227. Mechanics Of Trampolining

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227. Mechanics Of Trampolining

 

 

CATEGORY: Sports & Recreation 250 Courses

COURSE NUMBER: 227

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Syllabus

ABSTRACT………………………………………………………………………………………………. i
ACKNOWLEDGMENTS …………………………………………………………………………. iii
Contents …………………………………………………………………………………………………….v
List of Figures………………………………………………………………………………………….. xi
List of Tables ……………………………………………………………………………………………xv
Chapter 1: Introduction ………………………………………………………………………………..1
1.1 Previous Trampolining Research ……………………………………………………..2
1.2 Statement of Purpose………………………………………………………………………3
1.3 Research Questions ………………………………………………………………………..3
1.4 Chapter Organisation………………………………………………………………………4
Chapter 2: Review of Literature…………………………………………………………………….6
2.1 Chapter Overview…………………………………………………………………………..6
2.2 Overview of Trampolining Research ………………………………………………..6
2.2.1 Takeoff…………………………………………………………………………………..7
2.2.2 Height…………………………………………………………………………………….7
2.2.3 Rotation………………………………………………………………………………..10
2.2.4 Inter-relationship of Height and Rotation ………………………………….11
2.2.5 Summary ………………………………………………………………………………12
2.3 The Trampoline ……………………………………………………………………………12
2.3.1 Modelling the Trampoline ………………………………………………………13
2.3.2 Measuring Trampoline Parameters…………………………………………..15
2.3.3 Limitations of Previous Trampoline Models……………………………..17
2.4 Computer Simulation Models ………………………………………………………..17
2.4.1 Overview………………………………………………………………………………17
2.4.2 Trampolining Simulation Models…………………………………………….18

2.4.3 Non-trampolining Takeoff Simulation Models…………………………..20
2.4.4 Wobbling Mass Models………………………………………………………….21
2.4.5 Summary ………………………………………………………………………………23
2.5 Simulation Model Input…………………………………………………………………24
2.5.1 Strength Parameters ……………………………………………………………….24
2.5.1.1 Muscle Modelling……………………………………………………………24
2.5.1.2 Strength Measurement……………………………………………………..27
2.5.1.3 Summary………………………………………………………………………..30
2.5.2 Body Segmental Inertia Parameters………………………………………….30
2.5.3 Kinematic Data ……………………………………………………………………..32
2.5.3.1 Image Analysis ……………………………………………………………….32
2.5.3.2 Data Processing ………………………………………………………………33
2.6 Optimisation ………………………………………………………………………………..34
2.7 Chapter Summary…………………………………………………………………………35
Chapter 3: Data Collection………………………………………………………………………….37
3.1 Chapter Overview…………………………………………………………………………37
3.2 Kinematic Data Collection …………………………………………………………….37
3.2.1 Camera Set-up……………………………………………………………………….37
3.2.2 Data Collection ……………………………………………………………………..38
3.2.3 Body Segmental Inertia Parameters………………………………………….41
3.3 Kinematic Data Processing ……………………………………………………………44
3.3.1 Joint Centre Positions……………………………………………………………..44
3.3.2 Joint Angle Time Histories……………………………………………………..47
3.3.3 Trampoline Bed Movement …………………………………………………….51
3.4 Chapter Summary…………………………………………………………………………52
Chapter 4: Model Development…………………………………………………………………..53
4.1 Chapter Overview…………………………………………………………………………53

4.2 The Trampolinist Model………………………………………………………………..53
4.3 Foot/Suspension-System Interface ………………………………………………….54
4.3.1 Kinetics of the Foot/Suspension-System Interactions …………………55
4.3.2 Locating the Centre of Pressure during Foot Contact………………….59
4.3.3 Determining the Natural Slope of the Surface of the Suspension
System during Depression ……………………………………………………………………62
4.3.4 Equations of Motion……………………………………………………………….63
4.4 Chapter Summary…………………………………………………………………………64
Chapter 5: The Angle-Driven Model……………………………………………………………65
5.1 Chapter Overview…………………………………………………………………………65
5.2 Visco-Elastic Parameter Determination …………………………………………..65
5.2.1 Model Inputs…………………………………………………………………………66
5.2.2 Cost Function ………………………………………………………………………..67
5.2.3 Results………………………………………………………………………………….68
5.3 Evaluation of the Angle-Driven Model……………………………………………71
5.4 Chapter Summary…………………………………………………………………………73
Chapter 6: The Torque-Driven Model ………………………………………………………….74
6.1 Chapter Overview…………………………………………………………………………74
6.2 Structure of the Torque-Driven Model…………………………………………….74
6.3 Torque Generators………………………………………………………………………..76
6.3.1 Torque – Angle – Angular Velocity Relationship ………………………77
6.3.1.1 Torque – Velocity Relationship…………………………………………77
6.3.1.2 Differential Activation……………………………………………………..79
6.3.1.3 Torque – Angle Relationship…………………………………………….80
6.3.2 Strength Parameters ……………………………………………………………….81
6.3.3 Muscle Activation Profiles………………………………………………………82
6.3.4 Strength Parameter Scaling Factors………………………………………….84

