Axial Line Research Articles

FINDING THE RELATIVE TRAJECTORY OF THE CARGO IN THE BODY OF A VEHICLE WHICH IS GOING DOWN OR UP ON A CURVED SECTION OF THE ROAD

With a certain assumption, the load, which during relative movement along the bottom of the body makes translational movement, can be taken as a material point. In this case, finding the relative movement of the load in the body when the car moves along the road with a spatial axis is reduced to finding the relative trajectory of the material point. In known works, it is proposed to use the accompanying trihedron of the trajectory of the transfer motion and Frenet's formula to find the absolute acceleration vector of a point. The independent variable is not time, as in traditional problems, but the arc coordinate of the transfer trajectory, since only under this condition can Frenet's formulas be applied. The vector of absolute acceleration is obtained in projections onto the vertices of the moving accompanying trihedron, without looking for individual components (transfer, relative, and Coriolis acceleration), as is done in traditional approaches. The purpose of the study is to investigate the relative movement of the load, taken as a material point, along the bottom of the body of a truck moving along a curvilinear section of the road with a spatial axis during its ascent or descent. The spatial curve is characterized by two parameters that depend on the kinematics of the accompanying Frenet trihedron. These parameters are the curvature k and the twist σ of the curve. Their values at any point of the curve will be determined if the dependencies k=k(s) and σ=σ(s) are known, where s is the arc coordinate (the arc length of the curve). It is assumed that such a spatial curve is the axis of a curved section of the road that goes uphill or downhill. The application of the accompanying trihedron of the curve and Frenet's formulas made it possible to describe the relative motion of the cargo in the body of a car moving along a road having a spatial axis with constant and variable speeds. The regularities of the relative movement of the cargo when the car is moving on the road, the axis of which is a helical line with constant curvature and twist, have been found. It was found that there is no significant difference between the value of the relative speed of the cargo when the car moves at a constant speed down or uphill at the initial stage. When braking on a descent, a significant relative movement of the cargo is observed, which increases with an increase in the braking acceleration, and when climbing, on the contrary, the relative movement decreases with an increase in the braking acceleration. The regularity of the relative movement of the cargo when the car moves along the road with variable curvature and torsion of the axis line depends on the type of these dependencies as a function of the length of the arc of the axis line.

Mechanical behaviour of bolted connection in bending evaluated with small-scale specimen

A tensile experiment is usually adopted to evaluate the mechanical behaviour of bolted connections, such as slip, yield, and ultimate behaviours or resistances. Tensile force is given by a universal test machine. A small-scale specimen of a bolted connection with a few bolts in a half side is used for the experiment. The small-scale experiment gives the mechanical behaviours easily. Tensile force applies to the specimen in the experiment; however, the bolted connection in an actual structure is exposed not only to tensile force but also to shear force or bending moment. In this study, a small-scale bolted connection for a specimen was developed to evaluate the bending behaviour of the bolted connection. The bolted connection was cranked at the centre. The crank is intended to generate the bending moment by the eccentricity of the applying tensile force and the force axis line. The mechanical behaviour of the bolted connection was investigated by finite element analysis. The bending moment is obtained theoretically as a product of the force and the eccentricity. However, the analysis reduced the applied bending moment by 75% from the theoretical value. The cause of the reduction was the support condition at the ends of the bolted connection. In a theoretical pinned supported case, the applied moment was not reduced; on the other hand, in a clamped supported case, which was assumed clamping by chucks in a universal test machine, the applied moment was reduced. From this finding, the behaviour of bolted connection in bending would be obtained in a small-scale experiment; however, the specimen is needed to design considering the support condition at the ends of the specimen.

STUDY ON AUTOMATIC REGISTRATION METHOD OF SOURCE DATA FOR CIM BUILDING MODEL CONSTRUCTION

Abstract. The City Information Model (CIM) is a digital model designed to describe, analyze, and manage urban spatial information. It integrates various urban elements, providing decision support for urban planning, design, and management. This study focuses on the construction of building models in CIM, particularly the issue of automatic registration of source data. We propose an automatic registration method based on DWG-format architectural design drawings and SHAPE-format remote sensing building outline information. This method extracts the axis line information of the building from the plan design drawings, indirectly obtains feature points, and selects registration base points, thereby achieving the registration of real estate subdivision data. Meanwhile, by automatically fitting the outer bounding rectangle of the building and dynamically adjusting the angle, this study realizes the automatic registration of the aligned multilayer real estate subdivision data with the building outline data obtained from remote sensing images. This research provides an effective method for the automatic and batch accurate alignment of data for the construction of CIM building models, thereby enhancing the precision and reliability of the modeling.

Analysis on Hydraulic Design of Runner Blades of Francis Turbine

Francis turbine is the most widely used model in hydropower station, and the hydraulic design of runner blades affects the efficiency of the unit. This paper discusses how to complete the hydraulic design of Francis turbine runner blades according to the given parameters. In hydraulic design of Francis turbine runner, firstly, the structural scheme is determined according to the given parameters. On the basis of referring to excellent hydraulic model, a Francis turbine runner blade is designed according to the given head. By analyzing and calculating the data, the geometric parameters and axial projection of the Francis turbine runner flow channel are determined, and the axial flow network is drawn and checked, so as to complete the calculation of axial vortex line and blade drawing. Finally, the airfoil is thickened by a certain thickening principle.

