Linear Velocity Vector Research Articles

Normal impact of a ball rotating around its linear velocity.

We report on an experimental study of the normal impact on a solid surface of a table tennis ball that rotates around its linear velocity vector. We observe that the ratio of the reflected velocity to the incident velocity does not depend on the initial spin. In contrast, the reflected spin depends not only on the incident spin but also on the incident velocity. The experimental results, which reveal the tricky role played by the friction in the region of contact, are accounted for by simple theoretical arguments.

KINEMATIC STUDY OF A FOURTH-CLASS MECHANISM WITH THREE TRANSLATIONAL AND OTHER ROTATIONAL KINEMATIC PAIRS

The structural groups of links, composed of six links and nine kinematic pairs, form the basis for synthesizing a significant number of complex planar mechanisms, such as mechanisms of the third, fourth, fifth, and sixth classes. The investigation of these mechanisms presents certain difficulties as each complex mechanism requires an individual approach to its analysis. It should be noted that for many complex mechanisms of higher classes, a specific sequence of actions needs to be developed. Therefore, new research on such mechanisms is necessary and relevant. A study was conducted on the kinematic parameters of a fourth-class mechanism with one driving link, three translational pairs, and other rotational kinematic pairs. This mechanism is formed by the initial mechanism and the structural group of fourth-class links, where two translational pairs are internal, and one is external. The structural group of fourth-class links forms a closed loop consisting of one translational and three rotational kinematic pairs. In general, the structural group, consisting of six links and nine kinematic pairs, belongs to the group of fourth-class links of the third order and serves as the basis for a complex planar mechanism of the corresponding class. Using the method of conditional structural changes to the actual driving link of the fourth-class mechanism, another conditionally possible sequence was developed, and a kinematic study of the fourth-class mechanism with three translational and other rotational kinematic pairs was carried out. Linear velocity vectors of the mechanism’s points were determined. For kinematic investigation, a graph-analytical method was applied, allowing the solution of vector kinematic equations for the fourth-class mechanism in the form of graphical constructions. These constructions were initially performed in an arbitrarily chosen scale and then refined, taking into account the kinematic parameters of the specific study. The obtained research results can be beneficial, particularly for researchers dealing with planar mechanisms of the fourth and higher classes, conducting similar investigations.

PTA-Sync: Packet-Train-Aided Time Synchronization for Underwater Acoustic Applications

In underwater acoustic applications, time synchronization errors accumulate severely with time, owing to the unpredictable propagation delay change induced by mobility and low sound propagation speed. In previously reported schemes, error accumulation during underwater acoustic time synchronization occurred, decreasing their performance and affecting their applicability. To overcome this limitation, we propose packet-train-aided time synchronization (PTA-Sync) for underwater acoustic application. The proposed PTA-Sync adaptively tracks one-way travel time (OWTT) change using three-dimensional linear velocity vector, the transmit time difference and arrival time difference of two adjacent packets in a packet train, and the position information of a mobile reference node. Thus, this scheme enables us to reduce the synchronization error accumulation rate by estimating the propagation delay change more accurately. Simulation results show PTA-Sync achieves higher accuracy than existing OWTT-based synchronization schemes. Thus, PTA-Sync can be effectively used in underwater exploratory activities because it can successfully reduce time synchronization errors.

Математическая модель, алгоритм формирования вектора состояния и техническая реализация многокоординатного задающего органа внутрикамерных манипуляторов

