Rotational Trajectories Research Articles

A Magnetometer Calibration Method Using Single-Axis Motion Trajectory and Unscented Kalman Filter for Body Motion Capture Applications

Magnetometer calibration is a pre-processing step in the Attitude and Heading Reference Systems (AHRS) which has an essential role in many applications. The main purpose of this article is to derive an innovative and precise calibration approach for a magnetometer set installed on human body. To execute this calibration method, all the error parameters of multiple magnetometers are considered in an Unscented Kalman Filter (UKF) model for accurate estimation of calibration parameters. As achieving a precise estimation in Kalman filters-based algorithms needs an accurate and complete observation model, a special single-axis rotation trajectory for Inertial Measurement Unit (IMU) is performed to increase the observability rank of the calibration model. To evaluate the proposed method, five body-mounted sensors were experimented in the laboratory at the same time for applying in the body motion capture system. The results showed that all five sensors were well-calibrated without any need to be detached from the body and using any rotational robot arm. The resolution and precision of the proposed calibration method are assessed by the ellipsoid-fitting representation method. Consequently, all the body-mounted magnetometers were calibrated, on average, by about 1% uncertainty. The method can be used in every motion capture and AHRS applications due to its feasibility and simplicity.

Dynamic rotational trajectory planning of a cable-driven parallel robot for passing through singular orientations

This paper presents a dynamic trajectory planning scheme for passing through singular orientations of a three degree-of-freedom (DOF) rotational cable-driven parallel robot (CDPR) that uses a rigid link to restrict its translational DOFs. The kinematics, dynamics and actuation singularity loci of this CDPR are analyzed. Singularity loci divide the workspace into four independent parts, which significantly limit the motion performance of the mechanism. To this end, consistency conditions that can allow the robot to steadily pass through singular orientations are studied. The vector inner product form of consistency conditions is derived, which can simplify the determination of the conditions of a more complex parallel robot. A sequence of target orientations are reached by planning dynamic trajectories using the unit quaternion. A modified spherical linear interpolation with a fifth degree polynomial as the time function is used for the generation of a trajectory which does not contain a singular orientation. Moreover, a transition segment using a seventh degree polynomial is designed to merge into the fifth degree polynomial in order to satisfy the consistency conditions and pass through singular orientations. Simulations are provided to verify the proposed technique.

The design and implementation of "teaching-reproduction" algorithm for servo motor based on RFC 470 PLC

Aiming at the characteristics of more swing and less rotation of the nozzle at the end of teaching-type sand-blasting robots, a motion control algorithm which can reproduce the swing and rotation trajectory of the servo motor is designed. The RFC 470 PLC of PHOENIX Contact is used as the control core to build the hardware experimental platform in this paper. In the process of teaching, the trajectories of the servo motor are saved to the data storage of the RFC 470 PLC by the algorithm and then the trajectories can be reproduced automatically. The experimental results show that the designed algorithm has high accuracy and can meet the needs of practical engineering application.

Differences in kinematic parameters between male and female hammer throw finalists of the World Championship in Daegu in 2011

Background and Study Aim. Hammer throwing is the most complex athletic throwing discipline with rotational trajectory and strong effect of several different forces that try to disable the projected throwing trajectory. Kinematic parameters are an important segment in the analysis of athletic disciplines, including hammer throw. They are an indicator of influence and often a difference between competitors of different or the same rank of the competition.
 The aim of the study was to determine the spatial and temporal differences of kinematic parameters between male and female elite hammers.
 Material and Methods. The study was conducted on sample of 16 Daegu World Championship finalists in 2011, to analyse differences in kinematic parameters between male and female throwers hammer. To obtain the required results, t-test for small independent samples was applied.
 Results. The data obtained in the study were given as Mean and Standard deviation. Statistically significant differences between male and female finalists were confirmed in the rate of ejection (t=3.684; p<0.004) and the speed of the fourth turn (t=4.396; p<0.002). The male finalists achieved an average ejection velocity of 27.91m/s and the female finalists 27.17m/s, with an average turn speed of 4.67m/s (male) and 4.03m/s (female).
 Conclusions. The research has shown that significant differences were made between male and female finalists in Daegu in 2011. The causes of differences can be found in length of training, different training process, technical mastery, competitor experience, morphological profile, motor and anatomical structures, movement technique and biomechanical parameters, which were not taken into the research.

