Analyzing compound pendulum data

To determine the value of earth’s gravitational acceleration, physical pendulum experiment is preferred over simple pendulum experiment that was previously more popular. In physical pendulum experiment, the object is a rigid body. The swing period and swing shaft position are measured. From these two variables and using the applicable laws of motion, equations can be determined that involve constants which imply the value of the earth’s gravitational acceleration and the moment of inertia of objects pivoting at the center of mass. The independent variable in the equation is a function of the distance of the pendulum shaft to the center of mass based on the parallel-axis theorem, while the dependent variable is a swing period. Difficulty in solving equations is found because of the terms of the equation involving variables in different ranks. In order for the equation to be linear, a dependent variable and an independent variable are combined into new variables. After that, with the linear regression method, the constants of the equation can be determined which can then be determined the value of the earth’s gravitational acceleration and the moment of inertia of the object. The results obtained are quite satisfactory with a relatively smaller error value of 5%. Thus this physical pendulum experiment can be used to determine the earth’s gravitational acceleration and the moment of inertia of an object simultaneously.

Individuals with Parkinson disease exhibit decreased axial head-pelvis rotation. Consequently, they turn more en bloc than healthy controls, which may contribute to freezing during turning. We wanted to understand the influence of auditory cueing and an attentional strategy on turning and how this related to freezing of gait (FOG). Fifteen participants with Parkinson disease and FOG were asked to turn 180° during baseline condition, unilateral cueing, and an attentional strategy prompting to start the turn with head rotation first. FOG occurrence, axial rotation, center of mass (COM) deviation, knee-flexion amplitude, and total turn velocity were measured using 3D motion analysis while off-medication. Normal reference values were obtained from 14 age-matched controls. Thirty-nine FOG episodes occurred in 5 participants. FOG occurred in 52.8% of baseline trials compared with 34.6% of trials using the head-first strategy, and 3.8% of the auditory cueing trials. During the head first strategy, the initiation of head, trunk, and pelvic rotation as well as the head-pelvis separation resembled turning patterns of healthy controls, but the COM shift to the inside of the turn was exaggerated. By contrast, during cueing, turning became more en bloc, with decreased head-pelvis separation and knee-flexion amplitude. Cueing reduced FOG but did not correct axial movement deficits. The head-first strategy improved head-pelvis dissociation but had only limited effects on FOG. These results suggest that axial and COM deviation impairments are not directly related to FOG but may rather indicate a compensatory mechanism. Cueing reinforced the en-bloc movement and might as such help prevent FOG by triggering an alternative neural mechanism for movement generation.Video Abstract available for more insights from the authors (see Video, Supplemental Digital Content 1, http://links.lww.com/JNPT/A163).

The Inverted Pendulum model is one of favorite algorithm used to calculate the length of gait. The human locomotion is approximated by simple pendulum, the influence of knee and ankle movements are not considered. The gait length is calculated from the extremes of vertical position of human Center of Mass (CoM) during gait. This approach is usually used in measurements which uses inertial sensors to measure the position of CoM. The position of CoM is after that calculated usually as double integration of acceleration. This approach causes errors in calculation, which are given by method (integration) and also by tilt of inertial sensor during movement of CoM. The influence of the Inverted Pendulum approach is not usually considered. This article shows the influence of Inverted Pendulum model as a methodology to calculate the length of gait. There were done measurement of human walk by precise Video System.

Previous studies on sprinting biomechanics have identified a variety of biomechanical characteristics that describe the outcome of improved sprint technique but in doing so have neglected to identify the postural control strategies that lead to improved sprint performance. The purpose of this study was to evaluate the relationship between frontal plane displacement of the center of mass (CoM) and sprint velocity, and to understand if multijoint coordination of the limbs and trunk were associated with minimizing the displacement. The results from this study suggest that stance phase frontal plane CoM cumulative path length is significantly associated with sprint velocity. Further, a multivariate linear regression model revealed that coordinative couplings of the bilateral limbs and trunk were associated with the minimization of the frontal plane CoM displacement. Specifically, the coordination of the knees (flexion-extension) and axial rotation of the thorax-pelvis were the most important interjoint couplings in minimizing frontal plane CoM displacement. Frontal plane CoM displacement provides coaches, athletes, and performance professionals with an interpretable metric to identify sprint technique quality in field using wearable sensors. Future work needs to further advance our understanding of postural control during sprinting so that effective coaching and rehabilitation interventions can be designed.

