Linear Motion - Minimum Movement Time Overground (Running, Walking, & Road Cycling) 2 Biomechanical Model: Linear Mo1on Minimum Movement Time (Overground) Slide 1 of 3 Movement Time Linear Distance Speed Factors that Slow Factors that Speed the Body Down Less the Body Up More Joint Linear Joint Linear Joint Linear Sum of Speeds 1 Speeds 2 Speeds 3 Joint Forces External Application Time Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of Mass Forces of each External Force Velocity Rotation Velocity Rotation Velocity Rotation Slowing the Body Down Drag Friction Joint Application Time Angular Joint Application Time Angular Joint Application Time Angular Force Force Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Fluid Coefficient Area Relative Vertical Ground Coefficient of Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Reaction Force Friction Force Arm Resistance Force Arm Resistance Force Arm Resistance Linear Application Time of Mass Speed The Internal Forces External Slowing the Body Down Forces Friction Slide 3 of 3 Force Vertical Ground Coefficient of Reaction Force Friction Slide 2 of 3 3 Biomechanical Model: Linear Mo1on Minimum Movement Time (Overground) (Slide 1 of 3) Linear Speed Principle Movement Time Linear Conservation of Momentum Principle Linear Distance Speed Factors that Slow Factors that Speed the Body Down Less the Body Up More 4 Biomechanical Model: Linear Mo1on Minimum Movement Time (Overground) (Slide 2 of 3) Sum of Joint Linear Speeds Principle Factors that Speed the Body Up More Angular Linear Speed – Angular Joint Linear Joint Linear Impulse – Momentum Joint Linear Speeds 1 Velocity Principle Speeds 2 Speeds 3 Principle Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of Velocity Rotation Velocity Rotation Velocity Rotation Joint Application Time Angular Joint Application Time Angular Joint Application Time Angular Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Force Arm Resistance Force Arm Resistance Force Arm Resistance Joint Torque External Action - Reaction Angular Inertia Principle Forces Principle Principle External Forces Friction Principle Force Vertical Ground Coefficient of Reaction Force Friction Friction Force Principle 5 Biomechanical Model: Linear Mo1on Minimum Movement Time (Overground) Linear Factors that Slow the Body Down Less (Slide 3 of 3) Impulse-Momentum Principle 2 Sum of Joint Forces External Forces External Application Time of Principle Mass Forces each External Force Slowing the Body Down Drag Force Principle Drag Friction Force Force Friction Force Principle Fluid Coefficient Area Relative Vertical Ground Coefficient of Density of Drag of Drag Velocity Reaction Force Friction Linear Application Time of Mass Linear Speed The Internal Forces Slowing the Body Down Impulse-Momentum Principle 1 6 Biomechanical Model: Linear Mo1on Minimum Movement Time Movement Linear Speed Principle Time l Linear t = Distance s Speed 7 Biomechanical Model: Linear Mo1on Minimum Movement Time Linear Linear Conservation of Speed Momentum Principle Factors that Slow Factors that Speed the Body Down Less the Body Up More 8 Biomechanical Model: Linear Mo1on Minimum Movement Time Factors that Speed Sum of Joint the Body Up More Linear Speeds Principle Joint Linear Joint Linear Joint Linear Speeds 1 Speeds 2 Speeds 3 9 Biomechanical Model: Linear Mo1on Minimum Movement Time Joint Linear Speed – Angular Linear Speeds Velocity Principle Joint Angular Radius of Velocity Rotation s = ωrrt 10 Biomechanical Model: Linear Mo1on Minimum Movement Time Joint Angular Angular Impulse – Velocity Momentum Principle Joint Application Time Angular Tt Torque of the Joint Torque Inertia ω = I 11 Biomechanical Model: Linear Mo1on Minimum Movement Time Joint Joint Torque Principle Torque TJ = FMd ⊥ Muscle Moment Force Arm 12 Biomechanical Model: Linear Mo1on Minimum Movement Time Angular Angular Inertia Principle Inertia 2 Radius of I = mr Mass rs Resistance 13 Biomechanical Model: Linear Mo1on Minimum Movement Time Muscle Action – Reaction Principle Force External Forces 14 Biomechanical Model: Linear Mo1on Minimum Movement Time External Forces Principle Speeding up (a) and slowing down (b) sides of the model External External Forces (a) Forces (b) Vertical Ground Friction Drag Vertical Ground Friction Reaction Force Force Force Reaction Force Force Back to Speed Up Side Back to Slow Down Side 15 Biomechanical Model: Linear Mo1on Minimum Movement Time Friction Friction Force Principle