Angular Trajectory Research Articles

Computer motion simulation for sagittal plane lifting activities

In ergonomics, the biomechanical approach provides estimation of various mechanical stresses acting on the body while a person manually handles an object. Although motion analysis systems are available for dynamic biomechanical analyses, the use of such systems are mostly performed in laboratory due to high cost of the equipment and the expertise required in using them. Industrial ergonomists have limited access to dynamic biomechanical analyses. This paper reports a dynamic simulation model developed for biomechanical analyses of lifting activities performed in the sagittal plane. The model simulates the dynamic motion of lifting tasks for five body joints: the elbow, shoulder, hip, knee, and ankle. The inputs of the model include initial and final joint postures; gender, weight, and height; weight of load; lifting height; and container dimensions. In the output, the angular trajectories of the five joints are predicted. The model without any video inputs predicts the motion patterns of the lift. Actual motion data were collected using 10 subjects in the laboratory for 360 lifts which included 12 lifting tasks in combination of two lifting heights, two container sizes, and three weights of load. Good results were found for the dynamic planar motion simulation model. The predicted motion pattern from the simulation closely resembles the observed motion pattern. Relevance to industry The lifting motion simulation model reported in this paper can be used to predict motions for various sagittal plane lifting tasks. The motion profiles can then be used in the dynamic biomechanical analysis without having to obtain the filmed motion. This allows field industrial ergonomists to perform better job analysis involving dynamic models.

Adaptation of center of mass control under microgravity in a whole-body lifting task

Human balance in stance is usually defined as the preservation of the vertical projection of the center of mass (COM) on the support area formed by the feet. Under microgravity conditions, the control of equilibrium seems to be no longer required. However, several reports indicate preservation of COM control in tasks such as arm or leg raising, tiptoe standing, or trunk bending. It is still unclear whether COM control is also maintained in complex multijoint movements during short term exposure to microgravity. In the current study, the dynamics of equilibrium control were studied in four subjects performing two series of seven whole-body lifting movements under microgravity during parabolic flights. The aims of the study were to examine whether the trajectory of horizontal COM motion during lifting movements changes in short-term exposure to microgravity and whether there is any sign of recovery after several lifting movements. It was found that, compared with control movements under normal gravity, the horizontal position of the COM was shifted backward during the entire lifting movement in all subjects. In the second series of lifting movements under microgravity, a partial recovery of the COM trajectory toward the normal gravity situation was found. Under microgravity, angles of the ankle, knee, hip, and lumbar joints differed significantly from the angles found under normal gravity. Recovery of joint angular trajectories in the second series of lifting movements mainly occurred for those angles that could contribute to a reduction of the backward COM shift. It is to be pointed out that COM control under microgravity is not redundant but functional. Persisting COM control under microgravity may be required for pure mechanical reasons, since rotational movements of the body are dependent on adequate control of the COM position with respect to external forces. It is shown that, from a mechanical perspective, subjects can benefit from a backward displacement of the COM in the downward as well as the upward phase of the lifting movement under microgravity.

Aerial performance of Drosophila melanogaster from populations selected for upwind flight ability.

A computerized system for three-dimensional tracking of large numbers of individual free-flying insects was used to assess the performance of Drosophila melanogaster from populations that had undergone 160 generations of selection for upwind flight ability. Compared with control lines, the selected lines showed significant increases in mean flight velocity, decreases in angular trajectory and a significant change in the interaction between velocity and angular trajectory. Maximal flight velocity was apparent as a sharply defined upper boundary of the distribution of horizontal and vertical velocity as a function of angular trajectory; this upper bound (0.85 ms-1) differed little between the selected and control lines, although individuals from the selected lines attained maximal performance levels much more frequently. Maximum induced power output was calculated directly from the product of maximum vertical velocity and body weight. This measure (28 W kg-1 muscle) was closely predicted by a scaling relationship derived from the load-lifting limits of larger insects and vertebrates, as well as tethered D. melanogaster stimulated via their optomotor reflex to produce maximal lift. These results indicate that selection for flight performance can readily alter the relative effort and/or the frequency of phenotypes capable of attaining population-wise maximal performance levels, but shows little ability to increase population-wise maximal performance.

