Pace Length Effects in Human Walking: “Groucho” Gaits Revisited

Competing Models of Work in Quadrupedal Walking: Center of Mass Work is Insufficient to Explain Stereotypical Gait

The walking gaits of cursorial quadrupedal mammals tend to be highly stereotyped as a four-beat pattern with interspersed periods of double and triple stance, often with double-hump ground reaction force profiles. This pattern has long been associated with high energetic economy, due to low apparent work. However, there are differing ways of approximating the work performed during walking and, consequently, different interpretations of the primary mechanism leading to high economy. A focus on Net Center of Mass (COM) Work led to the claim that quadrupedal walking is efficient because it effectively trades potential and kinetic energy of the COM. Individual Limbs COM Work instead focuses on the ability of the limbs to manage the trajectory of the COM to limit energetic losses to the ground (“collisions”). By focusing on the COM, both these metrics effectively dismiss the importance of rotation of the elongate quadrupedal body. Limb Extension Work considers work required to extend and contract each limb like a strut, and accounts for the work of body pitching. We tested the prescriptive ability of these approximations of work by optimizing them within a quadrupedal model with two approximations of the body as a point-mass or a rigid distributed mass. Perfect potential-kinetic energy exchange of the COM was possible when optimizing Net COM Work, resulting in highly compliant gaits with duty factors close to one, far different than observed mammalian gaits. Optimizing Individual Limbs COM Work resulted in alternating periods of single limb stance. Only the distributed mass model, with Limb Extension Work as the cost, resulted in a solution similar to the stereotypical mammalian gait. These results suggest that maintaining a near-constant limb length, with distributed contacts, are more important mechanisms of economy than either transduction of potential-kinetic energy or COM collision mitigation for quadrupedal walking.

Load carrying with flexible bamboo poles: optimization of a coupled oscillator system

In Asia, flexible bamboo poles are routinely used to carry substantial loads on the shoulder. Various advantages have been attributed to this load-carrying strategy (e.g. reduced energy consumption), but experimental evidence remains inconsistent – possibly because carriers in previous studies were inexperienced. Theoretical models typically neglect the individual's capacity to optimize interactions with the oscillating load, leaving the complete dynamics underexplored. This study used a trajectory optimization model to predict gait adaptations that minimize work-based costs associated with carrying compliant loads and compared the outcomes with naturally selected gait adaptations of experienced pole carriers. Gait parameters and load interactions (e.g. relative amplitude and frequency, phase) were measured in rural farmworkers in Vietnam. Participants carried a range of loads with compliant and rigid poles and the energetic consequences of step frequency adjustments were evaluated using the model. When carrying large loads, the empirical step frequency changes associated with pole type (compliant versus rigid) were largely consistent with model predictions, in terms of direction (increase or decrease) and magnitude (by how much). Work-minimizing strategies explain changes in leg compliance, harmonic frequency oscillations and fluctuations in energetic cost associated with carrying loads on a compliant bamboo pole.

Compliant walking appears metabolically advantageous at extreme step lengths

BACKGROUND

Humans alter gait in response to unusual gait circumstances to accomplish the task of walking. For instance, subjects spontaneously increase leg compliance at a step length threshold as step length increases. Here we test the hypothesis that this transition occurs based on the level of energy expenditure, where compliant walking becomes less energetically demanding at long step lengths.

RESEARCH QUESTION

To map and compare the metabolic cost of normal and compliant walking as step length increases.

METHODS

10 healthy individuals walked on a treadmill using progressively increasing step lengths (100%, 120%, 140% and 160% of preferred step length), in both normal and compliant leg walking as energy expenditure was recorded via indirect calorimetry. Leg compliance was controlled by lowering the center-of-mass trajectory during stance, forcing the leg to flex and extend as the body moved over the foot contact.

RESULTS

For normal step lengths, compliant leg walking was more costly than normal walking gait, but compliant leg walking energetic cost did not increase as rapidly for longer step lengths. This led to an intersection between normal and compliant walking cost curves at 114% relative step length (regression analysis; r² = 0.92 for normal walking; r² = 0.65 for compliant walking).