In this paper, a new model is proposed based on the three-mass inverted pendulum for generating real-time walking pattern for biped robots. To generate walking pattern for biped robots, the Center of Mass (COM) trajectory is calculated using a designed ankle trajectory and the inverted pendulum model. For this purpose, a new three-mass inverted pendulum model is proposed to improve the accuracy of the simple inverted pendulum. These obtained trajectories for the ankle and COM are mapped into the joint space, using inverse kinematics. Finally, by exploiting the computed trajectories in joint space, the exact location of the Zero Moment Point (ZMP) is calculated and the results of the proposed model are compared to the existing models in terms of model accuracy. Simulation results show that approximation of robot dynamics is improved using the proposed model.

The free-fall absolute gravimeter is commonly used for precise gravitational acceleration measurement. The g value is obtained through quadratic fitting of the position-time data pairs of the freely falling test mass. However, recoil vibrations are generated during the release of the test mass resulting from the movement of the center of mass of the chamber, and errors may arise from these vibrations in the measurement process. To solve the recoil vibration problem, previous researchers have developed the recoil compensation structure to achieve a basically stationary center of mass during the drop. In this paper, counterweights of a variety of masses are tested on our recoil compensated gravimeter, while recoil vibrations are recorded and analyzed accordingly. The multibody simulation indicates that compensated counterweights can significantly reduce the recoil vibration amplitude, making a more precise measurement attainable. In the experiments, accelerometers and seismometers are employed respectively in the simultaneous measurement of recoil vibrations of dropping chamber and reflector. Then all the vibration signals are analyzed and compared, and the outcome confirms the effectiveness of the gravimeter in performing high precision measurement as what is observed in the previous simulations. With a proper design of the counterweight mass, the recoil effect can be significantly reduced during the test procedure, which indicates a potential for high precision measurement.

SUMMARYThe local domain‐free discretization method is extended in this work to simulate fluid–structure interaction problems, the class of which is exemplified by the self‐propelled anguilliform swimming of deforming bodies in a fluid medium. Given the deformation of the fish body in its own reference frame, the translational and rotational motions of the body governed by Newton's Law are solved together with the surrounding flow field governed by Navier–Stokes equations. When the body is deforming and moving, no mesh regeneration is required in the computation. The loose coupling strategy is employed to simulate the fluid–structure interaction involved in the self‐propelled swimming. The local domain‐free discretization method and an efficient algorithm for classifying the Eulerian mesh points are described in brief. To validate the fluid–structure interaction solver, we simulate the ‘lock‐in’ phenomena associated with the vortex‐induced vibrations of an elastically mounted cylinder. Finally, we demonstrate applications of the method to two‐dimensional and three‐dimensional anguilliform‐swimming fish. The kinematics and dynamics associated with the center of mass are shown and the rotational movement is also presented via the angular position of the body axis. The wake structure is visualized in terms of vorticity contours. All the obtained numerical results show good agreement with available data in the literature. Copyright © 2011 John Wiley & Sons, Ltd.

Purpose This paper aims to introduce a grasping configuration planning method suitable for grippers featuring three individually controllable fingers. This approach can effectively improve the stability of grasping for objects of various shapes. Design/methodology/approach Inspired by the Fermat point in geometric triangles, this paper establishes two planning objectives: minimizing the distance from the palm axis to the object’s center of mass and maximizing the displacement of the three fingers. Based on these objectives, this paper proposes specific steps for the grasping configuration planning method. In addition, by considering the effect of gravity on grasping, this paper analyzes the trends in contact point frictions under different planning objectives. The position of the palm axis is further determined by identifying the configuration that maximizes static friction. Findings Simulation and experiment results demonstrate the feasibility of applying the grasp configuration planning method to specific grippers, which can improve both the success rate and stability compared to manual grasping. Originality/value This paper proposes a new grasping configuration planning method based on the Fermat point principle, which is introduced step by step with a focus on two planning objectives and considers the effect of friction changes on grasping under the influence of gravity.