Apparent polar wander and reversal stratigraphy of the Palaeo-Mesoproterozoic southeastern McArthur Basin, Australia

Approximately 1800 samples from volcanic, clastic and carbonate sequences of the southeastern McArthur Basin in northern Australia were analysed palaeomagnetically to define in detail the Australian apparent polar wander path (APWP) for a period centred at ∼ 1670 Ma and to develop a Proterozoic reversal stratigraphy for correlation and dating. Twelve palaeomagnetic poles are interpreted as primary, including two that are preliminary. These increase the Australian palaeomagnetic database for the Proterozoic by ∼ 30%. Another ten poles record three, or possibly four, periods of overprinting. The study also yields one of the oldest reversal records reported so far. The ten better-established primary poles were obtained from the lower three of the four main stratigraphic sub-divisions of the Basin: the Tawallah, McArthur and Nathan Groups. These poles define an angular trajectory of about 120° for a time span of at least 75 m.y., and possibly exceeding 100 m.y. They confirm earlier preliminary results that suggested a major revision of the Proterozoic APWP for Australia. The two preliminary poles were obtained from the youngest sub-division of the Basin, the Roper Group, and confirm a large age gap between the Nathan and Roper Groups. The poles for the oldest overprints were from igneous units in the Tawallah Group and appear to record metasomatism at the end of the last major period of volcanism in the basin. The pole for the next overprint falls on the path near the apex of a hairpin bend; it coincides with a likely period of rifting and high heat flow that accompanied the deposition of the upper McArthur Group. The third overprint, apparently acquired during the long time-break separating the Nathan and Roper Groups, was found mostly in red dolomitic rocks. The geomagnetic reversal record from this study represents an accumulated stratigraphic thickness of 2100 m, excluding gaps where the polarity remained undetermined because of overprinting, unstable remanences, intervals not sampled, or other causes. Reversal patterns from duplicate sections at different localities were compared for two formations, and were found to be consistent. Several parts of the reversal column appear to be distinctive enough for use in stratigraphic correlation.

Precise computation of electron-beam radiation in nonuniform magnetic fields as a tool for beam diagnostics

Visual range radiation emitted by an ultrarelativistic electron beam at bending magnet edges and within elements of the beam optics (steering magnets, quadrupole lenses, etc.) in storage rings is very sensitive to horizontal and vertical angular divergences, transverse sizes, emittances, energy, position, and trajectory tilts of the electron beam. Precise computation of the radiation intensity distributions with due regard for nonzero beam emittances, layout of storage ring magnet structure, and measurement scheme peculiarities allows one to obtain the electron-beam parameters from the measured radiation intensity distributions. The radiation computation technique and the experimental equipment adjusted for the beam diagnostics on the Siberia-1 electron storage ring are described. Experimental results on measurements of the radiation intensity distributions in the Siberia-1 ring and the corresponding electron-beam parameters determined by the method under discussion are presented.

Kinematic analysis of reaching in the cat

The present study examines the kinematic features of forelimb movements made by cats reaching for food in horizontal target wells located at different heights and distances. Wrist paths consisted of two relatively straight segments joined at a "via-point" in front of the aperture of the food well. In the initial lift phase, the paw was raised to the via-point in front of the target. In the second, or thrust phase, the paw was directed forward into the food well. During the lift, the paw was moved toward the target primarily by elbow flexion, accompanied by a sequence of biphasic shoulder and wrist movements. Thrust was accomplished primarily by shoulder flexion while the wrist and the paw were maintained at near-constant angles. The animals varied the height of the reach primarily by varying elbow flexion with proportional changes in elbow angular velocity and angular acceleration and with corresponding variations in wrist speed. Thus, cats reached for targets at different heights by scaling a common kinematic profile. Over a relatively large range of target heights, animals maintained movement duration constant, according to a simple "pulse-height" control strategy (isochronous scaling). For reaches to a given target height, animals compensated for variability in peak acceleration by variations in movement time. We examined the coordination between the shoulder and the wrist with the elbow. Early during the lift, peak shoulder extensor and peak elbow flexor accelerations were synchronized. Late during the lift phase, wrist extensor acceleration was found to occur during the period of elbow flexor deceleration. We hypothesize that these linkages could, in part, be due to passive mechanical interactions. To determine how the angular trajectories of the different joints were organized in relation to target location, we plotted joint kinematic changes directly on the wrist and MCP joint paths. These plots revealed that for all target heights and movement speeds, wrist extensor deceleration occurred at approximately the same spatial location with respect to the target. This analysis also demonstrated that the second phase of MCP flexion occurred when the paw was below the lower lip of the food well, while the subsequent extension occurred after the tip cleared this obstacle. During thrust, wrist and MCP angles were maintained, reflecting the need to align the paw within the food well. Our findings suggest that cats plan the reaching phase of prehension as a sequence of discrete movement segments, each serving a particular goal in the task, rather than as an single unit.