The purpose of the study is a development of a mathematical model and an algorithm for the calculation of the state vector of a multi-axes delta-type control joystick for moving special purposes arm manipulators by a human operator in the loop. Research methods. The paper considers the existing methods of remote control of intrachambers special purpose arm manipulators with a human operator in the control loop, identifies the advantages and disadvantages of existing solutions. The task of synthesizing the optimal control stick to ensure driving of the manipulator in 3D-space was set. Today, nuclear industry enterprises widely use hermetic chambers in which copy-type electromechanical manipulators are installed. The manipulation system includes an arm manipulator installed directly in a sealed chamber, and its kinematically similar control arm. The operator manually moves the control arm, the trajectory of which is repeated inside the chamber by the arm manipulator. Taking into account moral and physical obsolescence, the introduction of modern approaches to the human-machine interaction is required. The paper proposes a mathematical model for calculation the state vector (linear and angular coordinates) of a delta-type control stick from measured information about the relative angular position in its rotational kinematic pairs. Results of the study. An algorithm for calculating the coordinates of the handle of the control stick is synthesized based on a priori information about the relative position of the elements in the delta-mechanism. Taking into account the additional discrete and proportional controls located on the handle of the control stick, the proposed algorithm and its practical implementation make it possible to introduce effective manipulator control modes. Conclusion. The main results of the work include a mathematical model and an algorithm for generating the state vector of the delta-type control stick, which allows the operator to form the linear and angular velocity vectors of the arm manipulator and its gripper movement by one hand. The technical implementation of the control stick and algorithm, as well as its test operation with a dual arm manipulator system, showed the high efficiency of the proposed solutions.

Kinematic Analysis in 3-Dimensional Generalized Space

In this paper, we have first obtained the derivatives of spherical and spatial motions by using the special matrix group in generalized space E3(α,β). The rotation matrices and tangent operators were found by using derivatives of one- and multi-parameters motions in E3(α,β). Also, we obtained the angular velocity matrix of the moving body and its linear velocity vector. Finally, we gave some examples including applications of tangent operators and rotation matrices in support of our results.

Aerodynamic-Torque Induced Motions of a Spinning Football and Why the Ball’s Longitudinal Axis Rotates with the Linear Velocity Vector

This paper presents an explanation of why a spinning football rotates so that the spin axis remains nearly aligned with the velocity vector, and approximately parallel to the tangent to the trajectory. The paper derives the values of the characteristic frequencies associated with the football’s precession and nutation. The paper presents a graphical way of visualizing how the motions associated with these frequencies result in the observed “wobble” of the football. A solution for the linearized dynamics shows that there is a minimum amount of spin required for the motion to be stable and for the football not to tumble. This paper notes the similarity of this problem to that of spun projectiles. The results show that the tendency of a football to align itself with and rotate with the velocity vector is associated with an equilibrium condition with a non-zero aerodynamic torque. The torque is precisely the value required for the football to rotate at the same angular rate as the velocity vector. An implication of this is that a release with the football spin axis and velocity vector aligned (zero aerodynamic torque) is not the condition that results in minimum motion after release. Minimum “wobble” occurs when the ball is released with its symmetry axis slightly to the right or left of the velocity vector, depending on the direction of the spin. There are additional forces and moments acting on the football that affect its trajectory and its stability, but it is not necessary to consider these to explain the tendency of the ball to align with the velocity vector and to ”wobble.” The results of this paper are equally applicable to the spiral pass in American football and the screw kick in rugby.

Vector Kinematics Modelling and Simulation Analysis of Half-rotating Walking Mechanism

In order to solve the stability problem existing in the robot mobile system based on the two-stage half-rotating mechanism, a swing balanced configuration is proposed. Combining the vector method and the D-H method, a forward kinematics modelling and analysis method for the half-rotating walking mechanism is proposed. First of all, using vector kinematics, according to the characteristics of the walking mechanism, combined with the D-H method to establish the relevant coordinate system and the transformation matrix between each coordinate system, derived the position vector, angular velocity vector, linear velocity vector and other relevant kinematic characteristic expressions of the key points of the mechanism, and calculated in MATLAB software to get its theoretical analytical curve. At the same time, the kinematics model of the half-rotating walking mechanism is established in the ADAMS software, and the ADAMS simulation results are compared with the theoretical analysis results. The two are basically consistent, which verifies the correctness of the forward kinematics modelling method of this half-turn walking mechanism.

