the ground [18]. . . . . . .  14
2.7 The pathway of the center of mass in locomotion [19]. . . . . . . . .  15
2.8 The vertical displacements of the center of mass. [20]. . . . . . . .  16
2.9 The thigh motion for normal gait in percent of gait cycle, [17]. . . . 17
2.10 Normal range of Knee mtiont during a gait cycle for free walking [17] 17
3.1 Icons used in this thesis . . . . . . . . . . . . . . . . . . . . . .  20
3.2 The AK prosthesis model with RecurDyn . . . . . . . . . . . . . . . .  20
3.3 The MR damper model with RecurDyn . . . . . . . . . . . . . . . . . .  21
3.4 The MR damper model with RecurDyn . . . . . . . . . . . . . . . . . .  22
3.5 Slider-crank configuration of MR damper in the AK Prosthesis . . . . . 23
4.1 Semi-active control systems for a plant integrated with a MR damper .  26
4.2 Graphical representation of algorithm for selecting control voltage
    [24]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  27
4.3 Graphical representation of modified algorithm. . . . . . . . . . . .  28
5.1 Control diagram for AK Prosthesis system using MR damper. . . . . . .  29
5.2 Responses of knee angle with modified version Heaviside function
    method (flexion negative). . . . . . . . . . . . . . . . . . . . . . . 31
5.3 The ground reaction force with modified version Heaviside function
    method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  32
5.4 Input voltage v and damping force Frh with modified version Heaviside
    function method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.5 Responses of knee angle and the ground reaction force with Heaviside
    function method (flexion negative). . . . . . . . . . . . . . . . . .  33
5.6 Responses of knee angle and the ground reaction force for v = 0V
    (flexion negative). . . . . . . . . . . . . . . . . . . . . . . . . .  33
5.7 Responses of knee angle and the ground reaction force for v = 2.5V
    (flexion negative). . . . . . . . . . . . . . . . . . . . . . . . . .  34
5.8 Responses of knee angle and the ground reaction force at cadence
    = 96 steps/min (flexion negative). . . . . . . . . . . . . . . . . . . 36
5.9 Input voltage v and damping force Frh at cadence = 96 steps/min . . .  36
5.10 Responses of knee angle and the ground reaction force at cadence
     = 119 steps/min (flexion negative). . . . . . . . . . . . . . . . . . 37
5.11 Input voltage v and damping force Frh at cadence = 119 steps/min.     37
A.1 The simplified model of human lower limb . . . . . . . . . . . . . . . 40

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