Moving target imaging and trajectory computation using ISAR

Novel algorithms for moving target imaging and trajectory computation using a two-receiver radar are presented. The range-bin alignment is implemented with an adaptive method using the envelope correlation feature of different returns and the angular trajectory equation is solved using a linear least squares method combined with a unique phase-unwrapping technique. The angular positions of the synthetic array elements are determined from the trajectory computation. Three target models moving along a perturbed straight line are used to verify the proposed algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Gravitational and zero-drag motion of a spheroid adjacent to an inclined plane at low Reynolds number

The first highly accurate solutions for the resistance tensor of an oblate or prolate spheroid moving near a planar wall obtained by Hsu &amp; Ganatos (1989) are used to compute the translational and angular velocities and trajectories of a neutrally buoyant spheroid in shear flow and the gravitational settling motion of a non-neutrally buoyant spheroid adjacent to an inclined plane. The neutrally buoyant spheroid in shear flow undergoes a periodical motion toward and away from the wall as it continually tumbles forward. For some orientation angles it is found that the wall actually enhances the angular velocity of the particle. For certain inclinations a spheroid settling under gravity near an inclined plane reaches an equilibrium position, after which it translates parallel to the wall without rotation.

Effect of post-training unilateral labyrinthectomy in a spatial orientation task by guinea pigs

The effects of unilateral labyrinthectomy in guinea pigs have been studied on an angular orientation task consisting, in an open field, of running to a hidden goal oriented at 45 degrees with respect to the cephalocaudal axis of the animal placed in a starting-box. The task was conducted in light but in an homogeneous environment, i.e. without visual, auditory or olfactory cues indicating the location of the goal. A second group of animals was submitted to a similar task running to a hidden goal but the place of the goal was indicated by a colored card. All the animals were trained before the lesion and tested in their respective task for 1 month after the lesion. In the task conducted without conspicuous cues, animals were dramatically disturbed. In contrast, animals pretrained in the visually guided task were not impaired after the lesion. These results point out the important role of vestibular information in performing spatial tasks based on angular estimation, since, even if proprioceptive and visuokinesthetic information remain available, subjects seemed not able to maintain a correct angular trajectory. The trajectories being not disturbed in the visually guided task, one can exclude the hypothesis that such deficit was due to a purely motor disturbance.

Motor control of voluntary arm movements. Kinematic and modelling study.

The motor control of pointing and reaching-to-grasp movements was investigated using two different approaches (kinematic and modelling) in order to establish whether the type of control varies according to modifications of arm kinematics. Kinematic analysis of arm movements was performed on subjects' hand trajectories directed to large and small stimuli located at two different distances. The subjects were required either to grasp and to point to each stimulus. The kinematics of the subsequent movement, during which subject's hand came back to the starting position, were also studied. For both movements, kinematic analysis was performed on hand linear trajectories as well as on joint angular trajectories of shoulder and elbow. The second approach consisted in the parametric identification of the black box (ARMAX) model of the controller driving the arm movement. Such controller is hypothesized to work for the correct execution of the motor act. The order of the controller ARMAX model was analyzed with respect to the different experimental conditions (distal task, stimulus size and distance). Results from kinematic analysis showed that target distance and size influenced kinematic parameters both of angular and linear displacements. Nevertheless, the structure of the motor program was found to remain constant with distance and distal task, while it varied with precision requirements due to stimulus size. The estimated model order of the controller confirmed the invariance of the control law with regard to movement amplitude, whereas it was sensitive to target size.

