Inertia Of Body Research Articles

Joint kinematics and kinetics of overground accelerated running versus running on an accelerated treadmill

Literature shows that running on an accelerated motorized treadmill is mechanically different from accelerated running overground. Overground, the subject has to enlarge the net anterior-posterior force impulse proportional to acceleration in order to overcome linear whole body inertia, whereas on a treadmill, this force impulse remains zero, regardless of belt acceleration. Therefore, it can be expected that changes in kinematics and joint kinetics of the human body also are proportional to acceleration overground, whereas no changes according to belt acceleration are expected on a treadmill. This study documents kinematics and joint kinetics of accelerated running overground and running on an accelerated motorized treadmill belt for 10 young healthy subjects. When accelerating overground, ground reaction forces are characterized by less braking and more propulsion, generating a more forward-oriented ground reaction force vector and a more forwardly inclined body compared with steady-state running. This change in body orientation as such is partly responsible for the changed force direction. Besides this, more pronounced hip and knee flexion at initial contact, a larger hip extension velocity, smaller knee flexion velocity and smaller initial plantarflexion velocity are associated with less braking. A larger knee extension and plantarflexion velocity result in larger propulsion. Altogether, during stance, joint moments are not significantly influenced by acceleration overground. Therefore, we suggest that the overall behaviour of the musculoskeletal system (in terms of kinematics and joint moments) during acceleration at a certain speed remains essentially identical to steady-state running at the same speed, yet acting in a different orientation. However, because acceleration implies extra mechanical work to increase the running speed, muscular effort done (in terms of power output) must be larger. This is confirmed by larger joint power generation at the level of the hip and lower power absorption at the knee as the result of subtle differences in joint velocity. On a treadmill, ground reaction forces are not influenced by acceleration and, compared with overground, virtually no kinesiological adaptations to an accelerating belt are observed. Consequently, adaptations to acceleration during running differ from treadmill to overground and should be studied in the condition of interest.

Jump training with different loads: effects on jumping performance and power output

To investigate the selective effects of different types of external loads applied in vertical jump training on both the performance and muscle power output of the squat (SJ) and countermovement jump (CMJ). Physically active males practiced maximum unconstrained vertical jumps over an 8-week period with no load, with either a negative or positive load exerted by a nearly constant external force that altered their body weight, and with a loaded vest that increased both the body weight and inertia. The magnitude of all applied loads corresponded to 30% of body weight. A similar training-associated increase in jump height was observed in all experimental groups in both CMJ (7.4-11.8%) and SJ (6.4-14.1%). The relative increase in power output was comparable to the increase in jump height in SJ (7.4-11.5%), while the power increase in CMJ was relatively small and load-specific (0.5-9.5%). The observed differences could originate from the changes in the CMJ pattern, reflected through the depth of the counter movement that particularly increased after the training with negative load (42%) and no load (21%). The same participants also revealed increased CMJ duration, reduced ground reaction forces, as well as reduced maximum and average power output when compared with other training groups. Jump training with the applied loads could lead to a comparable improvement in jumping performance. However, the observed load-specific adaptations of CMJ pattern could decouple the training-associated increase in jump height from the increase in muscle power output.

On the Groundless Use of Mathematics Concerning the d’Alembert’s Rule

The paper discusses the groundless use of mathematics. This question has been explained mainly based on example of the so called d`Alembert’s rule which unfortunately still functions in science none the less it has been based on a fiction, contrary to the truth cognition as the fundamental purpose of science. That pejorative feature of the mentioned paradigm is marked very clearly in the paper to evaluate it negatively as the only one possible note. Next the adequate characteristics of variable body motion has been presented and the description of Atwood device given in view of explaining the essence of a real equilibrium of the system of material bodies where their real inertia is of importance. In conclusion the characteristics of real inertia force being the measure of this inertia is presented. The erroneous up-to-date view concerning the measure of body inertia, assuming mass as the measure of this magnitude enabling free manipulation of the acceleration value, has been revealed. At the end it is stressed that acceleration is always positive in its nature and is existent in each condition of the material reality.