Variational formulation of dynamic problems for a nonlinear Cosserat medium

Abstract A variational formulation of dynamic problems for a geometrically and physically nonlinear elastic Cosserat medium is obtained in the form of the problem of finding the stationary point of Hamilton's functional. Variations of the strain and rotation tensors and the linear and angular velocity vectors are calculated. The equivalence of the Euler equations with natural boundary conditions to the equations of motion with the original boundary conditions in the case of potential force and torque loads is proved. A nontrivial potentiality condition of the torque (bulk and surface) loads is obtained.

Uniform circular motion concept attainment through circle share learning model using real media

Uniform circular motion is an important concept and has many applications in life. Student’s concept understanding of uniform circular motion is not optimal because the teaching learning is not carried out properly in accordance with the characteristics of the concept. To improve student learning outcomes required better teaching learning which is match with the characteristics of uniform circular motion. The purpose of the study is to determine the effect of real media and circle share model to the understanding of the uniform circular motion concept. The real media was used to visualize of uniform circular motion concept. The real media consists of toy car, round table and spring balance. Circle share model is a learning model through discussion sequentially and programmed. Each group must evaluate the worksheets of another group in a circular position. The first group evaluates worksheets the second group, the second group evaluates worksheets third group, and the end group evaluates the worksheets of the first group. Assessment of learning outcomes includes experiment worksheets and post-test of students. Based on data analysis we obtained some findings. First, students can explain the understanding of uniform circular motion whose angular velocity and speed is constant correctly. Second, students can distinguish the angular velocity and linear velocity correctly. Third, students can explain the direction of the linear velocity vector and the direction of the centripetal force vector. Fourth, the student can explain the influence of the mass, radius, and velocity toward the centripetal force. Fifth, students can explain the principle of combined of wheels. Sixth, teaching learning used circle share, can increase student activity, experimental results and efficiency of discussion time.

Radiation and dynamics of a nanoparticle in equilibrium background radiation upon translational–rotational motion

We have obtained general expressions for the intensity of radiation and tangential force of a small polarizable particle in the process of translational-rotational motion in equilibrium radiation background (thermalized photon gas) of certain temperature at an arbitrary relative orientation of the linear and angular velocity vectors. It is shown that in cold vacuum background the translational velocity of particle is independent of time and the intensity of its spontaneous emission is determined by the angular velocity and imaginary part of the polarizability.

Main Contributors to the Baseball Bat Head Speed Considering the Generating Factor of Motion-dependent Term

Motion-dependent term (MDT), which consists of centrifugal force, Coriolis force and gyro moment expressed in the equation of motion for a multi-link system, plays significant roles in the generation of tip speed in a high speed swing motion. A phenomenon caused by the MDT is usually called as “whip-like effect” and “kinetic chain”. Since the baseball batting is one of high speed swing motion manipulating a bat by both hands, it is important to make clear the generating factor of MDT and main contributors to the generation of bat head speed. The purpose of this study was to quantify main contributors to the bat head speed considering the generating factor of MDT. The whole-body segments with bat were modelled as a system of sixteen-rigid linked segments. The equation of motion for the system was obtained by considering anatomical constraint axes at joints and modelling errors. A recurrence formula with respect to the generalized velocity vector consisting of linear and angular velocity vectors of all segments was derived. Five collegiate baseball players, participated as subjects, hit a teed ball as strong as possible. The kinematic and kinetic data were measured with the motion capture system with 3 force platforms and an instrumented bat. The results indicates that the abduction and extension torques at the knob-side shoulder joint and the forward rotation torque at the torso joint are the main positive contributors to the generation of bat head speed among the participants.