The article describes the possible disturbance of the Earth’s dynamic balance due to climate changes throughout the last 150 years and technogenic impact. An accident occurred on an oil platform in the Gulf of Mexico on April 20, 2010 is taken as an example of such impact. It is assumed that the accident may have accelerated the slowdown of the Gulf Stream and changed its path, which led to a change in temperature, salinity and density of significant ocean masses. Variations of ocean mass density in some areas could cause a shift of the Earth’s center of mass by 10–5 m and a deviation of its rotation axis by 2.9∙10–6 arcsec. It is shown that the process of disturbance of the Earth’s dynamic balance can be accompanied by an increase in the number of relatively weak earthquakes (in a range of magnitudes 4.2–4.8 by 41.5%) and the intensity of seismic noise (tremor), as shown by broadband seismic networks and satellite GPS navigation data.

We observe commonly disturbances in rotating machinery elements when driven to rotate. These disturbances present themselves as a displacement or trepidation caused by unbalanced masses. The occurrence of balancing depends on eccentricity present, which means that the center of mass and rotating element center are not coincident. The presence of these unbalanced forces - whose magnitude is proportional to the eccentricity, unbalanced mass, and the angular velocity squared - results in severe vibrations and can overload bearings with catastrophic consequences. The main origin of these unbalances is the heterogeneous distribution of the masses around the rotation axis. So, to avoid the overload on bearings and warp the shaft, some control methods such as balancing should be done. In the present work, a dynamic balancing was carried out with a specimen employing a balancer rig. In this experiment, different auxiliary equipment, computer systems, and proprietary software were used. It was possible with this software to automate the measurements, analyze, and obtain a report about balancing results as well. The specimen was made of steel and possessed two mounted nylon disks with oblong holes on them. These oblong holes permitted the fixation of trial masses and correction masses. The degree of balancing quality was determined according to the ISO standard G 6.3; these degrees of balancing guarantee an accuracy level of quality according to the specific application in rotating machines. The balancing on the specimen was correctly applied, and the results have demonstrated that this procedure, balancing, is essential to mitigating excessive vibration and preventing overload in bearings caused by unbalancing in rotating mechanical elements.

Objective: To understand the differences of step and turn parameters between freezers and non-freezers during turning and determine the influence of turn angle and turn characteristics on freezing of gait.Data sources: PubMed and Web of Science were searched from the earliest data available to August 2017.Study selection: Case–control studies that examined the differences in turning while walking between freezers and non-freezers were included. Two reviewers selected studies independently.Data extraction: Methodological quality was evaluated by two independent reviewers using the STROBE checklist for case–control studies. Mean differences and 95% confidence intervals were calculated from pooled data for turn duration, peak turn velocity, number of steps and cadence. Center of mass deviation, segmental rotation, phase coordination and freezing of gait frequency were also extracted. When possible, different turning angles or spatial confounds were compared.Data synthesis: Sixteen studies met the inclusion criteria. Freezing of gait occurred in 38.2% of the freezers. Freezing appeared most frequently at the end of a turn and at the inner leg of the turn cycle. The meta-analysis revealed that turning in freezers was characterized by an increased turn duration, cadence and number of steps and a decreased peak turn velocity. Qualitative analysis showed that results concerning step width, step length and step time variability were inconsistent. Turning was characterized by an increased head–pelvis coupling and worse coordination in freezers compared to non-freezers. A decreased medial deviation of the center of mass was present prior to a freezing episode.Conclusions: Both step and rotational parameters differed in freezers compared to non-freezers while turning. These differences increased with increasing task complexity (i.e., larger turning angle or spatial confounds during turning). The results suggest that improving axial rotation could be a valuable rehabilitation target to ameliorate freezing.Implications for rehabilitationPatients with freezing of gait turn with a larger arc and a smaller angle compared to non-freezing patientsFreezing–related turning deficits have both spatiotemporal and rotational motor control componentsImproving axial rotation could be a novel rehabilitation target to ameliorate freezing