Effect of particle content, size and temperature on magneto-thermo-mechanical creep behavior of composite cylinders

The effects of particle content, particle size, operating temperature and magnetic field on steady-state creep behavior of thick-walled rotating cylinders made of Al-SiC composites have been investigated. Loading is composed of a uniform magnetic field in axial direction, steady-state heat conduction in radial direction and an inertia body force due to rotation. The composite creep constitutive equation has been described by Norton’s law in which the creep parameters are functions of particle size, temperature and particle content. The composite properties are radial dependent based on volume fraction of SiC reinforcement. It has been found that the minimum effective creep strain rate belongs to a composite identified by 25% SiC at the inner and 5% at the outer surfaces. Therefore this composite has been selected for the design of the cylinder. It has been concluded that increasing particle size and operating temperature significantly increases the effective creep strain rates. It has also been illustrated that magnetic field decreases the stresses and the effective creep strain rates.

Biomechanics aspects of technique of high jump

The purpose of work consists in the theoretical ground of optimum biomechanics descriptions in high jumps. A mathematical model is developed for determination of influence on the height of jump: speed and corner of flight of centre-of-mass during pushing away, positions of centre-of-mass body of sportsman in the phases of pushing away and transition through a slat, forces of resistance of air environment, influences of moment of inertia of body. The basic technical run-time errors of sportsman are selected exercises. To biomechanics descriptions, to the step-up effectiveness of high jumps belong: speed of flight of centre-of-mass sportsman (4.2-5.8 meters in a second), corner of flight of centre-of-mass body (50-58 degrees), height of flight of centre-of-mass body (0.85-1.15 meter). Directions of choice of necessary biomechanics descriptions which a sportsman can realize are shown. Offered recommendation on the increase of effectiveness of high jumps.

Moments of Inertia of Disks and Spheres Without Integration

Calculation of moments of inertia is often challenging for introductory-level physics students due to the use of integration, especially in non-Cartesian coordinates. Methods that do not employ calculus have been described for finding the rotational inertia of thin rods and other simple bodies.1–3 In this paper we use the parallel axis theorem and the perpendicular axis theorem (both of which may be proved without calculus4), along with rotational symmetry, to determine, without using integration, the moments of inertia of uniform disks and spheres.

Evolution of motion of a rigid body with a fixed point and an ellipsoidal cavity filled with a viscous fluid

The inertial motion of a system consisting of a rigid body with a fixed point and a viscous incompressible fluid filling a spherical or ellipsoidal cavity inside this body is considered. The principal moments of inertia of the system about the fixed point are approximately equal to the principal moments of inertia of an axisymmetric body. The Reynolds number is inversely proportional to the viscosity of the fluid and is assumed to be small. For the description of motion, the generalized Andoyer canonical variables, the motion separation method, and the averaging method are used. It is shown that the motion of the system tends to the steady rotation about the axis of the largest inertia moment directed along the constant angular momentum vector of the system.

A New Active Body Weight Support System Capable of Virtually Offloading Partial Body Mass

This paper presents a novel active body weight support (BWS) method, which is capable of virtually offloading full or partial body mass for a potential application of enhancing treadmill-based locomotion rehabilitation. The mass-offloading capability is realized by actively compensating a desired amount of body weight and inertia force using an acceleration-feedback scheme. The method has been studied by dynamics simulations and a specially designed nonhuman experiment. In the simulation study, the human and the BWS device were modeled as a multibody dynamical system interacting dynamically with the treadmill. The ground reaction forces were recorded as the dynamic load on the person. A cam-slider-based experiment was designed and conducted to test the engineering feasibility of the mass-offloading capability. Both the simulation and experiment results demonstrated that the BWS system can compensate any desired amount of gravity force and inertia force and, therefore, has the effect of virtually reducing the mass of a person attached to the system.

