A simple strategy for jumping straight up

Jumping from a stationary standing position into the air is a transition from a constrained motion in contact with the ground to an unconstrained system not in contact with the ground. A simple case of the jump, as it applies to humans, robots and humanoids, is studied in this paper. The dynamics of the constrained rigid body are expanded to define a larger system that accommodates the jump. The formulation is applied to a four-link, three-dimensional system in order to articulate the ballistic motion involved. The activity of the muscular system and the role of the major sagittal muscle groups are demonstrated. The control strategy, involving state feedback and central feed forward signals, is formulated and computer simulations are presented to assess the feasibility of the formulations, the strategy and the jump.     

The effect of drop jump starting height and contact time on power, work performed, and moment of force

The purposes of this study are (a) to examine the effects of contact time manipulation on jump parameters and (b) to examine the interaction between starting height changes and contact time changes on important jump parameters. Fifteen male athletes performed a series of drop jumps from heights of 20, 40, and 60 cm. The instructions given to the subjects were (a) "jump as high as you can" and (b) "jump high a little faster than your previous jump." Jumps were performed at each height until the athlete could not achieve a shorter ground contact time. The data were divided into 5 groups where group 1 was made up of the longest ground contact times of each athlete and groups 2-4 were composed of progressively shorter contact times, with group 5 having the shortest contact times. The jumps of group 3 produced the highest maximum and mean mechanical power (p <0.05) during the positive phase of the drop jumps regardless of starting jump height. The vertical takeoff velocities for the first 3 groups did not show significant (p < 0.05) differences. These results indicate that the manipulation of jump technique plays larger role than jump height in the manipulation of important jump parameters.     

Firing statistics of inhibitory neuron with delayed feedback. I. Output ISI probability density

Activity of inhibitory neuron with delayed feedback is considered in the framework of point stochastic processes. The neuron receives excitatory input impulses from a Poisson stream, and inhibitory impulses from the feedback line with a delay. We investigate here, how does the presence of inhibitory feedback affect the output firing statistics. Using binding neuron (BN) as a model, we derive analytically the exact expressions for the output interspike intervals (ISI) probability density, mean output ISI and coefficient of variation as functions of model's parameters for the case of threshold 2. Using the leaky integrate-and-fire (LIF) model, as well as the BN model with higher thresholds, these statistical quantities are found numerically. In contrast to the previously studied situation of no feedback, the ISI probability densities found here both for BN and LIF neuron become bimodal and have discontinuity of jump type. Nevertheless, the presence of inhibitory delayed feedback was not found to affect substantially the output ISI coefficient of variation. The ISI coefficient of variation found ranges between 0.5 and 1. It is concluded that introduction of delayed inhibitory feedback can radically change neuronal output firing statistics. This statistics is as well distinct from what was found previously (Vidybida and Kravchuk, 2009) by a similar method for excitatory neuron with delayed feedback.     

Neuromechanical strategies employed to increase jump height during the initiation of the squat jump.

The maximal height attained in a vertical jump is heavily influenced by the execution of a large countermovement prior to the upward motion. When a jump must be executed without a countermovement, as in a squat jump, the maximal jump height is reduced. During such conditions, the human body may use other strategies in order to increase performance. The purpose of this research was to investigate the effects of two strategies employed during the initiation of the squat jump: the premovement silent period (PSP), and the small amplitude countermovement (SACM). Fifteen elite male volleyball players (20.6 +/- 1.6 years) and 13 untrained males (20.2 +/- 1.7 years) performed 10 maximal effort squat jumps from identical starting positions. The electromyographic activity of the vastus lateralis and biceps femoris was measured in conjunction with the vertical ground reaction force and vertical displacement. It was found that the presence of a PSP or a SACM of 1-3 cm did not increase maximal squat jump height significantly (p > 0.05), in neither the highly trained athletes nor the untrained individuals. These results suggest that these strategies do not play a major role in the determination of jump height. Researchers have assumed that a squat jump is purely concentric, and that there are no facilitating mechanisms present that may influence the performance of the jump. This study provides evidence to support this assumption.     

