Instantaneous Center Research Articles

Evaluation of the uniformity of the stroke depth of the working bodies of the combined slope treatment unit

Research has found that the parameters of the surface to be treated, the speed of the unit, the lateral movements of the working bodies and the instantaneous center of rotation, due to the redistribution of the gravity of the unit on the slopes, lead to uneven processing depth. To study the characteristics of the change in the stroke depth of the working bodies of the combined unit, according to the results of field experiments, an assessment was made of the uniformity of the stroke depth of the working bodies of the combined unit for slope treatment.

О влиянии на форму брахистохроны эффекта Магнуса

This paper studies the effect of the rotational motion of a body on the trajectory of its fastest descent into the gravity field. The body is considered as a ball rotating about its instantaneous axis, which is perpendicular to the pattern, with a variable angular frequency. The rotation of the ball creates a vortex flow that induces the highest pressure at the top of the ball and the least pressure at the bottom. Thus, the Magnus force (down-force), which is opposed to the reaction force of a trough, occurs. It provides an "antilifting" effect resulting in strong changes in the brachistochrone shape. Based on the fundamental principle of dynamics, a general vector equation of motion is obtained in the form of projections on a moving basis represented as unit vectors of the tangent and normal to the trajectory of the motion. A parametric solution to the equations describing the shape of the trough in Cartesian coordinates is obtained in the absence of dissipative forces. It follows from the resulting solution that the Magnus effect is most noticeable only for massive bodies of long radius. Using the numerical integration methods, various shapes of the deformed brachistochrone are presented as a result of the Magnus effect

Stationary and Transient Asymmetric Features in Tropical Cyclone Eye with Wavenumber-1 Instability: Case Study for Typhoon Haishen (2020) with Atmospheric Motion Vectors from 30-Second Imaging

Abstract Dynamics of low-level flows in the eye of Typhoon Haishen (2020) in its late phase of intensification are investigated with a special rapid-scan observation of the Himawari-8 geosynchronous satellite conducted every 30 s. This is accomplished by deriving storm-relative atmospheric motion vectors at an unprecedentedly high spatiotemporal resolution by tracking clouds across five consecutive visible-light reflectivity. The overall low-level circulation center was situated several kilometers away from the storm center defined in terms of the inner edge of the lower part of eyewall clouds. The shift direction is rearward of the storm translation, consistently with a numerical study of the tropical cyclone (TC) boundary layer. Over the analysis period of 10 h, azimuthal-mean tangential wind around this center was increased at each radius within the eye, and the rotational angular velocity was nearly homogenized. The instantaneous low-level circulation center is found to orbit around the overall circulation center at distances around 5 km. Its orbital angular speed was close to the maximum angular speed of azimuthal-mean tangential winds. This rotating transient disturbance is found to transport angular momentum inward, which explains the tangential wind increase and the angular velocity homogenization in the eye. These features are consistent with an algebraically growing wavenumber-1 barotropic instability, whose impact on TC structures has not been explored. This instability enhances wavenumber-1 asymmetry in ring-shaped vorticity, which can be induced by various processes such as translation, environmental shear, and exponential barotropic instability. Therefore, it may appear broadly in TCs to affect wind distribution in their eyes. Significance Statement Axially asymmetric transient features in the inner cores of tropical storms have been suggested to profoundly affect the structures and the time evolutions of tropical storms. However, the scarcity of observations has hindered studying such processes observationally. By using a specially conducted high-frequency satellite imaging of Typhoon Haishen (2020), we derived atmospheric motion vectors nearly homogeneously at an unprecedentedly high spatiotemporal resolution. Various kinds of asymmetric motions in low-level flows in the eye were found. Of particular interest is a special type of wavenumber-1 instability whose role has not drawn much attention; the instability was found to provide angular momentum transport consistent with the measured homogenization of the rotation.