Object-Agnostic Dexterous Manipulation of Partially Constrained Trajectories

We address the problem of controlling a partially constrained trajectory of the manipulation frame–an arbitrary frame of reference rigidly attached to the object–as the desired motion about this frame is often underdefined. This may be apparent, for example, when the task requires control only about the translational dimensions of the manipulation frame, with disregard to the rotational dimensions. This scenario complicates the computation of the grasp frame trajectory, as the mobility of the mechanism is likely limited due to the constraints imposed by the closed kinematic chain. In this letter, we address this problem by combining a learned, object-agnostic manipulation model of the gripper with Model Predictive Control (MPC). This combination facilitates an approach to simple vision-based control of robotic hands with generalized models, enabling a single manipulation model to extend to different task requirements. By tracking the hand-object configuration through vision, the proposed framework is able to accurately control the trajectory of the manipulation frame along translational, rotational, or mixed trajectories. We provide experiments quantifying the utility of this framework, analyzing its ability to control different objects over varied horizon lengths and optimization iterations, and finally, we implement the controller on a physical system.

A Comprehensive Study on the Variation Phenomena of AO 0235+164

Abstract The variation mechanism of blazars is a long-standing open question. Observations of polarization can provide us with more information to constrain models. In this work, we collect long-term multiwavelength data on AO 0235+164, and analyse the correlations between them by using the local cross-correlation function. We find that both γ-ray and the optical V-band light curves are correlated with the radio light curve beyond the 3σ significance level. The regions emitting the γ-ray and optical radiation coincide within errors, and are located pc upstream of the core region of 15 GHz, which is beyond the broad-line region. The color index shows the redder-when-brighter trend in the low flux state, but turns to the bluer-when-brighter trend in the high flux state, while the γ-ray spectral index always shows the softer-when-brighter trend. We propose that such complex variation trends can be explained by the increasing jet component with two constant components. The optical polarization degree (PD) flares and optical flux flares are not synchronous. It seems that one flux peak is sandwiched by two PD peaks, which have inverse rotation trajectories in the qu plane. The helical jet model can schematically show these characteristics of polarization with fine-tuned parameters. The change in viewing angle is suggested to be the primary variable that leads to all these variations, although other possibilities such as the shock-in-jet model or the hadronic model are not excluded completely.

Biomechanical Analysis Hammer Throw: The Influence of Kinematic Parameters on the Results of Finalists World Championships

Background: Hammer throw is the most complex athletic throwing discipline with a rotational trajectory and the strong action of several different forces that try to disable the projected throwing trajectory. Kinematic parameters are an important segment in the analysis of athletic disciplines, including hammer throw. Aim study: The aim of the study was to determine the influence of spatial and temporal biomechanical parameters on hammer throw results. Methods: The study was conducted on a sample of 56 male and female World Championship finalists (Berlin, 2009, Daegu, 2011, London, 2017). Multiple regression analysis was applied to determine the influence of defined kinematic parameters on the result performance of the throw. Result: The results of the male finalists confirmed the direct correlation between the starting speed (r=0.64 p=0.001), the first turn speed (r=0.47 p=0.017), the release velocity (r=0.86 p=0.000), the release of angle (r=0.37 p=0.049), and the inverse effect of the duration of the first (r=-0.40 p=0.046) and third turn (-0.46 p=0.020). The regression function of the male sample also confirmed the influence of starting speed, release of velocity (p=0.01 p) and angle of release (p=0.04 p). In the female finalists, the direct correlation is between the release of velocity (r=0.90 p=0.000), the angle of release (r=-0.62 p=0.000) and the fourth turn speed (r=0.50 p=0.002). The regression function for the female sample confirmed a high negative influence of the starting speed, while the direct influence was recorded at the release of velocity (p=0.02 p) at the given level of statistical significance of the regression function. Conclusion: The defined set of kinematic parameters had a significant impact on the result performance of male and female hammer throw finalists.