Models of dispersal in biological systems

In order to provide a general framework within which the dispersal of cells or organisms can be studied, we introduce two stochastic processes that model the major modes of dispersal that are observed in nature. In the first type of movement, which we call the position jump or kangaroo process, the process comprises a sequence of alternating pauses and jumps. The duration of a pause is governed by a waiting time distribution, and the direction and distance traveled during a jump is fixed by the kernel of an integral operator that governs the spatial redistribution. Under certain assumptions concerning the existence of limits as the mean step size goes to zero and the frequency of stepping goes to infinity the process is governed by a diffusion equation, but other partial differential equations may result under different assumptions. The second major type of movement leads to what we call a velocity jump process. In this case the motion consists of a sequence of runs separated by reorientations, during which a new velocity is chosen. We show that under certain assumptions this process leads to a damped wave equation called the telegrapher's equation. We derive explicit expressions for the mean squared displacement and other experimentally observable quantities. Several generalizations, including the incorporation of a resting time between movements, are also studied. The available data on the motion of cells and other organisms is reviewed, and it is shown how the analysis of such data within the framework provided here can be carried out.Supported in part by NIH Grant #GM 29123 and by NSF Grant #DMS-8301840Supported in part by NSF Grant #DMS-8301840Supported in part by the DFG Heisenberg Program     

Glycerolipids: common features of molecular motion in bilayers

In the present study, analysis of 2H NMR line-shape and spin-lattice relaxation behavior has been used to investigate the dynamics of several glycolipid and phospholipid bilayers. The gel-phase spectra of these lipids labeled at the C3 position of the glycerol backbone are broad (approximately 90 kHz) and characteristic of fast-limit axially asymmetric motion. Moreover, anisotropic spin-lattice relaxation is observed in all of these systems. The line-shape and relaxation features of the lipids in the gel phase were best simulated by using a fast-limit three-site jump model, with relative site populations of 0.46, 0.34, and 0.20. This motion is associated with an internal jump about the C2-C3 bond of the glycerol backbone. A second motion, rotation about the long axis of the molecule, is needed to account for the observed temperature dependence of the quadrupolar echo amplitude and the spectral line shape above and below the gel to liquid-crystalline phase transition temperature. On the other hand, the gel-phase spectra of phospholipids labeled at the C2 position of the glycerol backbone are also characterized by a fast internal motion, which is simulated by a two-site librational jump. The results indicate that the glycerol backbone dynamics of the glycolipid and phospholipid systems investigated in this study can be described in terms of common fast internal motions and a slower whole molecule axial motion. These results are compared with previous dynamic studies of similar systems.     

The relationship between joint strength and standing vertical jump performance

The effect of joint strengthening on standing vertical jump height is investigated by computer simulation. The human model consists of five rigid segments representing the feet, shanks, thighs, HT (head and trunk), and arms. Segments are connected by frictionless revolute joints and model movement is driven by joint torque actuators. Each joint torque is the product of maximum isometric torque and three variable functions of instantaneous joint angle, angular velocity, and activation level, respectively. Jumping movements starting from a balanced initial posture and ending at takeoff are simulated. A matching simulation reproducing the actual jumping movement is generated by optimizing joint activation level. Simulations with the goal of maximizing jump height are repeated for varying maximum isometric torque of one joint by up to +/-20% while keeping other joint strength values unchanged. Similar to previous studies, reoptimization of activation after joint strengthening is necessary for increasing jump height. The knee and ankle are the most effective joints in changing jump height (by as much as 2.4%, or 3 cm). For the same amount of percentage increase/decrease in strength, the shoulder is the least effective joint (which changes height by as much as 0.6%), but its influence should not be overlooked.     

Initiation of walk and tiptoe of a planar nine-link biped

A nine-link planar biped model is studied. Its nonlinear differential equations are derived. Constraints due to the connections of the links and the contact between the model and the ground are analyzed, and forces of constraint are specified as functions of the state and inputs. With large external forces acting on the model, connection constraints are maintained by the ligaments and other soft tissue structures. It is shown that ligamentious structures contribute to the stability of the system and help maintain the integrity of the joint. By using linear feedback control, the nine-link model is stabilized around the vertical stance. The stable motion of the system in the vicinity of the vertical is studied by computer simulation of walking and tiptoe gaits.     

Analytical and multibody modeling for the power analysis of standing jumps

Two methods for the power analysis of standing jumps are proposed and compared in this article. The first method is based on a simple analytical formulation which requires as input the coordinates of the center of gravity in three specified instants of the jump. The second method is based on a multibody model that simulates the jumps processing the data obtained by a three-dimensional (3D) motion capture system and the dynamometric measurements obtained by the force platforms. The multibody model is developed with OpenSim, an open-source software which provides tools for the kinematic and dynamic analyses of 3D human body models. The study is focused on two of the typical tests used to evaluate the muscular activity of lower limbs, which are the counter movement jump and the standing long jump. The comparison between the results obtained by the two methods confirms that the proposed analytical formulation is correct and represents a simple tool suitable for a preliminary analysis of total mechanical work and the mean power exerted in standing jumps.     