Determination of the Critical Speed of Tracked Vehicles on the Trajectory of Skidding

The author of the paper shows the degree of dependence and the degree of compliance of newly developed and modernized tracked vehicles with modern controllability requirements. The paper shows the definition of the displacement of the projection of the instantaneous center of rotation on the longitudinal axis of the machine when moving along a curve with a variable speed and a given turning radius. The result of the work is an assessment of the level of controllability. The conclusions to the work say that the controllability assessment should be carried out on the basis of an analysis of the estimated indicators determined on the basis of the initial data for each individual tracked unit.

Building a mathematical model of the oscillatory movement of a frontal installed machine for the beet’s greens harvesting

Building a mathematical model of the oscillatory movement of a frontal installed machine for the beet’s greens harvesting

ANALYSIS FLAT MECHANISM OF THE FOURTH CLASS WITH A MOVING CLOSED LOOP AND THREE COMPLEX LINKS

The study of complex structural groups of links of flat mechanisms allows to improve the existing technological equipment and design new machines. Such mechanisms, based on structural groups of the fourth and higher classes, can ensure the implementation of innovative technological processes of production. Kinematic studies of complex flat mechanisms of the fourth class and higher are certainly relevant, if we take into account the individual approach to their research. The use of such mechanisms is increasingly observed in modern equipment that ensures the execution of technological processes at enterprises of the fashion industry. The work developed a sequence of actions for finding the velocity vectors of the points of the fourth-class mechanism with a moving closed loop, which is formed by four links, three of which have the form of complex links, is developed. The linear vectors of the velocities of the points coinciding with the geometric centers of the kinematic pairs of the structural group of links of the fourth class of the third order were determined. We conditionally changed the input mechanism to another structurally possible in a flat mechanism. The research was carried out using the graph-analytical method. In order to carry out a kinematic analysis of the mechanism, it is proposed to take into account the presence of complex links in its structure, namely the structural feature of the formation of a sequential connection of three links in a kinematic chain of the type “rocker arm – connecting rod – rocker arm”. This made it possible to determine the position of the instantaneous center of velocity of the link, which has plane-parallel motion. Conditional rotation of another conditionally leading link around such an instantaneous center of rotation made it possible to simplify the graphic constructions of the study. The application of the graph-analytical method made it possible to perform vector graphic constructions in an arbitrarily chosen scale for the entire mechanism, and after their completion, to perform detailed calculations of the scale of a certain vector construction.

Fillet welding of skewed reinforcing steel to steel plate

Connecting or anchoring reinforcing steel to structural steel plate or shapes using fillet welds is a common detail in precast concrete construction. However, there is currently no guidance on the effects of skewing the reinforcing bar with respect to the plate. This paper reports findings from a study of the effects of a skewed reinforcing bar on both the effective weld area and the overall connection strength. Thirty-two samples of reinforcing bars welded to steel plates at various skew angles were fabricated and tested in tension to failure. These results were compared with an analysis based on the instantaneous center of rotation method presented in the American Welding Society’s Structural Welding Code—Steel (AWS D1.1-20). Recommendations are presented to revise the Structural Welding Code—Reinforcing Bars (AWS D1.4) to account for the effect of skewed reinforcing bars welded to structural steel plate or shapes.

Идентификация искажения формы цилиндрических деталей технологических агрегатов

The paper deals with the issues arising during the technological unit operation, in particular, the geometric characteristics control of large parts of the units. The main types of rolling the surface wear of cylindrical elements of various technological equipment are given (according to GOST 24642-81, GOST 18322-2016). The equipment wear patterns due to the operating conditions and the unit design, as well as differences in the part shape distortion with the roundness loss are highlighted. It is revealed that the uneven wear of the rolling surface of the technological cylindrical parts causes shape distortion. Considering this, the profile of a conditional round part in cross section relative to one centre is modelled. The appearance of ovality is accepted as the main defect of cylindrical parts. A calculation scheme is presented for constructing the distortion of the cylindrical body profile located on two round supports. An algorithm for computing the radii centre displacement is presented. Theoretical calculations and the algorithm are confirmed by a virtual kinematic model that displays rolling a non-circular body on two idlers. The method described in the paper for obtaining a visual kinematic model, based on an analytical description of rolling a non-circular body, is proposed to be used as a direct problem of searching for instantaneous centres of rotation. The kinematic model obtained by solving the direct problem can be applied for training a neural network that processes the measurement results of a real rolling body