Ultrasonography of a Helical Left Common Carotid Artery.

Case PresentationAn 83-year-old woman was admitted to the intensive care unit for septic shock at which point an internal jugular central venous line was placed. The patient’s common carotid artery was visualized in an atypical location, lateral to the internal jugular vein. Further inspection revealed the common carotid artery travelling in a rotational trajectory around the internal jugular vein.DiscussionFor at least two decades, point-of-care ultrasound has become the standard of care for placing central venous lines. This surprising anatomical orientation is rare and cautions physicians to fully explore a patient’s anatomy prior to placing central lines.

Geometric dependence of image quality in digital tomosynthesis: Simulations of X-ray source trajectories and scan angles

Digital tomosynthesis (DTS) is able to provide the 3-dimensional (3D) images of an object, while reducing radiation dose compared to computed tomography (CT). Despite these benefits, DTS has a geometric sensitivity because only a few dozen projections obtained with limited scan angles are used for DTS imaging. In this study, we evaluated the effects of X-ray source scan trajectories and angles on DTS images for investigating the geometric dependence in DTS. The DTS systems were simulated with linear, rotational and circular scan trajectories, and 54 projections were obtained from each of the four scan angle intervals of ± 17, ± 27, ± 37 and ± 47 degrees. The obtained projections were reconstructed by using a model-based filtered back-projection (FBP) technique. The characteristics of reconstructed DTS images were analyzed in terms of quantitative accuracy, noise property, contrast-to-noise ratio (CNR) and spatial resolution. The results showed that the quality of DTS images was highly dependent on the geometric variations, and the characteristics of DTS images differed according to the X-ray source scan trajectories and angles. In conclusion, the DTS geometries should be determined by considering image quality and characteristic in order to optimize their systems and applications.

Stepping in circles: how locomotor signals of rotation adapt over time

While it has been well described that prolonged rotational stepping will adapt the podokinetic sense of rotation, the mechanisms involved are not clearly understood. By studying podokinetic after-rotations following conditioning rotations not previously reported we have shown that slower rotational velocities are more readily adapted than faster velocities and adaptation occurs more quickly than previously thought. We propose a dynamic feedback model of vestibular and podokinetic adaptation that can fit rotation trajectories across multiple conditions and data sets. Two adaptation processes were identified that may reflect central and peripheral processes and the discussion unifies prior findings in the podokinetic literature under this new framework. The findings show the technique is feasible for people with locomotor turning problems. After a prolonged period stepping in circles, people walk with a curved trajectory when attempting to walk in a straight line without vision. Podokinetic adaptation shows promise in clinical populations to improve locomotor turning; however, the adaptive mechanisms involved are poorly understood. The first phase of this study asks: how does the podokinetic conditioning velocity affect the response velocity and how quickly can adaptation occur? The second phase of the study asks: can a mathematical feedback model account for the rotation trajectories across different conditioning parameters and different datasets? Twelve healthy participants stepped in place on the axis of a rotating surface ranging from 4 to 20degs-1 for durations of 1-10min, while using visual cues to maintain a constant heading direction. Afterward on solid ground, participants were blindfolded and attempted to step without rotating. Participants unknowingly stepped in circles opposite to the direction of the prior platform rotation for all conditions. The angular velocity of this response peaked within 1min and the ratio of the stimulus-to-response peak velocity fitted a decreasing power function. The response then decayed exponentially. The feedback model of podokinetic and vestibular adaptive processes had a good fit with the data and suggested that podokinetic adaptation is explained by a short (141s) and a long (27min) time constant. The podokinetic system adapts more quickly than previously thought and subjects adapt more readily to slower rotation than to faster rotation. These findings will have implications for clinical applications of the technique.

