Presentation on theme: "Models of Terrestrial Locomotion: From Mice to Men… to Elephants?"— Presentation transcript:
1 Models of Terrestrial Locomotion: From Mice to Men… to Elephants? 4/26/2017 5:22:02 AMModels of Terrestrial Locomotion: From Mice to Men… to Elephants?Justus D. OrtegaDept. of KinesiologyHumboldt State University
2 What do all these animals have in common? 4/26/2017 5:22:02 AMWhat do all these animals have in common?There are many aspects of biology and physiology that humans share with the other member of the animal kingdom. One of the most fundemental characteristics that all terestrial animals share is locomotion.
3 Locomotion4/26/2017 5:22:02 AMComplex interaction of the neuromuscular and musculoskeletal systemsComes in many forms:Bipedal:WalkRunSprintHopQuadipedalTrotGallopHow do we study something so complex?However, the systems and function of the body become increasing complex when we talk about the specific muscle, bones tendons and ligaments. As a result scientist attemped to first study animal locomotion starting at the level of the whole body and them progressing to to lower more complex levels.
4 4/26/2017 5:22:02 AMToday we’ll discuss models of locomotion for walking and running/hoppingWhole body level- mechanicsGround reaction forceMovement and mechanical energy of CoMBehavioral models of walking and runningThroughout this presentation, I will be comparing human locomotion to the locomotion of other terrestrial animals.By comparing diverse species we discover the common rules governing locomotion. But before we get started we frist need to distinguish the two most common forms of locomotion used by terrrestrial animals.
5 Basic patterns in walking and running 4/26/2017 5:22:02 AMBasic patterns in walking and runningWalkingDouble support: two feet on groundSingle support: One foot on groundRunningStance phase: one foot on groundAerial phase: no ground contactOther than the difference in aerial phase, one of the most distinct differences between waling and running is the pattern and magnitude of force involved.
6 Ground reaction force Force exerted by the ground on the feet 4/26/2017 5:22:02 AMForce exerted by the ground on the feetGreatly affect energetics of motionWe measure the forces in walking and running by measuring the ground reaction force.Define. …The ground reac
7 Ground reaction force in walking 4/26/2017 5:22:02 AMGround reaction force in walking
8 Running Ground Reaction Force 4/26/2017 5:22:02 AMRunning Ground Reaction ForceGround reaction force of walking and running is similar in wide variety of animals ranging in body size and # of legs.Differnce in GRF between Walk and run greatly affect CoM motion and ultimately mechancial energy patterns.But what do I mean when I say center of mass
9 Center of Mass Motion Center of mass- balance point of body 4/26/2017 5:22:02 AMCenter of Mass MotionCenter of mass- balance point of body
10 Center of Mass Motion Walking Running Describe CoM motion in walking 4/26/2017 5:22:02 AMCenter of Mass MotionWalkingRunningDescribe CoM motion in walkingThen describe CoM motion in runningThe motion of CoM directly effect mechanical energy of the body
11 Walk Velocity decreases Velocity increases Height increases Height decreases
12 Run Velocity decreases Velocity increases Height decreases Height increasesIn running, very different pattern of movement than in walkingV and r decrease in first half, and then both increase in second half
13 Mechanical Energy of Center of Mass 4/26/2017 5:22:02 AMMechanical Energy of Center of MassMechanical Energy- Energy of an object related to its motionTwo primary forms:Kinetic: energy in motionPotential: stored energy-Gravitational- elastic
14 Kinetic energy (Ek,t) v m Ek,t = 0.5 mv2 m = mass v = velocity 4/26/2017 5:22:02 AMKinetic energy (Ek,t)vmEk,t = 0.5 mv2Define kinetic energym = massv = velocityk = kinetic, t = translational
15 Gravitational potential energy (Ep,g) 4/26/2017 5:22:02 AMGravitational potential energy (Ep,g)mgEp,g = mgrymg = weight of objectry = vertical position of objectryDefine gravitation potential energyEmphasize that it depends on HEIGHT of CoM
16 Elastic energy: energy stored when a spring is stretched or compressed 4/26/2017 5:22:02 AMElastic energy: energy stored when a spring is stretched or compressedSpringRest length(no energy stored)Stretched(Energy stored)Compressed(Energy stored)