ОПРЕДЕЛЕНИЕ ПОПЕРЕЧНЫХ СИЛ, ДЕЙСТВУЮЩИХ НА КОЛЕСА ТРАНСПОРТНОЙ РОБОТИЗИРОВАННОЙ СИСТЕМЫ

A method for calculating the wheels lateral forces is proposed to analyze ways to increase the speed of the robotic system without wheel slippage appearance, The analysis of lateral forces allows to synthesize a rational algorithm for distributing the load between drives. In addition, it is proposed to use a vector space to represent kinematic energy, which simplify simulation of the instant center of rotation movements and simplify control system development. The first part of the article is devoted to finding the relationship between the summary lateral force and the drives traction forces; the changing the distance to the instant center of rotation; the lateral movement of the instant center of rotation and the current speed of the entire system. The listed relationships are found through kinematic constraints and the energy conservation law. The second part is devoted to the evaluation of the lateral force acting on each wheel. Thus, the value of the reduced reaction force and the quasi-static model of an elastic wheel are used. Examples of using the proposed method are shown: a comparison of the maximum possible speeds of motion without slippage for different distribution of moments between drives and for different arrangement of drive wheels in the system is carried out.

ОПРЕДЕЛЕНИЕ ПОПЕРЕЧНЫХ СИЛ, ДЕЙСТВУЮЩИХ НА КОЛЕСА ТРАНСПОРТНОЙ РОБОТИЗИРОВАННОЙ СИСТЕМЫ

A method for calculating the wheels lateral forces is proposed to analyze ways to increase the speed of the robotic system without wheel slippage appearance, The analysis of lateral forces allows to synthesize a rational algorithm for distributing the load between drives. In addition, it is proposed to use a vector space to represent kinematic energy, which simplify simulation of the instant center of rotation movements and simplify control system development. The first part of the article is devoted to finding the relationship between the summary lateral force and the drives traction forces; the changing the distance to the instant center of rotation; the lateral movement of the instant center of rotation and the current speed of the entire system. The listed relationships are found through kinematic constraints and the energy conservation law. The second part is devoted to the evaluation of the lateral force acting on each wheel. Thus, the value of the reduced reaction force and the quasi-static model of an elastic wheel are used. Examples of using the proposed method are shown: a comparison of the maximum possible speeds of motion without slippage for different distribution of moments between drives and for different arrangement of drive wheels in the system is carried out.

A Cadaveric Comparison of the Kinematic and Anatomical Axes and Arthrokinematics of the Metatarsosesamoidal and First Metatarsophalangeal Joints.

Presently, developments in weightbearing computed tomography and biplanar fluoroscopy technologies offer exciting avenues for investigating normative and pathologic foot function with increasing precision. Still, data quantifying sesamoid bone and proximal phalange motion are currently sparse. To express joint kinematics and compare various clinical cohorts, future studies of first ray motion will necessitate robust coordinate frames that respect the variations in underlying anatomy while also aligning closely with the functional, physiological axes of motion. These activity-dependent functional axes may be represented by a mean helical axis of the joint motion. Our cadaveric study quantified joint kinematics from weightbearing computed tomography scans during simulated toe lift and heel rise tasks. We compared the spatial orientations of the mean finite helical axes of the metatarsosesamoidal and metatarsophalangeal joints to the primary joint axis of two relevant methods for defining metatarsal coordinate frames: inertial axes and fitting of geometric primitives. The resultant kinematics exhibited less crosstalk when using a metatarsal coordinate system based on fitting cylindrical primitives to the bony anatomy compared to using principal component axes. Respective metatarsophalangeal and metatarsosesamoidal arthrokinematic contact paths and instantaneous centers of rotation were similar between activities and agree well with currently published data. This study outlines a methodology for quantitatively assessing the efficacy and utility of various anatomical joint coordinate system definitions. Improvements in our ability to characterize the shape and motion of foot bones in the context of functional tasks will elucidate their biomechanical roles and aid clinicians in refining treatment strategies.

