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Edward Muybridge 1830-1904 Locomotor kinematics = quantification of limb and body motion Locomotor dynamics = ana

Lecture # 16: Running and Walking. Edward Muybridge 1830-1904 Locomotor kinematics = quantification of limb and body motion Locomotor dynamics = analysis of forces and moments. Inverted pendulum . =. one stride. kinetic. gravitational potential.

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Edward Muybridge 1830-1904 Locomotor kinematics = quantification of limb and body motion Locomotor dynamics = ana

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  1. Lecture # 16: Running and Walking Edward Muybridge 1830-1904 Locomotor kinematics = quantification of limb and body motion Locomotor dynamics = analysis of forces and moments

  2. Inverted pendulum = one stride kinetic gravitational potential frictionless pendulum swings forever exchange kinetic & potential energy Walking

  3. Walking y Dy q v h, height of center of mass one stride h mgh (GPE) G.P.E. & K.E. are out of phase(exchange possible) v ½ mv2 (KE) stride 1 stride 2 • Walking • No aerial phase • exchange ofG.P.E. and K.E.

  4. Simulated Biped Robotic Biped

  5. v0 requiredcentripetal acceleration = v02/L L What keeps mass following this arc? Walking Walking Only source of downward acceleration is g. Therefore, mass follows arc if g > v02/L Only source of downward acceleration is g. Therefore, mass follows arc if g > v02/L…. …or v02/gL < 1 v02/gL is called Froude number (a dimensionless #), also defined as ratio of inertial to gravitational forces. DETERMINES WALK-TO-RUN TRANSITION!

  6. v0 L Walking Walking Example 1: Does this work for humans? What is predicted walk-to-run transition speed? V = (gL)-½ L = 0.9 m g = 9.8 m/s2 V = 3 m/s – ‘jogging’ speed for most people Example 3: What is walk-to-run transition for ant? V = (gL)-½ L = 0.001 m g = 9.8 m/s2 V = 0.1 m/s ~ 100 body lengths for humans ~ 3 body lengths Example 2: What is walk-to-run transition on moon? V = (gL)-½ L = 0.9 m g = 0.17 x 9.8 = 1.6 m/s2 V = 1.2 m/s – ‘jogging’ speed on moon

  7. Running spring mass model = stance swing stance swing

  8. stance swing -y dx/dt = constant x height, h L h GPE -k DLEPE E.P.E. & K.E. are partially out of phase(exchange possible) Uvert dy/dt KE KE-EPE exchange KE-EPE exchange ballistic ballistic Running

  9. actuator (muscle) structural element (bone) tensile element (ligament /tendon) elastic element (tendon)

  10. duty factor = stance stance+swing stance swing Left Right Run d.f. < 0.5 aerial phase Left Right Hop 0< d.f.<1 Left Right Running Walk d.f. >0.5 Gaits

  11. duty factor = stance stance+swing Walk always 3 feet on ground Left Front Left Hind Right Front Right Hind Run aerial phase Left Front Left Hind Right Front Right Hind Quadrapedal Gaits (trot)

  12. Run aerial phase Left Front Left Hind Right Front Right Hind Run aerial phase Left Front Left Hind Right Front Right Hind (pace) (bound)

  13. (gallop) Run aerial phase Left Front Left Hind Right Front Right Hind

  14. COM Left Front Left Middle Left Hind Right Front Right Middle Right Hind Hexapedal Gait = Tripod

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