Energy estimation for differential drive mobile robots on straight and rotational trajectories

Energy autonomy is an important aspect that needs to be improved in order to increase efficiency in mobile robotic tasks. Having accurate power models allows the estimation of energy consumption along different trajectories. This article proposes a power model for two-wheel differential drive mobile robots. The proposed model takes into account the dynamic parameters of the robot and its motors, and predicts the energy consumption for trajectories with variable accelerations and variable payloads. The experimental validation of the proposed model was performed with a Nomad Super Scout II mobile robot which was driven along straight and curved trajectories, with different payloads and accelerations. The experiments using the proposed model showed accuracies of 96.67% along straight trajectories and 81.25% along curved trajectories in the estimation of energy consumption.

Fast States Revealed by Theory of Jumps in F1-ATPase Rotation Experiments

Single-molecule spectroscopies revealed the stepping rotation of an F1-ATPase enzyme in which a substep can have microsecond transition dynamics. Here we describe a method for analyzing fast single molecule rotation trajectories in F1-ATPase monitored by a 40 nanometer probe. This method focuses on the rotation jumps that occur in the transitions during the steps between dwells in single molecule trajectories. These jumps are related to the instantaneous rotation velocity and they exhibit a bimodal distribution at certain angles, indicating that the system produces both forward and a backward torques at the same angle, due to being in either of two states. Two states at the same angle is a key assumption used to extracts rate constants in stalling experiments, so by observing the bimodal distributions we provide support for this assumption. To calculate the distribution of jumps, we use a multi-state theory to describe the visco-elastic fluctuation of the imaging probe. The predicted jump distribution in the transitions yields a relaxation time which agrees with its value of 14 microseconds in the dwell fluctuations. Using a sequence of three states, the theoretical profile of angular jumps agrees with experiment for most of the angular range, but full agreement between theory and experiment is reached if a fourth, 10 microsecond lifetime state is assumed with an effective dwell half way through the 80 degree substep. It suggests that the ATP binding in one subunit and the ADP release from another subunit occurs via this transient. The ability to detect a state that is comparable or shorter than the instrumental relaxation time indicates that this jump distribution based method can be used to effectively increase the time resolution of the imaging apparatus.

A Novel Local Smoothing Method for Five-Axis Machining With Time-Synchronization Feedrate Scheduling

This paper presents an analytical continuous smoothing method for the five-axis toolpath by simultaneously scheduling the tool position and tool orientation trajectories. In order to ensure the high-order continuous, the peak-controlled jerk and arclength-parameterized property, a novel curve “airthoid” is proposed for the first time. The biairthoid is involved to smooth the corners of the tool position in the workpiece coordinate system (WCS) and the corners of the tool orientation in the machine coordinate system (MCS), the geometries of which are analytically determined by the user-defined deviation errors. A time synchronization strategy is proposed to extend the duration of the predetermined cubic acceleration profile to a specified time. With the kinematic constraints of the tool position and the tool orientation, the transitional and rotational trajectories are analytically synchronized by sharing the same motion time. To comply with the constraints of the linear feed drives, an optimization strategy is conducted by adjusting the kinematics of the tool position. By doing so, the approximation errors of the tool position and tool orientation in the WCS are strictly satisfied. The analytical arclength expression of the smoothing curves is more suitable for the on-line interpolation. Due to the arclength-parametrized transition curve, the feedrate fluctuation is eliminated. With the proposed time synchronization strategy, the physical limits of the feed drives are all respected. Moreover, the high-order continuous airthoid makes the motion more smoothing-going. Simulations and experiments verify the effectiveness of the proposed algorithm.