6.3.5 Metatarsal-Phalangeal Joint …………………………………………………….85
6.4 Model Evaluation …………………………………………………………………………86
6.4.1 Model Input…………………………………………………………………………..87
6.4.2 Model Variables…………………………………………………………………….88
6.4.3 Cost Function ………………………………………………………………………..90
6.4.4 Strength Scaling Matching Results…………………………………………..93
6.4.4.1 Joint Angles……………………………………………………………………96
6.4.4.2 Joint Torque Activation Profiles………………………………………..99
6.4.4.3 Joint Torques ………………………………………………………………..101
6.4.4.4 Strength Scaling Factors…………………………………………………103
6.4.5 Fixed Strength Matching Results……………………………………………104
6.4.5.1 Joint Angles………………………………………………………………….106
6.4.5.2 Joint Torque Activation Profiles………………………………………108
6.4.5.3 Joint Torques ………………………………………………………………..110
6.4.6 Discussion …………………………………………………………………………..112
6.4.6.1 Joint Angles………………………………………………………………….112
6.4.6.2 Movement Outcomes at Takeoff ……………………………………..112
6.4.6.3 Summary………………………………………………………………………113
6.5 Chapter Summary……………………………………………………………………….113
Chapter 7: Optimisation and Applications…………………………………………………..114
7.1 Chapter Overview……………………………………………………………………….114
7.2 Application to Research Questions ……………………………………………….114
7.3 Calculation of Kinematic Variables………………………………………………115
7.3.1 Jump Height ………………………………………………………………………..115
7.3.2 Flight Time………………………………………………………………………….115
7.3.3 Rotation Potential…………………………………………………………………116
7.4 Optimisation Method…………………………………………………………………..117

7.4.1 Maximum Height Method……………………………………………………..117
7.4.2 Maximum Rotation Method…………………………………………………..118
7.5 Optimisation Results…………………………………………………………………..119
7.5.1 Maximum Jump Height Results……………………………………………..119
7.5.1.1 Joint Angles………………………………………………………………….123
7.5.1.2 Joint Torque Activation Profiles………………………………………126
7.5.1.3 Joint Torques ………………………………………………………………..130
7.5.1.4 Summary………………………………………………………………………132
7.5.2 Maximum Rotation Results …………………………………………………..132
7.5.2.1 Joint Angles………………………………………………………………….135
7.5.2.2 Joint Torque Activation Profiles………………………………………138
7.5.2.3 Joint Torques ………………………………………………………………..141
7.5.2.4 Summary………………………………………………………………………143
7.6 Discussion …………………………………………………………………………………143
7.7 Chapter Summary……………………………………………………………………….144
Chapter 8: Discussion and Conclusions………………………………………………………145
8.1 Chapter Overview……………………………………………………………………….145
8.2 Research Questions …………………………………………………………………….145
8.3 Discussion …………………………………………………………………………………147
8.3.1 Simulation Model…………………………………………………………………147
8.3.2 Foot-Suspension System Interface………………………………………….148
8.3.3 Performance Data…………………………………………………………………148
8.3.4 Anthropometric Data…………………………………………………………….149
8.3.5 Kinematic Data Processing ……………………………………………………149
8.3.6 Determination of Suspension System Interface Parameters ……….150
8.3.7 Torque Parameters ……………………………………………………………….150
8.3.8 Evaluation of the Torque-driven Model…………………………………..151

8.3.9 Cost Scores and Penalties ……………………………………………………..151
8.4 Future Research………………………………………………………………………….152
8.4.1 Robustness ………………………………………………………………………….152
8.4.2 Initial Conditions………………………………………………………………….153
8.4.3 Subject-Specific Parameters ………………………………………………….153
8.4.4 Sensitivity to Model Parameters…………………………………………….153
8.4.5 Application to Different Trampoline Contacts …………………………154
8.5 Conclusions……………………………………………………………………………….154
References………………………………………………………………………………………………155
APPENDICES ………………………………………………………………………………………..168
APPENDIX 1: Informed Consent Form ………………………………………………….169
APPENDIX 2: Anthropometric Measurements………………………………………..174
APPENDIX 3: AutolevTM 4.1 Command Files…………………………………………177
APPENDIX 4: Joint Torque Profiles from Angle-Driven Matching Simulations
…………………………………..191
APPENDIX 5: Torque Generator Activation Parameters from Strength Scaling
Torque-Driven Matching Simulations……………………………………………………..194
APPENDIX 6: Torque Generator Activation Parameters from Fixed Strength
Torque-Driven Matching Simulations……………………………………………………..197
APPENDIX 7: Torque Generator Activation Parameters from Optimisations200

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