Models of Terrestrial Locomotion: From Mice to Men… to Elephants? 4/26/2017 5:22:02 AM Models of Terrestrial Locomotion: From Mice to Men… to Elephants? Justus D. Ortega Dept. of Kinesiology Humboldt State University

What do all these animals have in common? 4/26/2017 5:22:02 AM What 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.

Locomotion 4/26/2017 5:22:02 AM Complex interaction of the neuromuscular and musculoskeletal systems Comes in many forms: Bipedal: Walk Run Sprint Hop Quadipedal Trot Gallop How 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.

4/26/2017 5:22:02 AM Today we’ll discuss models of locomotion for walking and running/hopping Whole body level- mechanics Ground reaction force Movement and mechanical energy of CoM Behavioral models of walking and running Throughout 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.

Basic patterns in walking and running 4/26/2017 5:22:02 AM Basic patterns in walking and running Walking Double support: two feet on ground Single support: One foot on ground Running Stance phase: one foot on ground Aerial phase: no ground contact Other than the difference in aerial phase, one of the most distinct differences between waling and running is the pattern and magnitude of force involved.

Ground reaction force Force exerted by the ground on the feet 4/26/2017 5:22:02 AM Force exerted by the ground on the feet Greatly affect energetics of motion We measure the forces in walking and running by measuring the ground reaction force. Define. … The ground reac

Ground reaction force in walking 4/26/2017 5:22:02 AM Ground reaction force in walking

Running Ground Reaction Force 4/26/2017 5:22:02 AM Running Ground Reaction Force Ground 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

Center of Mass Motion Center of mass- balance point of body 4/26/2017 5:22:02 AM Center of Mass Motion Center of mass- balance point of body

Center of Mass Motion Walking Running Describe CoM motion in walking 4/26/2017 5:22:02 AM Center of Mass Motion Walking Running Describe CoM motion in walking Then describe CoM motion in running The motion of CoM directly effect mechanical energy of the body

Walk Velocity decreases Velocity increases Height increases Height decreases

Run Velocity decreases Velocity increases Height decreases Height increases In running, very different pattern of movement than in walking V and r decrease in first half, and then both increase in second half

Mechanical Energy of Center of Mass 4/26/2017 5:22:02 AM Mechanical Energy of Center of Mass Mechanical Energy- Energy of an object related to its motion Two primary forms: Kinetic: energy in motion Potential: stored energy -Gravitational - elastic

Kinetic energy (Ek,t) v m Ek,t = 0.5 mv2 m = mass v = velocity 4/26/2017 5:22:02 AM Kinetic energy (Ek,t) v m Ek,t = 0.5 mv2 Define kinetic energy m = mass v = velocity k = kinetic, t = translational

Gravitational potential energy (Ep,g) 4/26/2017 5:22:02 AM Gravitational potential energy (Ep,g) mg Ep,g = mgry mg = weight of object ry = vertical position of object ry Define gravitation potential energy Emphasize that it depends on HEIGHT of CoM

Elastic energy: energy stored when a spring is stretched or compressed 4/26/2017 5:22:02 AM Elastic energy: energy stored when a spring is stretched or compressed Spring Rest length (no energy stored) Stretched (Energy stored) Compressed (Energy stored)

Mechanical energy in walking 4/26/2017 5:22:02 AM Mechanical energy in walking Some kinetic energy Some gravitational potential energy Little work done against aerodynamic drag Unless slipping, no work done against friction Not much bouncing (elastic energy)

Mechanical energy fluctuations in level walking 4/26/2017 5:22:02 AM Mechanical energy fluctuations in level walking Average Ek,t constant (average vx constant) Average Ep,g constant (average ry constant) HOWEVER Ek,t and Ep,g fluctuate within each stance

Mechanical Energy in Walking 4/26/2017 5:22:02 AM Mechanical Energy in Walking Mid-stance KE minimized at mid-stance and GPE maximized at mid-stance

Walking and Mechanical energy 1st half of stance: decrease Velocity & increase Height KE converted to GPE 2nd half of stance: increase Velocity & decrease Height GPE converted to KE KE and GPE are out of phase Because these energetic fluctuations are out of phase, believed to be exchanged (Conservation of mechancial energy) Bring PHET