The stability of the plane periodic motions of a symmetrical rigid body with a fixed point

A rigorous non-linear analysis of the orbital stability of plane periodic motions (pendulum oscillations and rotations) of a dynamically symmetrical heavy rigid body with one fixed point is carried out. It is assumed that the principal moments of inertia of the rigid body, calculated for the fixed point, are related by the same equation as in the Kovalevskaya case, but here no limitations are imposed on the position of the mass centre of the body. In the case of oscillations of small amplitude and in the case of rotations with high angular velocities, when it is possible to introduce a small parameter, the orbital stability is investigated analytically. For arbitrary values of the parameters, the non-linear problem of orbital stability is reduced to an analysis of the stability of a fixed point of the simplectic mapping, generated by the system of equations of perturbed motion. The simplectic mapping coefficients are calculated numerically, and from their values, using well-known criteria, conclusions are drawn regarding the orbital stability or instability of the periodic motion. It is shown that, when the mass centre lies on the axis of dynamic symmetry (the case of Lagrange integrability), the well-known stability criteria are inapplicable. In this case, the orbital instability of the periodic motions is proved using Chetayev's theorem. The results of the analysis are presented in the form of stability diagrams in the parameter plane of the problem.

Three-dimensional discontinuous deformation analysis (3-D DDA) method for particulate media applications

This paper presents a new numerical model for simulation of granular materials consisting of 3-D spheres bounded by rigid boundaries. The proposed model is based on Three-Dimensional Discontinuous Deformation Analysis (3-D DDA), a numerical method recently developed for simulation of particles in motion. Stiffness and force matrices due to body forces, point loading, inertia forces, and displacement and directional constraints are derived in detail. Moreover, an efficient model for particle contacts in 3-D is presented. In this model, sphere-sphere and sphere-boundary contacts are simply transformed into the form of point-to-plane contacts. Normal and shear contact forces as well as friction force for both sphere-sphere and sphere-plane contact types are derived by vector analysis and the penalty method. The numerical model developed herein is a simple and efficient method that can be easily coded into a computer program. The validity and capability of the model are demonstrated by numerical results obtained for several illustrative examples. Furthermore, some examples are presented and discussed to illustrate the application of the 3-D DDA to particulate media.

Bipedal Trajectory Generation Based on Combining Inertial Forces and Intrinsic Angular Momentum Rate Changes: Eulerian ZMP Resolution

This paper aims to present a technique to generate feasible and dynamically equilibrated ZMP-based center of mass trajectories that can be applied to bipedal robots. In this regard, we utilize the ZMP concept in the spherical coordinate frame so that we can fully exploit its properties as this strategy enables us to efficiently combine intrinsic angular momentum rate change terms with inertial force terms. That being said, this strategy has certain advantages: 1) In the case of bipedal walking, undesired torso angle fluctuations are more restrainable compared with other methods, in which angular momentum information is omitted or zero-referenced. 2) Composite rigid body inertia, which is a multibody property of robot dynamics, can be characterized during the trajectory generation task. Thus, relatively more dynamically consistent trajectories may be obtained. 3) The motion interference between the sagittal and lateral planes is naturally included. In this paper, we mainly investigate the first two advantages. Applying the method described above, we conducted bipedal walking experiments on our actual bipedal robot MARI-3. As the result, we obtained repetitive, continuous, and dynamically equilibrated walking cycles, in which undesired torso angles were well suppressed. Furthermore, ZMP error tends to decrease since inertial parameters of the robot are characterized. In conclusion, the method is validated to be efficient in inducing less ZMP error and in suppressing undesired torso angle variations, compared with both flywheel-superimposed and conventional ZMP-based trajectory generation methods.