Selected Accelerations and Orbital Elements of the Goce Satellite in the Time Domain

Human biped locomotion is an ultimate style of biological movement that is a highly evolved function. Biped locomotion by robots is a dream to be attained by the most highly evolved or integrated technology, and research on this has a history of over 30 years. Many methods of generating gaits have been proposed. There has been a tendency to reduce the complicated dynamics of a walking robot to a simple inverted pendulum (Hemami et al., 1973), and to control its motion according to pre-designed time-dependent trajectories while guaranteeing zero moment point (ZMP) conditions (Vukobratovi & Stepanenko, 1972). Although such approaches have successfully been applied to practical applications and nowadays successful biped-himanoids are developed by them, problems on gait performances still remain. Several advanced approaches on the other hand have taken the robot's dynamics into account for generating gaits based on natural dynamics. Miura and Shimoyama studied dynamic bipedal walking without ankle-joint actuation (Miura & Shimoyama, 1984) and they developed robots on stilts whose foot contact occurred at a point. Sano and Furusho accomplished natural dynamic biped walking based on angular momentum using ankle-joint actuation (Sano & Furusho, 1990). Kajita proposed a method of control based on a linear inverted pendulum model with a potential-energy-conserving orbit (Kajita et al., 1992). These approaches utilized the robot’s own dynamics effectively but did not investigate the energy-efficiency by introducing performance indices. It was unclear whether or not efficient gaits were generated. McGeer's passive dynamic walking (PDW) (McGeer, 1990) has provided clues to solve these problems. Passive-dynamic walkers can walk without any actuation on a gentle slope, and they provide an optimal solution to the problem of generating a natural and energy-efficient gait. The objective most expected to be met by PDW is to attain natural, high-speed energyefficient dynamic bipedal walking on level ground like humans do. However, we need to supply power-input to the robot by driving its joint-actuators to continue stable walking on level ground, and certain methods of supplying power must be introduced. Ankle-joint torque is mathematically very important for effectively propelling the robot's center of mass (CoM) in the walking direction, and it is thus required relatively more often than other joint torques. However, to exert ankle-joint torque on a passive-dynamic walker, we need to add feet and this creates the ZMP constraint problem. We clarified that there is a trade-off between optimal gait and ZMP conditions through parametric studies, and O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

Christopher Graney provides a fascinating description of Giovanni Battista Riccioli’s meticulous 17th-century experiments on free fall (Physics Today, September 2012, page 36). He notes that Riccioli’s results, converted to modern units, provide an estimate of g that is systematically 5% smaller than the current accepted value. The discrepancy might well be attributed to uncertainty over the modern equivalent of Riccioli’s unit of length, the Roman foot. However, one more insight can perhaps be wrung from the data.As Christiaan Huygens reported in his classic 1673 Horologium Oscillatorium, published 22 years after Riccioli’s Almagestum, the period of a pendulum of length l is T = 2π√l/g. Thereafter it is an easy exercise to show that a plot of the distance fallen versus the square of the fall time in units of the pendulum half-period T/2 is a straight line of slope π2l/2. That figure is independent of g and of the conversion to modern units.Plotting Riccioli’s data in that way reveals an accurate straight line from which one can deduce the pendulum length. The answer—with a generous error estimate—is l = 1.00 ± 0.05 Roman inches. As Graney notes, Riccioli himself reported the length to the center of the pendulum bob to be 1.15 inches. The 15% discrepancy—less than 4 mm—is plausibly excusable, though one might infer that Riccioli supposed his measurement was accurate to at least 0.05 inches (about 1 mm).Unfortunately, the discrepancy is in the wrong direction to be attributed either to the distinction between the center of mass and the center of oscillation of a compound pendulum or to the fact, known to Riccioli, that large-amplitude pendulum swings are not quite isochronous. Nevertheless, the discrepancy is intrinsic to Riccioli’s presented data and is not dependent on the disputed length of the Roman foot. One can only presume it reflects on the difficulty of subdividing a Roman foot into such fine equispaced divisions.© 2013 American Institute of Physics.

Geodetic reference systems for crustal motion studies