Characteristics of the rotation and flight trajectory of balls thrown by elite female softball pitchers

Characteristics of the rotation and flight trajectory of balls thrown by elite female softball pitchers

Finger Grasp Kinematics Towards Exoskeleton Development

Abstract This paper investigates the relationships between index finger joint rotations to determine whether a one degree of freedom (DOF) exoskeleton could produce natural finger motions for a range of different users and grasping conditions. Four healthy subjects each performed ten trials involving the grasp of two cylindrical objects with diameters of 66.5mm and 47mm. Finger trajectories for each trial were recorded using a motion capture system and were used to obtain joint rotational trajectories for the Metacarpo-phalangeal (MCP) Proximal-interphalangeal (PIP) and Distal-interphalangeal (DIP) joints. Joint ranges of motion (ROM) were largest for all subjects when grasping the smaller diameter object. This effect was also seen where subjects with longer fingers tended to use a larger MCP ROM for the same object. Subject 2 was an exception to this, using the smallest MCP and PIP ROM of all subjects when grasping the large diameter object: this anomaly is thought be caused by difference in palmar engagement with the object. The profile of the MCP-PIP trajectories were similar when normalised to their range of motion, with a maximum y-axis error of 22%. This implies that the MCP-PIP relationship for a cylindrical grasp can be approximated be a general scalable polynomial. We conclude that through parabolic coupling between MCP and PIP joints, a one-DOF exoskeleton is capable of producing functional grasping movements. Through an adjustable coupling mechanism between MCP and PIP, it is also believed that an exoskeleton can be successfully adapted for differing object and finger sizes.

Modeling of rotation accuracy of multi-support rotating machinery considering geometric errors and part deformation

PurposeThis paper aims to develop a theoretical method to analyze the rotation accuracy of rotating machinery with multi-support structures. The method effectively considers the geometric errors and assembly deformation of parts.Design/methodology/approachA method composed of matrix and FEA methods is proposed to do the analysis. The deviation propagation analysis results and external loads are set as boundary conditions of the model which is built with Timoshenko beam elements to calculate the spatial pose of the rotor. The calculation is performed repeatedly as the rotation angle increased to get the rotation trajectories of concerned nodes, and further evaluation is done to get the rotation accuracy. Additionally, to get more reliable results, the bearing motion errors and stiffness are analyzed by a static model considering manufacturing errors of parts.FindingsThe feasibility of the proposed method is verified through a case study of a high-precision spindle. The method reasonably predicts the rotation accuracy of the spindle.Originality/valueFor rotating machinery with multi-support structures, the paper proposes a modeling method to predict the rotation accuracy, simultaneously considering geometric errors and assembly deformation of parts. This would improve the accuracy of tolerance analysis.

Математическое описание вращения точки вокруг эллиптической оси в некоторых частных случаях

Previously, we developed a constructive method for modeling surfaces of rotation with axes, which were second-order curves such as circle, ellipse, parabola and hyperbola [1]. We also described the principle of constructing a mathematical model [23] corresponding to this constructive technique [2], and expressed the method in mathematical form. In this paper, we applied the previously developed mathematical model that allows us to determine the trajectory of rotation of a point around an elliptical axis to some special cases of the location of this point and identified the features of each of them. We applied the previously accepted terminology and the system of designating points, straight and curved lines involved in the search for circular trajectories of rotation of points. We analyzed the cases of the location of the generating point on the coordinate axes. We determined in mathematical form the trajectory of the point located in these positions. This entry is represented as systems of parametrically given equations. The article also describes a step-by-step algorithm used to find the equation of a circle, which is the trajectory of rotation of a point around an elliptic axis. We applied this algorithm to various positions of the generating point relative to the elliptic axis foci. We applied the previously developed criteria for selecting near and far centers of rotation relative to one of the focuses of the ellipse. The results of these mathematical studies will be used in the future to create a computer program capable of generating digital 3D-models of surfaces formed by the rotation of arbitrary sets forming points around the curves of the axes of the second order.