17 Mechanical energy in walking 4/26/2017 5:22:02 AMMechanical energy in walkingSome kinetic energySome gravitational potential energyLittle work done against aerodynamic dragUnless slipping, no work done against frictionNot much bouncing (elastic energy)
18 Mechanical energy fluctuations in level walking 4/26/2017 5:22:02 AMMechanical energy fluctuations in level walkingAverage Ek,t constant (average vx constant)Average Ep,g constant (average ry constant)HOWEVEREk,t and Ep,g fluctuate within each stance
19 Mechanical Energy in Walking 4/26/2017 5:22:02 AMMechanical Energy in WalkingMid-stanceKE minimized at mid-stanceand GPE maximized at mid-stance
20 Walking and Mechanical energy 1st half of stance: decrease Velocity & increase HeightKE converted to GPE2nd half of stance: increase Velocity & decrease HeightGPE converted to KEKE and GPE are outof phaseBecause these energetic fluctuations are out of phase, believed to be exchanged (Conservation of mechancial energy)Bring PHET
21 Vertical motion allows mechanical energy exchange 4/26/2017 5:22:02 AMWalking as Inverted PendulumPremise for idea that decreasing vert disp will decrease energy expenditure was that it would reduce work to lift the COMAfter the first paper by Saunders et al in 1953, researchers discovered the importance of energy exchangeAdd ‘IP’ & ‘Vert disp…’: idea that walkers vault over stance limbs like IPs and reduce mech work by passive exch of KE and GPEThis pattern of mechancial energy exchanges exists in not just bipedal animals but also quad.In quad (dog, horse, tortouise or even ghost crab), all legs in contact with ground act act like single strut to produce the similar CoM motiona and mechancial energy exchange.I a pefect IP, 100 mechanical energy is conserved.Alexander (1992)Vertical motion allows mechanical energy exchange
22 Perfect Inverted Pendulum 4/26/2017 5:22:02 AMPerfect Inverted PendulumSingle support phaseTotalenergyKineticenergyIdealized. Only single support shown.Note vaulting pattern in GPE of COMAdd KE: Note that KE is mirror image of GPEAdd total: instantaneous sum of KE & GPEif flat, no external work required to lift & accel COMoccurs if ∆GPE = ∆KE and out of phaseBut humans and animal legs do not act as pefect strut. (to reduce impact forces in walking)GravitationalPotentialEnergyTime (s)
23 Total KE GPE 60-70% of mechanical energy is conserved DS SS Time (s) 4/26/2017 5:22:02 AMWorkTotalGPEKE0.2 J/kgIn humans and oterh animalsGPE and KE are not same magnitude and not pefectly out of phase.Thus, Not all KE is exchanged to GPE in first half and not all GPE exchanged back in 2nd half.As result of these mismatches, total energy fluctuates, the fluctuation in total energy represent work performed by muscles to keep the body moving.So how much of the energy do humans and animals conserve.DSSS0.00.20.40.6Time (s)(Ortega and Farley,J. Applied Physiology, 2005)
24 Mechanical energy exchange and the cost of walking 4/26/2017 5:22:02 AMMechanical energy exchange and the cost of walking801201602007060Metabolic Costof Transport (mlO2/kg/km)50Mechanical Energy Exchange (%)40Energy transfer by IP reduces mechanical work for lift and accelerate and decres the cost of walking.As much as 60-70% received in humans. Part of the reason not 100% is- leg doe not act as perfect strut.- leg geometry: when walk with exaggerated joint flexion. Recovery decreases dramatically and cost in crease by nearly 200%. But flexion helps to reduce peak GRFSame relatinship exist in huge range of animals from mice to elephants with some slight differnces due to body size301.00.51.52.0Speed (m/s)
25 Effect of body size on mechanical energy recovery 4/26/2017 5:22:02 AM3-4 yearsEffect of body size on mechanical energy recovery11-12 yearsAs increase size, greatest recovery at faster speeds, but similar amountBody sizeOptimum speed for energy transfer lower for smaller animals (0.6 m/s for 2 yr old human) than larger(1.3 m/s)Similar difference for animal of different sizes- lizard (skink) recover at 50% at 0.15 m/s (Farley, 1997)-ram a recover 50% at 1.4 m/s Cavagna, 1977)Energy transfer by IP reduces mechanical work by similar fraction (50% for ram vs lizzard; for childvs adult)Cavagna, 1983
26 Mechanical Energy in Running 4/26/2017 5:22:02 AMMechanical Energy in RunningMid-stanceNow lets take a look at the mechancial energy fluctuation in running.KE and GPE minimized at mid-stance
27 KE (J) Stance phase of running GPE (J) Total Energy (J) Time (s) This figure show the kinetic and Poetnial enrgy of CoM during stacne pahe of runningTotalEnergy (J)Time (s)But what about EE?