Vision-based estimation of vertical dynamic loading induced by jumping and bobbing crowds on civil structures

People's motion on civil structures induces dynamic loading that may lead to excessive vibrations. The complete characterization of this force distribution over a wide area due to a large number of people is still an unsolved issue. This work presents a measuring technique for the vertical load estimation in case of jumping and bobbing crowd, based on the evaluation of the vertical inertia of the human body. Laboratory experiments verify the proposed model on a single volunteer through standard inertial sensors and then extend it introducing the non-contact measuring technique. The method validation is carried out in a real environment: a stand of the G. Meazza stadium in Milan, dynamically characterized in terms of frequency response function. The load induced by groups of jumping people is estimated with the proposed method and the resulting structure accelerations are computed: the comparison between measured and estimated vibrations shows a very high correspondence in both time domain and main spectral components and, above all, the performances do not get worse as the number of volunteer increases.

Modelling lateral manoeuvres in fish

AbstractWe propose a method to model manoeuvres in self-propelled flexible-bodied fish by modelling the hydrodynamics coupled to the body inertia. Flexible body motion is prescribed and the equations of motion are solved for the position of the centre of mass and rotation of the body. The governing equations are formulated by applying the conservation of linear and angular momentum. Two independent methods to model the fluid dynamics are pursued: Model 1 is an extension of elongated-body theory, modified for self-propulsion and flexible motion. Model 2 applies a numerical boundary-element formulation with the fish modelled as an infinitely thin rectangular body. The manoeuvring response to an impulsive input is first examined to understand the rigid-body characteristics of the fish. A flexible bend action is included to model C-bends of the type observed during escapes in fish. Models 1 and 2 are used to cross-verify the respective implementations as well as to develop physical insights into manoeuvring. A parameter study shows that fish of intermediate body depths are best adapted to rapid turns whereas the initial dynamic state of the fish is instrumental in affecting the sign as well as the magnitude of the turn angle, for a prescribed bend deflection. Computations for combined swimming and turning show that the initial rigid-body dynamics of the fish is much more effective than the induced effect of the prior shed wake in enhancing the turning response.

Finding Principal Axes of Complex Plane Rigid Body with Rending-Image of MATLAB

In order to find the principal axes of inertia and calculate their moment of inertia to any plane homogeneous rigid body for calculating easily the moment of inertia to any axis of this rigid body, the principal axes could be found and their moment of inertia could be calculated automatically by using the reading-image of MATLAB to read the image messages about the flat surface of the rigid body and by the procedures which ware made according to the logic relation about the principal axis and the moment of inertia of the rigid body. Applying this method in a homogeneous cube, a result was acquired, error of which is small compared with the theoretical value. So this method is reliable, convenient and practical

Investigation of a method for the three-dimensional rigid body dynamics inverse problem

The three-dimensional rigid body dynamics inverse problem is cast as a discrete optimal control problem and solved using dynamic programming. The optimal control problem uses a forward dynamic model to provide estimates of unknown forces while matching noisy measurement histories. An L curve analysis is used to objectively select the amount of smoothing by trading off the magnitude of the estimated unknown forces with the fit to the noisy measurements. The forward dynamic model is derived using finite-element methodology and accounts for the inertia and mass properties of rigid bodies with the use of natural coordinates. The advantages of this forward model are that the large displacements’ nonlinearities can be routinely represented in the inverse problem and that it also allows the use of an exact energy conserving method to numerically integrate the equations of motion. A numerical example of a large displacement three body model is included to demonstrate the performance of the methodology.

Experimental validation of a complex, large-scale, rigid-body mechanism

This study presents an approach to an experimental validation of a complex, large-scale, multi-body mechanism model with diverse body inertia and geometry properties, exposed to an arbitrary kinematic excitation. Such an approach was used to analyze and predict the dynamical behaviour of a complex, 24-DOF, pendulum system with a relatively large dimensions. To obtain the theoretical dynamical response a computational dynamics approach was used in order to establish a constraint-based, simplified, planar, rigid-body numerical model. To validate the model, a special experimental approach was employed that overcame the difficulties related to the analyzed system’s size, many rotating components and simultaneous measuring requirements. Consequently, a combination of conventional and wireless signal-streaming measuring setups, which transmitted the signal through the purposely set-up wireless network, were employed. The model is validated by comparing the simulated and experimentally obtained kinematical and dynamical quantities to justify rigidity of the model’s components and the simplified planar modelling. The validated model’s ability to predict hard-to-measure system’s response is demonstrated.