Walking cycle recording and analysis for FNS-assisted paraplegic walking

In closed-loop functional neuromuscular stimulation (FNS)-assisted paraplegic walking, there is a need for reference leg motion trajectories that describe the desired walking cycle. These reference trajectories were defined as the angular changes between the leg segments, as measured by an electrogoniometer system. For each leg, the hip, knee and ankle trajectories of normal individuals during slow walking were measured and sampled over a number of cycles. Additionally, foot contact with the ground was measured to synchronise the various walking trajectories. Each joint's angular trajectory was averaged over a number of walking cycles, using an interpolation method based on a discrete Fourier transform (DFT) and inverse DFT technique, to expand all the signals to the same length. In this way an average walking cycle was obtained for each trial, representing the six averaged leg motion trajectories for one walking cycle. Angular trajectories and walking parameters for slow and normal walking were compared so as to investigate principles of walking cycle adaptation necessary to stabilise the body during slow walking. In general, angular trajectories were similar for different subjects, but different for different walking speeds, due to the greater demands on maintaining stability during slow walking. It can be concluded that normal speed walking consists of separate, unstable phases, whereas slow speed walking, relevant for paraplegic walking, requires stabilising each separate phase of the walking cycle.

Kinematic analysis of the defense response in crayfish

1. A threatening visual stimulus frequently elicits the defense response (DR) in crayfish, a behavior that comprises orienting the body to face the stimulus, raising the thorax, and extending and opening the claws. Although this behavior has been reported previously, its kinematics have not been characterized. This work employs kinematic analysis to provide a quantitative description of the claw (cheliped) as it is moved during the DR. 2. The cheliped was modeled as an open kinematic chain with three segments and 4 df. Simulations employing the model were compared with actual cheliped trajectories during the DR to ascertain the applicability of the model. The model was then employed to demonstrate the effects of individual joint rotations on the overall trajectory of the claw. 3. The individual segments of the cheliped were monitored during the DR, and spatial trajectories, tangential velocities, and intersegmental joint angles were calculated. 4. The joint angles assumed at the final position of the DR were highly stereotyped. This constancy in joint angle at the endpoint of the movement stands in contrast to the variability in both the angular and spatial trajectories of the cheliped as it was moved towards the final position. 5. Movement time was relatively constant. Larger amplitude movements were performed with a proportional increase in velocity similar to arm movements in primates. 6. The DR positions the cheliped in a fixed location in the workspace. Unlike the primate arm during reaching, the cheliped does not proceed towards the endpoint with a smooth controlled trajectory characteristic of a system with fine interjoint coordination. Instead, it appears that individual joint rotations are performed independently, thus precluding trajectory control although permitting an accurate specification of the endpoint.

Asymptotic oscillations in the tracking behaviour of the fly Musca domestica

From recent theoretical work (Poggio and Reichardt, 1981), high frequency oscillations are expected in the angular trajectory of houseflies tracking a moving target if the target's retinal position controls the flight torque by means of a stronger optomotor response to progressive than to regressive motion. Experiments designed to test this conjecture have shown that (a) asymptotic non-decaying oscillations are found in the torque of female houseflies tracking targets moving at constant angular velocity; (b) the magnitude of the oscillations grows monotonically with mean retinal excentricity of the target; (c) the period of the oscillation is around 180–200 ms. The experimental findings are consistent with the hypothesis that a “progressive-regressive mechanism” plays a significant role in the tracking behaviour of female houseflies. From this phenomenological point of view a flicker mechanism that is active only for nonzero motion is equivalent to a progressive-regressive system. The relatively long period of the oscillation requires more complex reaction dynamics than a pure single dead-time delay. As a specific example we show that a model where the reaction to progressive motion is “sticky”, holding for a longish time after the ending of the stimulus, is consistent with the experimental data.