SIGNIFICANCE

Compliant leg walking is less energetically demanding at longer step lengths where a spontaneous shift to compliant walking has been observed, suggesting the human motor control system is sensitive to energetic requirements and will employ alternate movement patterns if advantageous strategies are available. The transition could be attributed to the interplay between (i) leg work controlling body travel during single stance and (ii) leg work to control energy loss in the step-to-step transition. Compliant leg walking requires more stance leg work at normal step lengths, but involves less energy loss at the step-to-step transition for very long steps.

Minimally Actuated Walking: Identifying Core Challenges to Economical Legged Locomotion Reveals Novel Solutions

Terrestrial organisms adept at locomotion employ strut-like legs for economical and robust movement across the substrate. Although it is relatively easy to observe and analyze details of the solutions these organic systems have arrived at, it is not as easy to identify the problems these movement strategies have solved. As such, it is useful to investigate fundamental challenges that effective legged locomotion overcomes in order to understand why the mechanisms employed by biological systems provide viable solutions to these challenges. Such insight can inform the design and development of legged robots that may eventually match or exceed animal performance. In the context of human walking, we apply control optimization as a design strategy for simple bipedal walking machines with minimal actuation. This approach is used to discuss key facilitators of energetically efficient locomotion in simple bipedal walkers. Furthermore, we extrapolate the approach to a novel application-a theoretical exoskeleton attached to the trunk of a human walker-to demonstrate how coordinated efforts between bipedal actuation and a machine oscillator can potentially alleviate a meaningful portion of energetic exertion associated with leg function during human walking.

Biomechanics and energetics of walking on uneven terrain

Walking on uneven terrain is more energetically costly than walking on smooth ground, but the biomechanical factors that contribute to this increase are unknown. To identify possible factors, we constructed an uneven terrain treadmill that allowed us to record biomechanical, electromyographic and metabolic energetics data from human subjects. We hypothesized that walking on uneven terrain would increase step width and length variability, joint mechanical work and muscle co-activation compared with walking on smooth terrain. We tested healthy subjects (N=11) walking at 1.0 m s(-1), and found that, when walking on uneven terrain with up to 2.5 cm variation, subjects decreased their step length by 4% and did not significantly change their step width, while both step length and width variability increased significantly (22 and 36%, respectively; P<0.05). Uneven terrain walking caused a 28 and 62% increase in positive knee and hip work, respectively, and a 26% greater magnitude of negative knee work (0.0106, 0.1078 and 0.0425 J kg(-1), respectively; P<0.05). Mean muscle activity increased in seven muscles in the lower leg and thigh (P<0.05). These changes caused overall net metabolic energy expenditure to increase by 0.73 W kg(-1) (28%; P<0.0001). Much of that increase could be explained by the increased mechanical work observed at the knee and hip. Greater muscle co-activation could also contribute to increased energetic cost but to unknown degree. The findings provide insight into how lower limb muscles are used differently for natural terrain compared with laboratory conditions.

Redirection of center-of-mass velocity during the step-to-step transition of human walking

Simple dynamic walking models based on the inverted pendulum predict that the human body's center of mass (COM) moves along an arc during each step, with substantial work performed to redirect the COM velocity in the step-to-step transition between arcs. But humans do not keep the stance leg perfectly straight and need not redirect their COM velocity precisely as predicted. We therefore tested a pendulum-based model against a wide range of human walking data. We examined COM velocity and work data from normal human subjects (N=10) walking at 24 combinations of speed (0.75 to 2.0 m s(-1)) and step length. These were compared against model predictions for the angular redirection of COM velocity and the work performed on the COM during redirection. We found that the COM is redirected through angular changes increasing approximately linearly with step length (R(2)=0.68), with COM work increasing with the squared product of walking speed and step length (R(2)=0.82), roughly in accordance with a simple dynamic walking model. This model cannot, however, predict the duration of COM redirection, which we quantified with two empirical measures, one based on angular COM redirection and the other on work. Both indicate that the step-to-step transition begins before and ends after double support and lasts about twice as long - approximately 20-27% of a stride. Although a rigid leg model can predict trends in COM velocity and work, the non-rigid human leg performs the step-to-step transition over a duration considerably exceeding that of double support.