Two second order instantaneous invariants of axodes

It is well established that generalized spatial motion of a rigid body can be defined in terms of two axodes; a fixed axode and a moving axode. These axodes are ruled surfaces that uniquely roll and slide upon one another. Presented are two instantaneous invariants that define relative motion between two axodes. These invariants are based on the instantaneous screw axis (ISA) or line-tangency shared by two axodes in mesh. One invariant is the relative angular displacement (rolling) about the ISA and the other invariant is the relative axial displacement (sliding) along the ISA. Both invariants are ratios expressed in terms of the normal curvature and geodesic torsion for any point on the ISA. An induced curvature is introduced to quantify the combined rolling and sliding displacement. Two osculating hyperboloids are established in terms of induced curvature, which when combined, create a skew axis gear pair with uniform motion that matches the instantaneous invariants of the axodes. A skew axis gear set with elliptical motion is presented to demonstrate generalized axodes, instantaneous invariants, induced curvature, and osculating hyperboloids.

Effect of the soft tissue artifact on marker measurements and on the calculation of the helical axis of the knee during a squat movement: A study on the CAMS-Knee dataset.

Marker-based motion capture recordings of human body segments are often affected by soft tissue artifact (STA). The undesired and uncontrolled motion of the skin may introduce errors in the estimation of motion and position of body segments and, consequently, in the calculation of the relative functional quantities. This study exploited a recently published dataset consisting of six adult subjects that underwent a total knee arthroplasty. The subject performed squat tasks while the motion was concurrently recorded by passive markers attached to the skin of the lower limbs, an optoelectronic system, and a fluoroscope. The STA of shank and thigh was decomposed in local deformation and rigid motion. Additionally, we studied how the instantaneous helical axis (IHA) calculation is affected by STA. The cluster most affected by STA rigid motion was the thigh. The largest estimated effects were about 7deg. and about 20mm. The largest effect of local deformation was about 25mm, and it was observed on the thigh cluster. The STA made the estimation of the IHA unreliable for both position and direction. The choice of the reference configuration influenced the results of the STA analysis.

Correspondence between scapular anatomical coordinate systems and the 3D axis of motion: A new perspective on an old challenge

Several scapular anatomical coordinate systems have been reported in the literature to describe shoulder kinematics. Unfortunately, the use of different conventions hinders comparison across studies. Further, inconsistencies between a coordinate system and the scapula’s 3D axis of motion means that scapular motion will be incorrectly attributed to axes about which it did not rotate. The objectives of this study were to: 1) determine the extent to which the axes of four common scapular coordinate system conventions correspond to the 3D axis of scapular motion (i.e., instantaneous helical axis, IHA), and 2) report the prevalence of scapulothoracic gimbal lock for each convention. Shoulder kinematics were tracked during scapular plane abduction in 45 participants using biplane videoradiography. Scapulothoracic kinematics were described using the original convention proposed by van der Helm, the convention recommended by the International Society of Biomechanics (ISB), a glenoid-based coordinate system, and a glenoid-oriented coordinate system. The 3D angle was calculated between the IHA and each axis of the four conventions (IHA-axis angular deviations). A repeated measures ANOVA was used to compare IHA-axis angular deviations between conventions. The glenoid-oriented and ISB conventions resulted in the smallest and largest IHA-axis angular deviations, respectively (21.7°±3.6° vs. 30.5°±5.2°, p < 0.01). Gimbal lock was approached in 17.8% of participants when using the original convention, 2.2% when using the ISB convention, and 0% when using the glenoid-based or -oriented conventions. These findings suggest the glenoid-oriented coordinate system may be worthy of further consideration when investigating shoulder kinematics during scapular plane abduction.

Preliminary Results of Instantaneous Centre of Rotation Change after Thoracic Instrumentation in Adolescent Idiopathic Scoliosis Patients.

