Lecture 2: Terrestrial Locomotion I Simple Analyses of Ballistic Movement. 1. Recap: Jumping... Comfort level with 2. Current approaches for analyzing terrestrial physics: 3.32 + 0.84 locomotion. 3. Gaits and patterns of limb motion Comfort level with 4. Ballistic walking and the inverted pendulum calculus: 2.80 + 1.12 m= 3 10-3 kg No air resistance |uo| = 3.4 m/s u = [u cos α, u sin α] o o o y α = 55 x After take-off forces sum to zero Survey question: the moon has 1/6 earth g. Because of that lower gravitational acceleration (a)You would walk faster on the moon (b)You would walk slower on the moon (c)There would be no difference in your walking speed 1. Recap: Jumping... 2. Current approaches for analyzing terrestrial locomotion. 3. Gaits and patterns of limb motion 4. Ballistic walking and the inverted pendulum Cost (P/WV; E/Wd) of transport declines with body size 2.0 BIG DOG mouse ant lizard 1.0 rabbit humanASIMO fly bee bat dog 0 chetah human fish Log Cost of TransportLog Cost pigeon elephant -1.0 shark dolphin -2.0 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Log Body Mass (kg) Muscle forces are manifest as ground reaction forces and energy (PE,KE) exchanges of the body Is KE red or blue? KE = mv2/2 PE = mgh Movement Biomechanics 1. Recap: Jumping... 2. Current approaches for analyzing terrestrial locomotion. 3. Gaits and patterns of limb motion 4. Ballistic walking and the inverted pendulum time (s) -> 0 0.5 1.0 stride length GAITS •stride length: distance between footfalls of the same foot •stride frequency: number of footfalls per time •duty factor: fraction of stride time that a foot is on the ground (human walking = 0.5 - 0.6, running = 0.35). Gaits with duty factors less than 0.5 imply airborne phases. •relative phase: time a foot is set down as a fraction of the stride time. Ballistic Walking: The Inverted Pendulum V Ballistic Walking: The Inverted Pendulum V Ballistic Walking: The Inverted Pendulum V stride length Ballistic Walking: The Inverted Pendulum Ballistic Walking: The Inverted Pendulum Survey question: the moon has 1/6 earth g. Would you be able to walk faster on the moon? Modifiers of the radius of curvature Lumbar flexion Pelvic rotation Pelvic tilt Lumbar flexion Pelvic rotation Pelvic tilt Plantar flexion http://www.biomotionlab.ca/Demos/BMLwalker.html How fast did T. rex run? S L 10 5 S/L 2 1 Relative Stride Length Stride Relative 0.1 0.5 1 2 5 10 20 Fr = V2/ g L.