Correlation of symmetrical gaits and whole body mechanics: debunking myths in locomotor biodynamics

Independent maturation of gait (Hildebrand) and whole body mechanics (Cavagna et al.) traditions in locomotor analyses has led to conflicting terminology. Re-evaluation of these traditions yields three primary insights. First, walking and running should be recognized by their fundamentally different mechanics. Because duty factor fails to consistently distinguish these mechanics, its use in discriminating walks from runs should be abandoned in preference to parameters that more accurately reflect the movements of the center of mass (COM; phase difference in external mechanical energy or Froude number). Second, "trot" should be reserved as a descriptor of a particular footfall pattern. This and all gait terms lack explicit information about limb compliance and thus COM movements. Third, symmetrical gait definitions should be broadened to reflect the four primary footfall patterns: the lateral-couplet dominated pattern of the pace, the diagonal-couplet dominated pattern of the trot and the more independent sequencing of footfalls of the two singlefoots. Intermediate gaits (perennially confusing and a mouthful to pronounce) are thereby subsumed by these four discrete gaits. Confusion between gait terminologies would be avoided if limb phase were consistently reported.

Locomotor mechanics of the tölt in Icelandic horses

OBJECTIVE

To evaluate the locomotor mechanics of the tölt in Icelandic horses.

ANIMALS

10 adult Icelandic horses with no history of lameness.

PROCEDURES

Force platform data were captured for 27 trials for horses ridden at a tölt in a lateral sequence single-foot gait at a steady speed from 0.89 to 5.98 m/s. Simultaneous kinematic data were obtained by tracking retroflective markers overlying the right fore- and hind limbs. These kinetic and kinematic data were combined to evaluate 3 mechanical approaches, duty factor, Froude number, and center of mass (COM) mechanics, and to evaluate the capacity to recover mechanical energies during tölting via inverse pendulum and spring-mass (bouncing) mechanics.

RESULTS

Tölting horses had in-phase fluctuations of gravitational potential and kinetic energies of their COM and a capacity to recover mechanical energy through elastic recoil of spring elements in their limbs. These characteristics, along with Froude numbers exceeding values expected for the walk-run transition, are indicative of bouncing mechanics and, hence, most strongly ally tölting with running. Only the footfall pattern of a lateral sequence single-foot gait and low vertical excursions of the COM are more commonly associated with walking.

CONCLUSIONS AND CLINICAL RELEVANCE

At the tölt, horses have unique mechanical characteristics that should be understood for veterinary care. Differences in interlimb coordination between tölting and trotting mask the overall similarities in most other aspects of their locomotor dynamics.

Computer optimization of a minimal biped model discovers walking and running

Although people's legs are capable of a broad range of muscle-use and gait patterns, they generally prefer just two. They walk, swinging their body over a relatively straight leg with each step, or run, bouncing up off a bent leg between aerial phases. Walking feels easiest when going slowly, and running feels easiest when going faster. More unusual gaits seem more tiring. Perhaps this is because walking and running use the least energy. Addressing this classic conjecture with experiments requires comparing walking and running with many other strange and unpractised gaits. As an alternative, a basic understanding of gait choice might be obtained by calculating energy cost by using mechanics-based models. Here we use a minimal model that can describe walking and running as well as an infinite variety of other gaits. We use computer optimization to find which gaits are indeed energetically optimal for this model. At low speeds the optimization discovers the classic inverted-pendulum walk, at high speeds it discovers a bouncing run, even without springs, and at intermediate speeds it finds a new pendular-running gait that includes walking and running as extreme cases.