The instantaneous centre of rotation (ICR) is the centre of motion with zero velocity where a rigid body moves in a particular plane. ICR, as a dynamic measurement, gives more accurate results in terms of quality and quantity of the vertebral motions compared to range of motion (ROM). We aimed to determine the effect of thoracic instrumentation on cervical movement of adolescent idiopathic scoliosis (AIS) patients who had undergone thoracic level instrumentation by measuring pre-operative and post-operative ICR change in a pilot study. A total of 25 AIS patients were included in this study. C4-C5 and C6-C7 segmental ICR were determined by pre-operative and post-operative cervical flexion-extension radiographs. In addition, cervical sagittal parameters and global sagittal parameters were investigated. There was no statistically significant change in ICR location post-operatively in both x and y coordinates at C4-C5 segment (p: 0.326 and p: 0.946, respectively) and C6-C7 segment (p: 0.209, p: 0.086, respectively). There was a positive correlation between LCL and C4-C5 ICR y coordinate (r: 0.481), but not with C6-C7 ICR y coordinate (r: -0.2, p: 0.398). T5-T12 kyphosis decreased (p: 0.002) and T1 pelvic angle (0.003), SVA (0.02) and sacral slope (0.049) increased significantly post-operatively. T1S was correlated with LCL (r: 0.595, p: 0.002), T5-T12 kyphosis (r: 0.423, p: 0.035), SVA (r: 0.658, p<0.001) and C2-C7 SVA (r: 0.416, p: 0.039). The ICR for cervical region was not changed post-operatively in AIS patients with thoracic instrumentation. There was no relationship found between the development of post-operative cervical kyphosis or lordosis and ICR, which represents the quality and quantity of intervertebral motion. The T1 vertebra plays a key role for cervical, thoracic, and global parameters interaction.

An optimal method for calculating an average screw axis for a joint, with improved sensitivity to noise and providing an analysis of the dispersion of the instantaneous axes.

The instantaneous (ISA) and average (ASA) screw axes are techniques commonly adopted in motion analysis to functionally locate the rotation axis and center of rotation of a joint. Several approaches for calculating such axes were proposed in literature and the main limitations were identified as the need for using a threshold on angular displacements or velocities for handling the cases where the ISA is ill-defined and the need for a method for reliably estimating the center or rotation in limit cases, such as a purely rotational motion in the three-dimensional space. Furthermore, in many applications, such as in biomechanics, it is useful to statistically estimate the dispersion or variation of the ISA with respect to the ASA. In this paper we propose a novel method for estimating an ASA. Our method represents an improvement over previous methods as it: (i) exploits an optimization procedure based on the instantaneous differential kinematics (screw twist); (ii) removes the need for a threshold by introducing a weighting based on the norm of angular velocity; (iii) handles the singular cases where the position of the ASA is ill-defined by proposing a regularization term in the optimization. In addition, we proposed a method for estimating the uncertainty in the ASA calculation. The same quantities serve as a measure of the dispersion of the ISAs with respect to the ASA. The method was tested on real data and surrogate data: (i) a human gait analysis trial representing the motion of a knee, (ii) the experimental recording of the free swing motion of a mechanical hinge and (iii) synthetically generated motion data of a purely rotational (cylindrical) motion. The results showed that the new method had a lower sensitivity to noise, was able to reasonably handle the singular cases and provide a detailed analysis of ISA dispersion.

Knee joint prototype based on cam mechanism – design and video analysis

The paper is focused on a design of mechanism accurately reproducing a complex motion in the sagittal plane of a human knee joint. The desired movement is modelled by applying specially designed shapes of cooperating cam elements based on the fixed and moving centroids of knee joint’s instantaneous centre of rotation. The mechanism’s CAD model and prototype are built using 3D printed elements, providing the possibility of interchanging the elements with cam profiles and adjusting the mechanism’s movement to individual needs. The mechanism movement is measured by analysing a video in Matlab and tracking colour markers on the prototype.