Measurements and modeling of instantaneous particle orientation within abrasive air jets and implications for particle embedding

Previous theoretical studies indicate that the material removal mechanism and the likelihood of particle embedding in solid particle erosion processes strongly depend on instantaneous particle orientation at impact. The present study utilized pulsed laser shadowgraphy to measure the size, shape, and instantaneous orientation distributions of particles within a micro-abrasive jet at various pressures, particle sizes, and nozzle standoff distances. A particle orientation angle was defined as the angle between the particle linear velocity vector (approximately parallel to the jet centerline axis) and the line connecting the center of mass to the furthest downstream particle vertex. Particles were considered to be ‘oriented’, i.e. in a configuration favorable to embedding, if this angle was between 0 and 10°. The measurements revealed that, at all pressures (i) between 24% and 29.5% of the particles were oriented at the nozzle exit; (ii) the percentage of oriented particles increased slowly with standoff distance; (iii) larger particles had a stronger tendency to orient than smaller ones; (iv) particles having larger aspect ratios had a stronger tendency to aerodynamically align with the jet, and (v) although not all particles that were oriented actually embedded, the measured percentage of embedded particles on Al 6061-T6 surfaces nevertheless correlated with the percentage of oriented particles. A model capable of predicting the instantaneous particle orientation and velocity within and downstream of the nozzle was presented and shown to agree well with measurements. To the knowledge of the authors, these are the first measurements of the instantaneous orientation of abrasive particles under conditions that are typical of abrasive air jets. The results may have important implications for optimizing solid particle erosion tests and in abrasive jet machining applications.

Characterization and Modeling of Micro Swimmers With Helical Tails and Cylindrical Heads Inside Circular Channels

Micro swimming robots offer many advantages in biomedical applications, such as delivering potent drugs to specific locations in targeted tissues and organs with limited side effects, conducting surgical operations with minimal damage to healthy tissues, treatment of clogged arteries, and collecting biological samples for diagnostic purposes. Reliable navigation techniques for micro swimmers need to be developed for navigation, positioning, and localization of robots inside the human body in future biomedical applications. In order to develop simple models to estimate trajectories of magnetically actuated micro swimmers blood vessels and other conduits, effects of the channel wall must be understood well. In this study, swimming of one-link robots with helical tails in stationary fluids inside channels is modeled with Stokes equations and solved numerically with the finite-element method. Lateral and angular velocities of the robot are obtained from force free swimming conditions. Effects of the amplitude and number of helical waves, and the relative size of the body of the swimmer and its radial position on angular and linear velocity vectors of the swimmer are presented.

Extracting Rolling Element Bearing Faults From Noisy Vibration Signal Using Kalman Filter

Vibration analysis has been widely accepted as a common and reliable method for bearing fault identification, however, the presence of noise in the measured signal poses the maximum amount of difficulty. Therefore, for the clearer detection of defect frequencies related to bearing faults, a denoising technique based on the Kalman filtering algorithm is presented in this paper. The Kalman filter yields a linear, unbiased, and minimum mean error variance recursive algorithm to optimally estimate the unknown states of a dynamic system from noisy data taken at discrete real time intervals. The dynamics of a rotor bearing system is presented through a linear model, where displacement and velocity vectors are chosen as states of the system. Process noise and measurement noise in the equations of motion take into account the modeling inaccuracies and vibration from other sources, respectively. The covariance matrix of the process noise has been obtained through the transfer function approach. The efficiency of the proposed technique is validated through experiments. Periodic noise and random noises obeying the white Gaussian, colored Gaussian and non-Gaussian distribution have been simulated and mixed with a clean experimental signal in order to study the efficiency of the standard Kalman filter under various noisy environments. Additionally, external vibrations to the test rig have been imparted through an electromechanical shaker. The results indicate an improvement in the signal to noise ratio, resulting in the clear identification of characteristic defect frequencies after passing the signal through the Kalman filter. The authors find that there is sufficient potential in using the Kalman filter as an effective tool to denoise the bearing vibration signal.

Analysis and Calculation of Transmission Ratio of Simpson Planetary Gear Mechanism Based on Velocity Graphic Method

The paper summarizes the principle of applying velocity graphic method to analyze Simpson planetary gear mechanism, which provides guidance for analysis procedure. The movement of each element in the mechanism can be intuitively understood through drawing the linear velocity vectors of three constant velocity points. The similar triangle principle is used to calculated transmission ratio of each transmission scheme in the linear velocity vector diagram, and the correctness of the analysis method and process is verified by the transmission ratio calculated by velocity graphic method and analytic method.