Explanation of the bilateral deficit in human vertical squat jumping.

In the literature, it has been reported that the mechanical output per leg is less in two-leg jumps than in one-leg jumps. This so-called bilateral deficit has been attributed to a reduced neural drive to muscles in two-leg jumps. The purpose of the present study was to investigate the possible contribution of nonneural factors to the bilateral deficit in jumping. We collected kinematics, ground reaction forces, and electromyograms of eight human subjects performing two-leg and one-leg (right leg) squat jumps and calculated mechanical output per leg. We also used a model of the human musculoskeletal system to simulate two-leg and one-leg jumps, starting from the initial position observed in the subjects. The model had muscle stimulation as input, which was optimized using jump height as performance criterion. The model did not incorporate a reduced maximal neural drive in the two-leg jump. Both in the subjects and in the model, the work of the right leg was more than 20% less in the two-leg jump than in the one-leg jump. Peak electromyogram levels in the two-leg jump were reduced on average by 5%, but the reduction was only statistically significant in m. rectus femoris. In the model, approximately 75% of the bilateral deficit in work per leg was explained by higher shortening velocities in the two-leg jump, and the remainder was explained by lower active state of muscles. It was concluded that the bilateral deficit in jumping is primarily caused by the force-velocity relationship rather than by a reduction of neural drive.     

Bound ligand motion in crystalline carboxypeptidase A.

Deuterium NMR spectra for the phenyl ring deuterons have been obtained for D-phenylalanine, L-phenylalanine, phenylacetic acid, and phenyl propionic acid in randomly oriented crystals of carboxypeptidase A as a function of water content. The spectra are analyzed using a two-site jump model for phenyl ring pi-flips when the ligand is bound to the protein, and the model includes the possibility that the ligand may exchange with isotropic or unbound environments within the crystal. Although the binding pocket may impose local dynamical constraints, a complete pi-flip motion is consistent with the spectra of all ligands at all water contents. The rate constants for the pi-flip at 298 K are found to be 7.5 x 10(5) S-1, 1.9 x 10(6) S-1, 4.0 x 10(6) S-1, and 4.0 x 10(6) S-1 for L-phenylalanine, D-phenylalanine, phenyl propionic acid, and phenylacetic acid, respectively, at water activity of 0.98. The pi-flip rate for the ligand bound to the enzyme increases with water content. Assuming that the activation barrier may be written, delta G+2 = delta G+2o + baw, where aw is the water activity, and the value of b is -1.9 kcal/mol for phenylacetic acid and phenyl propionic acid, -1.3 kcal/mol for L-phenylalanine, and -2.1 kcal/mol for D-phenylalanine. Phenylacetic acid crystals were studied as an example of a phenyl ring motion that is highly constrained by a known and symmetrical packing environment. The deuterium spectra are complex and are not consistent with pi-flip motions, but they are consistent with a superposition of ring jump motions of 24 degrees, 34 degrees, and 72 degrees, with probabilities in the ratio of 1:1:2. Because of the limited space for motion imposed by the tight packing in the crystal, these motions must be highly cooperative and probably locally coherent; however, the spectra by themselves do not prove this intuitively reasonable hypothesis.     

Neural Mechanisms of Cortical Motion Computation Based on a Neuromorphic Sensory System

The visual cortex analyzes motion information along hierarchically arranged visual areas that interact through bidirectional interconnections. This work suggests a bio-inspired visual model focusing on the interactions of the cortical areas in which a new mechanism of feedforward and feedback processing are introduced. The model uses a neuromorphic vision sensor (silicon retina) that simulates the spike-generation functionality of the biological retina. Our model takes into account two main model visual areas, namely V1 and MT, with different feature selectivities. The initial motion is estimated in model area V1 using spatiotemporal filters to locally detect the direction of motion. Here, we adapt the filtering scheme originally suggested by Adelson and Bergen to make it consistent with the spike representation of the DVS. The responses of area V1 are weighted and pooled by area MT cells which are selective to different velocities, i.e. direction and speed. Such feature selectivity is here derived from compositions of activities in the spatio-temporal domain and integrating over larger space-time regions (receptive fields). In order to account for the bidirectional coupling of cortical areas we match properties of the feature selectivity in both areas for feedback processing. For such linkage we integrate the responses over different speeds along a particular preferred direction. Normalization of activities is carried out over the spatial as well as the feature domains to balance the activities of individual neurons in model areas V1 and MT. Our model was tested using different stimuli that moved in different directions. The results reveal that the error margin between the estimated motion and synthetic ground truth is decreased in area MT comparing with the initial estimation of area V1. In addition, the modulated V1 cell activations shows an enhancement of the initial motion estimation that is steered by feedback signals from MT cells.     

Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics

To establish the relationship between locomotory behavior and dynamics of neural circuits in the nematode C. elegans we combined molecular and theoretical approaches. In particular, we quantitatively analyzed the motion of C. elegans with defective synaptic GABA and acetylcholine transmission, defective muscle calcium signaling, and defective muscles and cuticle structures, and compared the data with our systems level circuit model. The major experimental findings are: (1) anterior-to-posterior gradients of body bending flex for almost all strains both for forward and backward motion, and for neuronal mutants, also analogous weak gradients of undulatory frequency, (2) existence of some form of neuromuscular (stretch receptor) feedback, (3) invariance of neuromuscular wavelength, (4) biphasic dependence of frequency on synaptic signaling, and (5) decrease of frequency with increase of the muscle time constant. Based on (1) we hypothesize that the Central Pattern Generator (CPG) is located in the head both for forward and backward motion. Points (1) and (2) are the starting assumptions for our theoretical model, whose dynamical patterns are qualitatively insensitive to the details of the CPG design if stretch receptor feedback is sufficiently strong and slow. The model reveals that stretch receptor coupling in the body wall is critical for generation of the neuromuscular wave. Our model agrees with our behavioral data (3), (4), and (5), and with other pertinent published data, e.g., that frequency is an increasing function of muscle gap-junction coupling. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Program and feedback in the systems organization of a motor act

After simultaneous visual dereceptation, aimed jumps in cats, reinforced by electric shocks, are restored, while those with food reward are irreversibly lost. Yet, after a two-stage dereceptation, the aimed jumps reappeared even in case when they had food reinforcement. The adequacy of their performance depended on the stability of the distance between the starting sites. The possibility of local cortical control of motor units was demonstrated which is considered as a component of the general mechanism of urgent identification of the motor system state, via somatic afferent pathways. The ablation of their higher link (the medial lemniscus) at the level where it enters the thalamus, disturbs the biomechanics of the aimed jump, increasing the number of multisensory responses of single sensorimotor cortical units. It is suggested that the motivation and the program of the movement corrected by feedback, provide for its adaptive character.     

CPG Control for Biped Hopping Robot in Unpredictable Environment

A CPG control mechanism is proposed for hopping motion control of biped robot in unpredictable environment.Based on analysis of robot motion and biological observation of animal's control mechanism,the motion control task is divided into two simple parts:motion sequence control and output force control.Inspired by a two-level CPG model,a two-level CPG control mechanism is constructed to coordinate the drivers of robot joint,while various feedback information are introduced into the control mechanism.Interneurons within the control mechanism are modeled to generate motion rhythm and pattern promptly for motion sequence control; motoneurons are modeled to control output forces of joint drivers in real time according to feedbacks.The control system can perceive changes caused by unknown perturbations and environment changes according to feedback information,and adapt to unpredictable environment by adjusting outputs of neurons.The control mechanism is applied to a biped hopping robot in unpredictable environment on simulation platform,and stable adaptive motions are obtained.     

Individual flight styles in ski jumping: results obtained during Olympic Games competitions

From the physics point of view, the jump length in ski jumping depends on: the in-run velocity v(0), the velocity perpendicular to the ramp v(p0) due to the athlete's jumping force, the lift and drag forces acting during take-off and during the flight, and the weight of the athlete and his equipment. The aerodynamic forces are a function of the flight position and of the equipment features. They are a predominant performance factor and can largely be influenced by the athlete. The field study conducted during the Olympic Games competitions 2002 at Park City (elevation: 2000 m) showed an impressive ability of the Olympic medallists to reproduce their flight style and remarkable differences between different athletes have been found. The aerodynamic forces are proportional to the air density. Elite athletes are able to adapt their flight style to thin air conditions in order to maximise jump length and to keep the flight stable. The effects of flight position variations on the performance have been analysed by means of a computer model which is based on the equations of motion and on wind tunnel data corresponding to the flight positions found in the field. Athletes have to solve extremely difficult optimisation problems within fractions of a second. The computer simulation can be used as a reliable starting point for the improvement of training methods and gives an insight into the "implicit" knowledge of physics that the ski jumping athlete must have available for a good performance.     