Method to extract multiple states in F1-ATPase rotation experiments from jump distributions

A method is proposed for analyzing fast (10 μs) single-molecule rotation trajectories in F1 adenosinetriphosphatase ([Formula: see text]-ATPase). This method is based on the distribution of jumps in the rotation angle that occur in the transitions during the steps between subsequent catalytic dwells. The method is complementary to the "stalling" technique devised by H. Noji et al. [Biophys. Rev. 9, 103-118, 2017], and can reveal multiple states not directly detectable as steps. A bimodal distribution of jumps is observed at certain angles, due to the system being in either of 2 states at the same rotation angle. In this method, a multistate theory is used that takes into account a viscoelastic fluctuation of the imaging probe. Using an established sequence of 3 specific states, a theoretical profile of angular jumps is predicted, without adjustable parameters, that agrees with experiment for most of the angular range. Agreement can be achieved at all angles by assuming a fourth state with an ∼10 μs lifetime and a dwell angle about 40° after the adenosine 5'-triphosphate (ATP) binding dwell. The latter result suggests that the ATP binding in one β subunit and the adenosine 5'-diphosphate (ADP) release from another β subunit occur via a transient whose lifetime is ∼10 μs and is about 6 orders of magnitude smaller than the lifetime for ADP release from a singly occupied [Formula: see text]-ATPase. An internal consistency test is given by comparing 2 independent ways of obtaining the relaxation time of the probe. They agree and are ∼15 μs.

Local characteristics of paraxial Laguerre–Gaussian vortex beams with a zero total angular momentum

ABSTRACT“We report a detailed study of paraxial Laguerre–Gaussian beams with a zero total angular momentum provided by opposite signs of the vortex phase singularity and circular polarization. These beams are characterized by the multi-ring structure. We have calculated analytically the components of the Umov–Poynting vector and the angular momentum density in the focal region. The local integral characteristics associated with the Umov–Poynting vector and angular momentum density are analyzed. The main attention is paid to the characteristics of the Umov–Poynting vector components in separate rings at different values of the radial index of the Laguerre–Gaussian modes. The multi-ring structure can be used to change the trajectory of the translational rotation of the trapped microparticles. We have shown that the ratio of the local integral angular projection of the Umov–Poynting vector to its longitudinal projection is slowly increases at growth of the radial index.

Janus micromotors for motion-capture-ratiometric fluorescence detection of circulating tumor cells

Abstract The rapid and sensitive detection of circulating tumor cells (CTCs) remains technical challenges due to extremely low abundance. In the current study, Janus micromotors (JMs) are developed to achieve motion-enhanced CTC capture and capture-induced ratiometric fluorescence signaling. JMs are constructed via catalase grafting on one side of Janus rods (JRs) to catalyze the decomposition of H2O2 as power source. JMs with different aspect ratios show random, spiral, rotational or linear motion trajectories, and JMs with the aspect ratio of 2 (JM-2) display rotational motion with significantly larger mean-square-displacement (MSD) values than other JMs. TLS11a aptamers are conjugated on the other side of JRs for specific capture of tumor cells, and tetraphenylethene (TPE) derivatives and fluorescein isothiocyanate (FITC) are labeled on aptamers via base-pair interactions. The competitive binding of tumor cells with aptamers causes the release of TPE and FITC from JMs, which relieves the aggregation-induced emission (AIE) effect of TPE and aggregation-caused quenching (ACQ) profile of FITC on JMs. Thus, JMs displays apparent ratiometric fluorescence changes from blue (I450) to green (I526) after capture of tumor cells. The fluorescence intensity ratios of I526/I450 could be fitted against cell levels, and the limit of detection is around 25 cells/mL within 1 min. In addition, the HepG2 detection by JM-2 exhibits no interference in the presence of other tumor cells (4T1 and H22), and the recovery rate of HepG2 cells in blood samples was over 95%. Thus, JMs demonstrate the motion-capture-ratiometric fluorescence sensing capabilities and provide a feasible strategy for real-time, rapid and sensitive detection of cells in laboratory, hospital and remote settings.