Design and Validation of a Polycentric Hybrid Knee Prosthesis With Electromagnet-Controlled Mode Transition

A hybrid knee prosthesis is proposed in this letter, which consists of a polycentric structure in passive mode for low-torque activities and a single-axis structure in active mode for high-torque activities. A novel mode transition mechanism controls self-holding electromagnets for switching modes between the four-bar linkage and single-axis structure. Compared with the conventional single-axis hybrid knee, the four-bar polycentric mechanism with varying instantaneous center of rotation (ICR) can enhance the geometric stability and increase the toe clearance in passive mode. For active mode, we developed a custom embedded electric system, employed torque control for stance and position control for swing. The results of bench tests indicated that the bandwidth of the controller was suitable for locomotion. The clinical test of level-ground walking without sudden buckling and stumble was validated by three subjects. Regarding climbing stairs, a typical high-torque activity in daily locomotion, all subjects reach the maximum knee torque around 0.95 Nm/kg comparable to the able-bodied.

Combination Strategy for the Geocentric Realization of Regional Epoch Reference Frames

AbstractFor high‐resolution regional geodetic applications, the International Terrestrial Reference Frame (ITRF) is complemented by regional densifications. These are realized either as multi‐year solutions related to a tectonic plate (e.g., EUREF for Europe) or as epoch reference frames (ERFs) to capture nonlinear geophysical station motions caused by, for example, earthquakes or non‐tidal loading (e.g., SIRGAS for Latin America). These Global Navigation Satellite Systems (GNSS)‐only based regional reference frames have in common that their geodetic datum is aligned with the ITRF datum at a specific epoch. The consequence is that their origin represents the Earth's center of figure and does not coincide with the instantaneous center of mass. Here, we present studies on a direct geocentric realization of regional ERFs. We propose to realize the geodetic datum for each epoch by combining global GNSS, Satellite Laser Ranging, and Very Long Baseline Interferometry networks via measured local ties at co‐located sites. A uniformly distributed global GNSS network is used to realize the orientation via a no‐net‐rotation constraint with respect to the ITRF and is densified by the stations of the regional subnetwork. The developed combination and filtering strategy aims to guarantee a stable datum realization for each epoch‐wise solution. Validating our results against global reference frames and geophysical loading models relating to the Earth's centers of mass and figure, we show that the realized displacement time series are geocentric and reflect seasonal geophysical processes. As the approach does not need to rely on co‐location sites in the region of interest, it is conceptually transferable to other regions on the globe.

Anterior-cruciate-ligament reconstruction does not alter the knee-extensor moment arm during gait

BackgroundThe ability of the quadriceps muscles to extend the knee depends on the moment arm of the knee-extensor mechanism, which is described by the moment arm of the patellar tendon at the knee. The knee-extensor moment may be altered by a change in quadriceps force, a change in the patellar tendon moment arm (PTMA), or both. A change in quadriceps muscle strength after anterior-cruciate-ligament-reconstruction (ACLR) surgery is well documented, however, there is limited knowledge about how this procedure affects the PTMA. Research questionDoes ACLR surgery alter the moment arm of the knee-extensor mechanism during gait? MethodsWe measured the PTMA in both the ACLR knee and the uninjured contralateral knee in 10 young active individuals after unilateral ACLR surgery. Mobile biplane X-ray imaging was used to measure the three-dimensional positions of the femur, tibia and patella during level walking and downhill walking over ground. The PTMA was found from the location of the instantaneous axis of rotation at the knee and the line-of-action of the patellar tendon. ResultsThere was a small but statistically significant difference in the mean PTMA calculated over one cycle of level walking between the ACLR knee and the contralateral knee, with the mean PTMA in the ACLR knee being 1.5 mm larger (p < 0.01). In downhill walking, statistically significant differences were found in the range 15°– 25° of knee flexion, where the PTMA was 4.7 mm larger in the ACLR knee compared to the contralateral knee (p < 0.01). SignificanceSignificant differences were evident in the mean PTMA between the ACLR knee and the contralateral knee in both activities, however, the magnitudes of these differences were relatively small (range: 3–10%), indicating that ACLR surgery successfully restores the moment arm of the knee-extensor mechanism during dynamic activity.