Visual fixation and tracking by flies: Mathematical properties of simple control systems

The study of the orientation behavior of flies requires the consideration of a few simple control systems for fixation and tracking. In this paper two such control systems are analyzed, in terms of the corresponding difference and differential equations. The first control system corrects with a delay ? the angular trajectory proportionally to the error angle ?; the second control system also corrects proportionally to the error angle ? but only when the absolute value of ? is increasing. The differential equations are $$\mathop \psi \limits^ \circ (t) = - \alpha '\psi (t - \varepsilon ) + A'$$ and $$\mathop \psi \limits^o (t) = - \alpha '\psi (t - \varepsilon ) \cdot u[\psi (t - \varepsilon )\mathop \psi \limits^o (t - \varepsilon )] + A'$$ u[ ] being the step function (u[x]=1 if x>0, otherwise u[x]=0). Under suitable restrictions on the parameters it is proved (a) that the difference equations $$x_{n + 1} = x_n - \alpha x_n + A$$ and $$x_{n + 2} = x_{n + 1} - \alpha x_{n + 1} \cdot u[x_{n + 1} \cdot (x_{n + 1} - x_n )] + A,$$ which can be associated to Eqs. (0) and (*), are "asymptotically equivalent" (for large n) if the time scale is "smoothed" over two time units and (b) that the second equation, with 0<?<2, always converge to a set of oscillating solutions of period 2 for arbitrary initial conditions. Numerical simulations show that the delay-differential equations behave in a similar way. We have also demonstrated with computer simulations that both control systems can satisfactorily predict the 3-D trajectory of a fly chasing another fly. The main biological implications of the analysis are: (1) The two control systems are practically equivalent descriptions of the fly's control of flight on a "coarse" time scale (2 times the fly's delay), consistently with an earlier more general derivation of Eq. (0) (Poggio and Reichardt, 1973). (2) On a fine time scale the second control system is characterized by an asymptotic oscillation with period twice the fly's delay. It is conjectured that a wide range of control systems of the same general type must have a similar oscillatory behavior. Finally, we predict the existence of asymptotic oscillations in the angular trajectory and the torque of tracking flies (if a control system of the second type is involved to a significant extent). Such oscillations should have a basic period of twice the effective reaction delay, and should be best detectable outside the binocular region. Closed loop experiments and the analysis of free flight trajectories may provide critical tests of this prediction.

Kinematics-free angular momentum trajectories. II. Yukawa-potential numerical examples

The kinematics-free angular momentum trajectory, called the ..gamma.. trajectory, is illustrated numerically in nonrelativistic potential scattering using Yukawa and exponential potentials of various strengths. The ..gamma.. trajectory, in contrast to the ..cap alpha.. (Regge) trajectory, is free of elastic kinematics and so is real for all energies above threshold and real for certain energies below threshold. Resonances are caused when the ..gamma.. trajectory passes through the resonance angular momentum at the resonance energy, and bound states are caused when the ..gamma.. trajectory passes near the bound-state angular momentum at the bound-state energy. Numerical illustrations of the following ..gamma.. trajectory characteristics are given: the reality of ..gamma.., bound-state and resonance production, threshold and high-energy behavior, and collisions of trajectories below threshold. In addition, general properties of ..gamma.. trajectories in the context of potential scattering are discussed.

Model of Positive-Parity Baryon Excited States

The occurrence in nature of very high-spin baryons leads to the suggestion that they can be described as composites of high-spin baryons and mesons with low orbital angular momentum. As a consequence, there appears to be no limit beyond which the baryon spectrum cannot extend. We implement these ideas with a dynamical bootstrap model of positive-parity baryons employing $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}O(3)$ symmetry. We prove the consistency of this symmetry with our dynamics, and predict a spectrum in accord with the latest phase-shift analysis of the pion-nucleon system. We indicate how our model is described in a Regge theory of angular momentum trajectories, and we conclude with a comment on the negative-parity baryon spectrum.

Trajectories in an Axial Focusing Double Lens Spectrometer

The trajectories of an electron with zero canonical angular momentum (p[open phi]−(erA[open phi]/c)=0) have been computed with third-order accuracy for a 1/(1+x2) axial field shape. By suitably matching the above solutions with a set of similar solutions obtained by shifting the origin, it is possible to obtain the complete zero canonical angular momentum trajectories corresponding to the double lens problem in which the axial field shape approximates rather closely one that is physically realizable. The numerical computations illustrate several typical trajectories. Design considerations are given to illustrate the utility and limitations of the theory.