Vertical motion allows mechanical energy exchange 4/26/2017 5:22:02 AM Walking as Inverted Pendulum Premise for idea that decreasing vert disp will decrease energy expenditure was that it would reduce work to lift the COM After the first paper by Saunders et al in 1953, researchers discovered the importance of energy exchange Add ‘IP’ & ‘Vert disp…’: idea that walkers vault over stance limbs like IPs and reduce mech work by passive exch of KE and GPE This 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

Perfect Inverted Pendulum 4/26/2017 5:22:02 AM Perfect Inverted Pendulum Single support phase Total energy Kinetic energy Idealized. Only single support shown. Note vaulting pattern in GPE of COM Add KE: Note that KE is mirror image of GPE Add total: instantaneous sum of KE & GPE if flat, no external work required to lift & accel COM occurs if ∆GPE = ∆KE and out of phase But humans and animal legs do not act as pefect strut. (to reduce impact forces in walking) Gravitational Potential Energy Time (s)

Total KE GPE 60-70% of mechanical energy is conserved DS SS Time (s) 4/26/2017 5:22:02 AM Work Total GPE KE 0.2 J/kg In humans and oterh animals GPE 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. DS SS 0.0 0.2 0.4 0.6 Time (s) (Ortega and Farley, J. Applied Physiology, 2005)

Mechanical energy exchange and the cost of walking 4/26/2017 5:22:02 AM Mechanical energy exchange and the cost of walking 80 120 160 200 70 60 Metabolic Cost of Transport (mlO2/kg/km) 50 Mechanical Energy Exchange (%) 40 Energy 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 GRF Same relatinship exist in huge range of animals from mice to elephants with some slight differnces due to body size 30 1.0 0.5 1.5 2.0 Speed (m/s)

Effect of body size on mechanical energy recovery 4/26/2017 5:22:02 AM 3-4 years Effect of body size on mechanical energy recovery 11-12 years As increase size, greatest recovery at faster speeds, but similar amount Body size Optimum 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; 60-70 for childvs adult) Cavagna, 1983

Mechanical Energy in Running 4/26/2017 5:22:02 AM Mechanical Energy in Running Mid-stance Now lets take a look at the mechancial energy fluctuation in running. KE and GPE minimized at mid-stance

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 running Total Energy (J) Time (s) But what about EE?

Running: Spring mechanism 4/26/2017 5:22:02 AM Running: Spring mechanism Ek,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.

Leg stiffness Ratio of peak force to maximum displacement 4/26/2017 5:22:02 AM Leg stiffness Ratio of peak force to maximum displacement Leg stiffness is defined as…… Calculated from peak GRF and CoM vertical postion Many aspects of running depend on leg stiffness: Time of ground contact, vertical excursion of CoM And ground reaction force ** Quads: average of combined stiffness of all limbs in contact with ground Blickhan, 1989

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., 1993 How do we do it?

Effect of speed on leg spring 4/26/2017 5:22:02 AM Effect of speed on leg spring How? By increasing angle swept As speed increases…. Peak force increases Compensate with greater angular excursion =  CoM disp.

Leg stiffness and speed in variety of running animal 4/26/2017 5:22:02 AM Stiffness Leg Angle Leg stiffness and speed in variety of running animal Variety 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 stiffness Farley et al., 1993 Speed (m/s) Speed (m/s)

Leg stiffness is proportional to body mass 4/26/2017 5:22:02 AM largeanimals have proportioally more stiff leg springs compared to small animals. Leg undergoes less excursion = reduces the torque about the joints Although 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.

Animals can adjust leg stiffness for different surface stiffnesses 4/26/2017 5:22:02 AM Animals can adjust leg stiffness for different surface stiffnesses Often, 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.

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

4/26/2017 5:22:02 AM Running Robots ?

Using spring mass model to improve performance 4/26/2017 5:22:02 AM Using spring mass model to improve performance Alt video

Why is it so hard to walk on the moon? 4/26/2017 5:22:02 AM Why is it so hard to walk on the moon?

How did dinosaurs walk and run? 4/26/2017 5:22:02 AM How did dinosaurs walk and run?

4/26/2017 5:22:02 AM Thank you