Force Speeding up and slowing down sides of the model Vertical Ground Coefficient Reaction Force of Friction FFR = µFVGR Back to Speed Up Side Back to Slow Down Side 16 Biomechanical Model Lowest Sum of Joint Forces When Landing aer a Jump Vertical Ground Linear Impulse – Reaction Force Momentum Principle 1 Linear Application Time Mass ms Speed of the Internal Forces F = Slowing the Body Down VGR t 17 Biomechanical Model: Linear Mo1on Minimum Movement Time Linear Impulse – Factors that Slow Momentum Principle 2 the Body Down Less Sum of ΣFt Joint Forces Δs = m External Application Time Mass Forces of each External Force Slowing the Body Down 18 Biomechanical Model: Linear Mo1on Minimum Movement Time Drag Drag Force Principle Force 1 2 Fluid Coefficient Area Relative FD = ρfluidCDAD (vrel ) 2 Density of Drag of Drag Velocity 19 Linear Motion - Minimum Movement Time Running & Walking 20 Biomechanical Model: Linear Mo1on Minimum Movement Time (Running & Walking) Movement Time Linear Distance Speed Factors that Slow Factors that Speed the Body Down Less the Body Up More Joint Linear Speed Joint Linear Speed Joint Linear Speed Sum of of the Ankle & All Joints of the Knee & All Joints of the Hip & All Joints Joint Forces Superior to the Ankle Superior to the Knee Superior to the Hip Application Time Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of External Mass Forces of each External Force Velocity Rotation Velocity Rotation Velocity Rotation Slowing the Body Down Drag Friction Ankle PF Application Time Angular Knee Ext Application Time Angular Hip Ext Application Time Angular Force Force Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Fluid Coefficient Area Relative Vertical Ground Coefficient of Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Reaction Force Friction Force Arm Resistance Force Arm Resistance Force Arm Resistance Linear Application Time of Mass Speed The Internal Forces External Slowing the Body Down Forces Friction Force Vertical Ground Coefficient of Reaction Force Friction 21 Linear Motion - Minimum Movement Time Road Cycling 22 Biomechanical Model: Linear Mo1on Minimum Movement Time (Road Cycling) Movement Time Linear Distance Speed Factors that Slow Factors that Speed the Body Down Less the Body Up More Joint Linear Speed Joint Linear Speed Joint Linear Speed Sum of of the Ankle & All Joints of the Knee & All Joints of the Hip & All Joints Joint Forces Distal to the Ankle Distal to the Knee Distal to the Hip Application Time Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of External Mass Forces of each External Force Velocity Rotation Velocity Rotation Velocity Rotation Slowing the Body Down Drag Friction Ankle PF & Application Time Angular Knee Ext & Application Time Angular Hip Ext & Application Time Angular Force Force DF Torques of the Joint Torque Inertia Flex Torques of the Joint Torque Inertia Flex Torques of the Joint Torque Inertia Fluid Coefficient Area Relative Vertical Ground Coefficient of Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Reaction Force Friction Force Arm Resistance Force Arm Resistance Force Arm Resistance Linear Application Time of Mass Speed The Internal Forces External Slowing the Body Down Forces Friction Force Vertical Ground Coefficient of Reaction Force Friction Linear Motion - Minimum Movement Time Through Water (Front Crawl Swimming) 24 Biomechanical Model: Linear Mo1on Minimum Movement Time (through water) Slide 1 of 3 Movement Time Linear Distance Speed Factors that Slow Factors that Speed the Body Down Less the Body Up More Slide 2 of 3 Sum of Joint Forces Joint Linear Joint Linear Joint Linear Speeds 1 Speeds 2 Speeds 3 External Application Time of each External Force Mass Forces Joint Radius of Joint Radius of Joint Radius of Slowing the Body Down Velocity Rotation Velocity Rotation Velocity Rotation Body Drag Force Joint Application Time Angular Joint Application Time Angular Joint Application Time Angular Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Fluid Coefficient Area Relative Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Force Arm Resistance Force Arm Resistance Force Arm Resistance Kick Buoyant External Force Force Slide 3 of 3 Forces Foot Drag Body Hand Drag Hand Lift Force Density Force Force Fluid Coefficient Area Relative Fluid Coefficient Area Relative Fluid Coefficient Area Relative Density of Drag of Drag Velocity Density of Drag of Drag Velocity Density of Lift of Lift Velocity 25 Biomechanical