Methods of Estimating Foot Power and Work in Standing Vertical Jump.

Experimental motion capture studies have commonly considered the foot as a single rigid body even though the foot contains 26 bones and 30 joints. Various methods have been applied to study rigid body deviations of the foot. This study compared 3 methods: distal foot power (DFP), foot power imbalance (FPI), and a 2-segment foot model to study foot power and work in the takeoff phase of standing vertical jumps. Six physically active participants each performed 6 standing vertical jumps from a starting position spanning 2 adjacent force platforms to allow ground reaction forces acting on the foot to be divided at the metatarsophalangeal (MTP) joints. Shortly after movement initiation, DFP showed a power absorption phase followed by a power generation phase. FPI followed a similar pattern with smaller power absorption and a larger power generation compared to DFP. MTP joints primarily generated power in the 2-segment model. The net foot work was -4.0 (1.0) J using DFP, 1.8 (1.1) J using FPI, and 5.1 (0.5) J with MTP. The results suggest that MTP joints are only 1 source of foot power and that differences between DFP and FPI should be further explored in jumping and other movements.

Theoretical justification for distal foot power equation.

The distal foot power equation is a simple yet powerful tool for estimating the power dissipation or generation within the foot even while modeling it as a rigid body. It was introduced over two decades ago, but has seen a resurgence of use in recent years. Nevertheless, the theoretical justification for this formula has thus far been limited. It is difficult to properly use any equation and interpret the results from analyses using it without a solid understanding of how it is derived as well as its underlying assumptions. In this communication, a thorough derivation of the distal foot power equation is provided first for the case where the foot is interacting with a rigid ground without sliding and then second generalized for situations when the foot may slide relative to a deformable ground surface. For the first case, the derivation makes clear that distal foot power represents the power due to the deviation of the foot from a rigid body state for the portion of the foot between its mass center (or other point of reference) and the center of pressure. For the second case, distal foot power represents not only the internal deformation power of the foot, but also the power due to sliding of the foot on the ground and the power due to deformation of the ground near the point of contact.

Effect of arm motion on standing lateral jumps.

The role of arm swing in jumping has been examined in numerous studies of standing jumps for height and forward distance, but no prior studies have explored its effect on lateral jumping. The purpose of the present study was to investigate the effect of arm motion on standing lateral jump performance and to examine the biomechanical mechanisms that may explain differences in jump distance. Six participants executed a series of jumps for maximum lateral distance from two in-ground force platforms for two jump cases (free and restricted arms) while an eight-camera, passive-reflector, motion capture system collected 3D position data throughout the movements. Inverse kinematics and dynamics analyses were performed for all jumps using three-dimensional (3D) link models to calculate segment angular velocities, joint moments, joint powers, and joint work. Free arm motion improved standing lateral jump performance by 29% on average. This improvement was due to increased takeoff velocity and improved lateral and vertical positions of the center of gravity (CG) at takeoff and touchdown. Improved velocity and position of the CG at takeoff resulted from a 33% increase in the work done by the body. This increase in work in free arm jumps compared to restricted arm jumps was found in both upper and lower body joints with the largest improvements (>30 J) occurring at the lower back, right hip, and right shoulder.

Exploration of the validity of the two-dimensional sagittal plane assumption in modeling the standing long jump.

Most previous standing long jump studies have been based on the assumption of two-dimensional sagittal plane motion with bilateral symmetry. The purpose of this study was to investigate the validity of this assumption. Standing long jump trials were collected using six adult male participants. Each participant stood with a foot on each of two force plates and performed eight standing long jumps for maximal distance. Inverse dynamics analyses were performed for two-dimensional (2D) and three-dimensional (3D) models, and joint moments, powers, and work values were compared. The differences between these models with respect to the validity of the common planar jumping assumption were analyzed. Good agreement was observed between 2D and 3D methods for the lower body, with minimal differences in sagittal plane moments, power, and work for the ankle, knee, and lower back. There were significant, but relatively small differences in the sagittal plane kinematics and kinetics at the hip. For the upper body, the results contradicted the sagittal plane assumption in that significant moments and power were generated about the abduction/adduction axis of the shoulder and a similar amount of work was performed about both abduction/adduction and flexion/extension axes of the shoulder. The elbow also showed significant differences in power and work. These results indicate that an assumption of planar motion should be sufficient for many studies of the standing long jump that only examine lower body movement. However, for studies that include upper body motion, diagnosing injury risk, or investigating gender differences, a 3D model may be more appropriate.

Optimal control simulations reveal mechanisms by which arm movement improves standing long jump performance.

Optimal control simulations of the standing long jump were developed to gain insight into the mechanisms of enhanced performance due to arm motion. The activations that maximize standing long jump distance of a joint torque actuated model were determined for jumps with free and restricted arm movement. The simulated jump distance was 40 cm greater when arm movement was free (2.00 m) than when it was restricted (1.60 m). The majority of the performance improvement in the free arm jump was due to the 15% increase (3.30 vs. 2.86 m/s) in the take-off velocity of the center of gravity. Some of the performance improvement in the free arm jump was attributable to the ability of the jumper to swing the arms backwards during the flight phase to alleviate excessive forward rotation and position the body segments properly for landing. In restricted arm jumps, the excessive forward rotation was avoided by "holding back" during the propulsive phase and reducing the activation levels of the ankle, knee, and hip joint torque actuators. In addition, swinging the arm segments allowed the lower body joint torque actuators to perform 26 J more work in the free arm jump. However, the most significant contribution to developing greater take-off velocity came from the additional 80 J work done by the shoulder actuator in the jump with free arm movement.

Role of arm motion in the standing long jump.

The role of arm motion on the performance of the standing long jump was investigated. Three males performed a series of jumps with free (JFA) and with restricted (JRA) arm motion to determine if arm swing improves jumping distance. The subjects jumped off a force platform and the motion of the body segments were recorded with a four-camera, passive motion-capture system. Jumping performance was defined as the horizontal displacement of the toe between the initial and landing (TD) positions. The subjects jumped 21.2% further on an average with arm movement (2.09+/-0.03 m) than without (1.72+/-0.03 m). Seventy-one percent of the increase in performance in JFA was attributable to a 12.7% increase in the take-off (TO) velocity of the center of gravity (CG). Increases in the horizontal displacement of the CG before TO and in the horizontal position of the toe with respect to the CG at TD accounted for the remaining 29% of the improvement in jumping distance. The added balance and control provided by the arms throughout the jumping motion contributed to performance improvement in JFA. The subjects were able to remedy excessive forward rotation about the CG by swinging the arms backwards during the flight phase. Without the freedom to swing the arms during flight, the subjects had to eliminate any excessive forward rotation while still in contact with the ground. This tendency in JRA was manifest in the premature decline in the vertical ground reaction force (VGRF) and the development of a counterproductive backward-rotating moment about the CG just before TO.