Triple -Diffusive Convection in a Magnetized Ferrofluid With MFD Viscosity: A Nonlinear Stability Analysis

A nonlinear stability analysis is performed for a triple- diffusive convection in a magnetized ferrofluid with magnetic field -dependent viscosity (MFD) for stress- free boundaries. The major mathematical emphasis is on how to control the non-linear terms caused by magnetic body force and inertia forces. A suitable generalized energy functional is introduced to perform the nonlinear energy stability analysis. It is found that nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of linear instability, and thus indicate that the subcritical instabilities are possible. However, it is noted that in case of non-ferrofluid global nonlinear stability Rayleigh number is exactly same as that of linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter �� 3 , solute gradients �� 1 & �� 2and MFD viscosity parameter �� , on the subcritical instability region have also been analyzed.

Electrothermomechanical behavior of a radially polarized rotating functionally graded piezoelectric cylinder

A hollow circular cylinder made of exponentially graded piezoelectric material, such as PZT_4, is considered. Loading is composed of internal and external pressures, a distributed temperature field due to steady state heat conduction with convective boundary condition, an inertia body force due to rotation with constant angular velocity and a constant electric potential difference between its inner and outer surfaces. The material properties except Poisson’s ratio and thermal conduction coefficient are assumed to be exponentially distributed along radius. The governing equation in polarized form is shown to reduce to a second-order ordinary differential equation with variable coefficients for the radial displacement. In this article, a closed form solution is presented for this ODE by employing hypergeometric functions such as Whittaker’s M and W functions. Also we have considered four different sets of boundary conditions. The electrothermomechanical induced stresses and the electric potential distributions are investigated for

Measurement of momentum transfer due to adhesive forces: On-ground testing of in-space body injection into geodesic motion

In the frame of many scientific space missions, a massive free-falling object is required to mark a geodesic trajectory, i.e., to follow inside a spacecraft an orbit that is determined only by the planetary gravity field. The achievement of high-purity geodesic trajectories sets tight design constraints on the reference sensor that hosts and controls the reference body. Among these, a mechanism may be required to cage the reference body during the spacecraft launch and to inject it into the geodesic trajectory once on-orbit. The separation of the body from the injection mechanism must be realized against the action of adhesion forces, and in the worst case this is performed dynamically, relying on the body's inertia through a quick retraction of the holding finger(s). Unfortunately, this manoeuvre may not avoid transferring some momentum to the body, which may affect or even jeopardize the subsequent spacecraft control if the residual velocity is too large. The transferred momentum measurement facility (TMMF) was developed to reproduce representative conditions of the in-flight dynamic injection and to measure the transferred momentum to the released test mass. In this paper, we describe the design and development of the TMMF together with the achieved measurement performance.

Energy-Based Attitude Control of Spherical Pendulum

In this paper, we study the attitude control problems based on model of spherical pendulum. Three degrees of freedom pendulum (3D pendulum) is a rigid body supported by a frictionless pivot. According to relative position of the center of mass and the fixed pivot without friction, the 3D rigid pendulum can be divided into two balanced attitudes, Hanging equilibrium and inverted equilibrium. For the axisymmetric 3D rigid pendulum, the axis of symmetry is equivalent to axis of inertia of rigid body, and angular velocity around the axis of symmetry is equal to zero, as a result, the 3D rigid pendulum can be equal to the spherical pendulum. According to the motion attitude of spherical pendulum, one control method based on passive theory is proposed in this paper, Firstly, we use the passive theory to research the equilibrium stability of spherical pendulum. Secondly, passive theory and the Lyapunov function are utilized to deduce the control law .Finally, the spherical pendulum reach asymptotically stable in equilibrium position.