28 Running: Spring mechanism 4/26/2017 5:22:02 AMRunning: Spring mechanismEk,t & Ep,g are in phase. Elastic energy is stored in leg.In running, can’t be substantial IP energy exchange between KE and GPE because they are in phase.KE and GPE minimized at mid-stance . As result only 5% recovered by exchange of KE and PE.However, substantial energy conserved through storage in elastic tissues (tendons.Because motion of CoM is similar to bouncing ball , running is modeled as a simple spring-mass model that consists of a single leg spring and point mass equivalent to body mass. In running the leg spring compress in first half of stance and lengthens during second half of ground contact. spring gait..Similar pattern occurs at fast gait in other animals such as dog, cat, running turkey, even running cockroachs)Because running modeled as spring mass, leg stiffness play a key role in dynamic interaction between the body and ground.
29 Leg stiffness Ratio of peak force to maximum displacement 4/26/2017 5:22:02 AMLeg stiffnessRatio of peak force to maximum displacementLeg stiffness is defined as……Calculated from peak GRF and CoM vertical postionMany aspects of running depend on leg stiffness:Time of ground contact,vertical excursion of CoMAnd ground reaction force** Quads: average of combined stiffness of all limbs in contact with groundBlickhan, 1989
30 Animals maintain same leg stiffness across many speeds Able to run at higher speeds with shorter ground contact without changing leg stiffness How do we and other animals do this?Farley et al., 1993How do we do it?
31 Effect of speed on leg spring 4/26/2017 5:22:02 AMEffect of speed on leg springHow? By increasing angle sweptAs speed increases….Peak force increasesCompensate with greater angular excursion = CoM disp.
32 Leg stiffness and speed in variety of running animal 4/26/2017 5:22:02 AMStiffnessLeg AngleLeg stiffness and speed in variety of running animalVariety of animals are able to maintain leg stiffness across wide range of speeds.Other animals do it the same way as humans….by changing the angle swept by the leg.Becaeu similar in different animals, research wanted to know how does body size affect leg stiffnessFarley et al., 1993Speed (m/s)Speed (m/s)
33 Leg stiffness is proportional to body mass 4/26/2017 5:22:02 AMlargeanimals have proportioally more stiff leg springs compared to small animals. Leg undergoes less excursion = reduces the torque about the jointsAlthough we can keep stiffness the same across a range of speeds and body mass greatly affect leg stiffness, human, as well as these large and small animals, can adjust leg stiffness to alter stride frequency, or even to offset running on different surfaces.
34 Animals can adjust leg stiffness for different surface stiffnesses 4/26/2017 5:22:02 AMAnimals can adjust leg stiffness for different surface stiffnessesOften, we don’t always run un the same surfaces. Sometimes we run on cement, thoer times on a cushy track. Each surface has a different stiffness. As a result we have to adapt in order to maintain safe and efficient motion.A study by Ferris an Farley in 1998 explored how humans adjust leg stiffness to different surfaces with varying amounts of stiffness.
35 Animal adjust leg stiffness so CoM movement is same By adjusting leg stiffness for different surface stiffness, can maintain similar peak forces, CoM motion, and contact times.Ferris & Farley, 1983