Recent advances in integrative studies of locomotion have revealed several general principles. Energy storage and exchange mechanisms discovered in walking and running bipeds apply to multilegged locomotion and even to flying and swimming. Nonpropulsive lateral forces can be sizable, but they may benefit stability, maneuverability, or other criteria that become apparent in natural environments. Locomotor control systems combine rapid mechanical preflexes with multimodal sensory feedback and feedforward commands. Muscles have a surprising variety of functions in locomotion, serving as motors, brakes, springs, and struts. Integrative approaches reveal not only how each component within a locomotor system operates but how they function as a collective whole.

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A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal's leg sti¡ness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg sti¡ness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered di¡erent surfaces in the natural world. We found that human runners adjust their leg sti¡ness to accommodate changes in surface sti¡ness, allowing them to maintain similar running mechanics on di¡erent surfaces. These results provide important insight into the mechanics and control of animal locomotion and suggest that incorporating an adjustable leg sti¡ness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.

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When humans hop in place or run forward, leg stiffness is increased to offset reductions in surface stiffness, allowing the global kinematics and mechanics to remain the same on all surfaces. The purpose of the present study was to determine the mechanism for adjusting leg stiffness. Seven subjects hopped in place on surfaces of different stiffnesses (23-35,000 kN/m) while force platform, kinematic, and electromyographic data were collected. Leg stiffness approximately doubled between the most stiff surface and the least stiff surface. Over the same range of surfaces, ankle torsional stiffness increased 1.75-fold, and the knee became more extended at the time of touchdown (2.81 vs. 2.65 rad). We used a computer simulation to examine the sensitivity of leg stiffness to the observed changes in ankle stiffness and touchdown knee angle. Our model consisted of four segments (foot, shank, thigh, head-arms-trunk) interconnected by three torsional springs (ankle, knee, hip). In the model, an increase in ankle stiffness 1.75-fold caused leg stiffness to increase 1.7-fold. A change in touchdown knee angle as observed in the subjects caused leg stiffness to increase 1.3-fold. Thus both joint stiffness and limb geometry adjustments are important in adjusting leg stiffness to allow similar hopping on different surfaces.

The storage and recovery of elastic energy in muscle-tendon springs is important in running, hopping, trotting, and galloping. We hypothesized that animals select the stride frequency at which they behave most like simple spring-mass systems. If higher or lower frequencies are used, they will not behave like simple spring-mass systems, and the storage and recovery of elastic energy will be reduced. We tested the hypothesis by having humans hop forward on a treadmill over a range of speeds and hop in place over a range of frequencies. The body was modeled as a simple spring-mass system, and the properties of the spring were measured by use of a force platform. Our subjects used nearly the same frequency (the "preferred frequency," 2.2 hops/s) when they hopped forward on a treadmill and when they hopped in place. At this frequency, the body behaved like a simple spring-mass system. Contrary to our predictions, it also behaved like a simple spring-mass system when the subjects hopped at higher frequencies, up to the maximum they could achieve. However, at the higher frequencies, the time available to apply force to the ground (the ground contact time) was shorter, perhaps resulting in a higher cost of generating muscular force. At frequencies below the preferred frequency, as predicted by the hypothesis, the body did not behave in a springlike manner, and it appeared likely that the storage and recovery of elastic energy was reduced. The combination of springlike behavior and a long ground contact time at the preferred frequency should minimize the cost of generating muscular force.

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When mammals run, the overall musculoskeletal system behaves as a single linear "leg spring". We used force platform and kinematic measurements to determine whether leg spring stiffness (k(leg)) is adjusted to accommodate changes in surface stiffness (ksurf) when humans hoop in place, a good experimental model for examining adjustments to k(leg) in bouncing gaits. We found that k(leg) was greatly increased to accommodate surfaces of lower stiffnesses. The series combination of k(leg) and ksurf [total stiffness (ktot)] was independent of ksurf at a given hopping frequency. For example, when humans hopped at a frequency of 2 Hz, they tripled their k(leg) on the least stiff surface (ksurf = 26.1 kN/m; k(leg) = 53.3 kN/m) compared with the most stiff surface (ksurf = 35,000 kN/m; k(leg) = 17.8 kN/m). Values for ktot were not significantly different on the least stiff surface (16.7 kN/m) and the most stiff surface (17.8 kN/m). Because of the k(leg) adjustment, many aspects of the hopping mechanics (e.g., ground-contact time and center of mass vertical displacement) remained remarkably similar despite a > 1,000-fold change in ksurf. This study provides insight into how k(leg) adjustments can allow similar locomotion mechanics on the variety of terrains encountered by runners in the natural world.