An underwater vehicles dynamics in the presence of noise and Fokker-Planck equations

In systems and control literature, underwater vehicles are studied extensively. The translational equations of motion coupled with rotational equations, which encompass the evolution of linear velocity vector in combination with angular velocity vector, describe the equation of motion of underwater vehicles. As a result of this, the underwater vehicle dynamics assumes the structure of a six-dimensional ordinary differential equation. Ocean current circulations influence stochastically the motion of underwater vehicles. In this paper, first we account the underwater vehicle-ocean current interaction in the stochastic framework that leads to a multi-dimensional Stochastic Differential Equation (SDE). Secondly, we accomplish the noise analysis of underwater vehicles using the Fokker-Planck technique. This paper will be of interest to mechanists, control theorists, naval scientists looking for research in autonomous systems under noise influence. Further research on stochastically perturbed underwater vehicles will refine existing results available in literature.

Test bed calibration of fog-based strapdown inertial measurement unit

The paper outlines the method for calibration of a strapdown inertial measurement unit (SIMU) based on fiber-optic gyros (FOG) in dynamic conditions on a test bed. Calculated components of linear velocity vector and position of SIMU accelerometer unit on the test bed platform are used as a reference. The accuracy of a proposed method is estimated by testing the SIMU based on FOGs by IXSEA (France) on three-axis rate table by Acutronic.

Real-Time Navigation of Nonholonomic Mobile Robots under Velocity Vector Control

In this paper, linear navigation law is studied in depth and we suggest an efficient, practical and simple approach for nonholonomic mobile robot navigation under velocity vector control based on the linear navigation law. First of all, an obstacle is equivalent to a velocity vector when detected by a robot's sensory system according to the relative distant and relative direction between the robot and the obstacle. Then the vector sum of all obstacles' equivalent velocity vectors (OEVVs) and the linear navigation velocity vector (LNVV) derived from the linear navigation law drives the robot to reach the desired goal position without colliding with any obstacle in the robot's workspace. Furthermore, during the process of driving the mobile robot under the resultant velocity vector, a set of strategies for velocity and acceleration constraints (VAC) is devised to make kinematic behaviours of the mobile robot more practical. Finally, to validate the effectiveness and superiority, extensive simulation results with no obstacles, a single obstacle and multiple obstacles are provided.

P-24 Study of humerus injury under impact loading for baseball

In the United States and Japan, baseball is a very popular sport played by a great many people. However the ball used is hard and moves fast. A professional baseball pitcher in good form can throw a ball at up to 41.7m/s (150km/hr). If a ball at this speed hits the batter, serious injury is quite likely. In this paper we will describe our investigations of the impact of a baseball with living tissues by numerical methods and experiments. The experiments were done to characterize the material and structure of the baseball. Baseballs were fired at a load cell plate using a specialized pitching machine previously described in publications. The pitching machine had three rollers which were controlled by a neural network to produce a desired combination of linear and angular ball velocity vectors. The dynamic properties of the ball were determined by comparing the experimentally measured force history to a FE model. A different FE model representing a human humerus and surrounding tissue was then used in simulated impact experiments. The properties of the human tissues were not measured here were taken from published results. The dynamic finite element analysis was done by ANSYS/LS-DYNA. The results include an estimate of the peak stress in the bone and confirm what we know from experience - that a fast ball can cause a bone to break. Some methods to practicably reduce the severity of injuries in the game of baseball are also discussed.

Interpretation of velocity measurements as indirect in the trajectory finding problem

It is shown that the necessary condition for the correct statement of the inverse trajectory problem in measuring the linear velocity vector of a material point in the gravitational field is the nondegeneracy of the matrix, i.e., the Hessian of the field potential function.