Countermovement strategy changes with vertical jump height to accommodate feasible force constraints

In this study, we developed a curve-fit model of countermovement dynamics and examined whether the characteristics of a countermovement jump can be quantified using the model parameter and its scaling; we expected that the model-based analysis would facilitate an understanding of the basic mechanisms of force reduction and propulsion with a simplified framework of the center of mass (CoM) mechanics. Ten healthy young subjects jumped straight up to five different levels ranging from approximately 10% to 35% of their body heights. The kinematic and kinetic data on the CoM were measured using a force plate system synchronized with motion capture cameras. All subjects generated larger vertical forces compared with their body weights from the countermovement and sufficiently lowered their CoM position to support the work performed by push-off as the vertical elevations became more challenging. The model simulation reasonably reproduced the trajectories of vertical force during the countermovement, and the model parameters were replaced by linear and polynomial regression functions in terms of the vertical jump height. Gradual scaling trends of the individual model parameters were observed as a function of the vertical jump height with different degrees of scaling, depending on the subject. The results imply that the subjects may be aware of the jumping dynamics when subjected to various vertical jump heights and may select their countermovement strategies to effectively accommodate biomechanical constraints, i.e., limited force generation for the standing vertical jump.     

Molecular motions and dynamics of a diunsaturated acyl chain in a lipid bilayer: implications for the role of polyunsaturation in biological membranes.

The nature and dynamics of the motions of a diunsaturated fatty acyl chain in a lipid bilayer were examined using a comprehensive simulation program for 2H NMR line shapes developed by Wittebort et al. [Wittebort, R. J., Olejniczak, E. T., & Griffin, R. G. (1987) J. Chem. Phys. 36, 5411-5420]. A motional model in which the isolinoleoyl chain (18:2 delta 6,9) adopts two conformations consistent with the low energy structures proposed for 1,4-pentadiene [Applegate, K. R., & Glomset, J. A. (1986) J. Lipid Res. 27, 658-680], but undergoes a rapid jump between these states, is sufficient to account for the experimentally observed quadrupolar couplings, the 2H-2H and 1H-2H dipolar couplings, the longitudinal relaxation times, and the changes in the average conformation of the chain that occur with a variation in temperature. The jump motion originates via rotations about the C7-C8 and the C8-C9 carbon bonds and leads to the low order parameters assigned to the C8 methylene segment (0.18) and the C9-C10 double bond (0.11). In contrast, the C6-C7 double bond, which is not involved in the two-site jump, characterized by a relatively large order parameter (0.56). Fatty acyl chains containing three or more double bonds likely cannot undergo the same jump motion and consequently will be highly ordered structures. Correlation times for diffusion of the molecular long axis of the diunsaturated acyl chain about the bilayer normal (approximately 10(-10) s) and for the local jump motion (approximately 10(-10) s) were calculated.(ABSTRACT TRUNCATED AT 250 WORDS)     

Feedback suppression of resistive wall modes in a tokamak

The possibility of feedback suppression of the external kink modes in a tokamak with a resistive wall is studied theoretically, assuming that the stabilizing conductors are located at a certain distance from the wall and without making any assumptions regarding the locations of the magnetic sensors that close the feedback circuit and the parameters (i.e., the particular components of the perturbed magnetic field or magnetic fluxes) measured by the sensors. It is shown that the efficiency of the stabilizing system can generally be analyzed within a two-parameter model. The parameters of the problem are the jump in the logarithmic derivative of the radial magnetic field in the region where the stabilizing conductors are positioned and the ratio of the minor radius of the torus on which the conductors are wound to the radius of the wall. However, specific calculations should be carried out with at least a three-parameter model: the final results should depend on the currents in the conductors and the locations of the conductors and magnetic sensors. The relation between the magnetic parameter in the criterion for the suppression of the resistive wall modes and the currents in the stabilizing conductors is clarified, and the current magnitudes required for the suppression are estimated.