Comparison of the Odontoid and Orbital-Coronal Vertical Axis Lines in Evaluating Coronal Alignment and Outcomes in Adult Spinal Deformity Surgery.

Asymptomatic Multi-Ethnic Alignment Normative Study (MEANS) cohort: cross-sectional, multicenter. Symptomatic cohort: retrospective, multisurgeon, single-center. To assess the association of odontoid-coronal vertical axis (OD-CVA) and orbital-coronal vertical axis (ORB-CVA) with radiographic parameters, patient-reported outcomes, and clinical outcomes. Previous literature studied the OD-CVA in an asymptomatic cohort and ORB-CVA in a symptomatic cohort, demonstrating their correlations with radiographic parameters and ORB-CVA with outcomes. A total of 468 asymptomatic adult participants were prospectively enrolled in the MEANS cohort. 174 symptomatic patients with adult spinal deformity with ≥6 fused levels and 2-year follow-ups were retrospectively enrolled in the symptomatic cohort. The association between OD-CVA and ORB-CVA, and radiographic parameters, perioperative variables, PROs, and outcomes were analyzed. Pearson correlation was used to assess correlation and logistic regression odds of outcomes. In the MEANS cohort, the ORB-CVA correlated with C7-CVA ( r = 0.58) and OD-CVA ( r = 0.74). In the symptomatic cohort, preoperative ORB-CVA correlated better with leg length discrepancy; r = 0.17, P = 0.029), whereas preoperative OD-CVA correlated better with C7-CVA ( r = 0.90, P < 0.001). Postoperative ORB-CVA correlated with postoperative C7-CVA ( r = 0.66, P < 0.001), and postoperative OD-CVA correlated strongly with postoperative C7-CVA ( r = 0.81, P < 0.001). Both preoperative OD-CVA ( r = 0.199) and ORB-CVA ( r = 0.208) correlated with the preoperative Oswestry Disability Index. ORB-CVA correlated better than OD-CVA in the preoperative Scoliosis Research Society-22r pain category but worse in total and other subcategories. Preoperative ORB-CVA was associated with increased odds of intraoperative complication (odds ratio = 1.28, 1.01-1.22), like OD-CVA (odds ratio = 1.30, 1.12-1.53). Neither preoperative ORB-CVA nor OD-CVA was associated with reoperations and readmissions after multivariate analysis. Preoperative OD-ORB mismatch >1.5 cm was not associated with increased odds of intraoperative and postoperative complications, reoperations, or readmissions. ORB-CVA and OD-CVA correlated with radiographic parameters, patient-reported outcomes, and intraoperative complications. ORB-CVA and OD-CVA can be used interchangeably as cranial coronal parameters in adult spinal deformity surgery.

ANALYSIS OF THE INFLUENCE OF THE POSITION OF THE FIRST THREAD TURN OF THE ROLLER ALONG ITS AXIS ON THE UNEVEN DISTRIBUTION OF THE LOAD IN A NUT-FREE ROLLER DRIVE

In mechanical engineering, screw drives are widely used, which convert rotational motion into translational motion. These include roller drives (RD), which have high performance characteristics and are by far the most promising. For the production of RD, special expensive imported machines are required, therefore, in Russia, as part of the import substitution program, nut-free RDs have been developed, the manufacture of which is possible on universal equipment. They are chosen as the object of research. For reliable, durable and economical operation of nut-free RDs, their reliable calculations are required according to the most important performance criteria. In this case, first, a force calculation of the transmission is performed, then its details, connections of details and transmission as a whole mechanism are calculated for strength, rigidity, durability, etc. The article considers the force calculation of nut-free RD, which have a number of features, including the feature of loading its intermediate parts - threaded rollers. A force from the actuator acts on the roller along its axial line, and roller is balanced by axial forces on the thread of the roller interacting with the thread of the screw. From here, the overturning moment from axial forces acts on the roller, which is balanced by the redistribution of forces on the thread of the roller and the forces from the two rings that keep the roller from radial movement. This leads to uneven distribution of the load between the thread turns of the roller, which is estimated by the coefficient of uneven loading. The article reveals a design parameter that leads to a change in the coefficient of uneven loading of a nut-free RD during operation. That parameter is the position along the axis of the first thread turn from the end of the roller, which receives the load (working thread turns) from the actuator, and other working thread turns along the axis of the roller. The reason for this change is the variation in the number of working threads turns of the roller and the distance of the balancing force on the working turns. At the same time, the range of the coefficient of uneven loading of a nut-free RD is quite large and must be taken into account in the calculations.

Discovering the Axial Lines of Bunus River as a Social Network in Kampong Bharu using Space Syntax Analysis

The global trend in modern development often fails to appreciate and damages the natural beauty of old rivers in central city districts. This issue is observed in the case of the Bunus River, which once served as the main transportationroute for early settlements in Kampong Bharu –a traditional village located in the heart of Kuala Lumpur city center. Despite its 9.2-kilometer length, the Bunus River is currently underutilized, unexploited, and lacks a sense of place. It has been covered with a pathway and used as a cycling track for city residents due to heavy pollution and significant floods in 2007 and 2011. However, the inefficient design of the pathway has left the river buried and unnoticed by most residents in the area. Therefore, this study aims to investigate the Axial Lines of the Bunus River as a social network in Kampong Bharu, utilizing Space Syntax analysis. The research method for this study employed mixed methods, focusing on the Bunus River in Kampong Bharu as the case study. Observational research was carried out along the Bunus Pathway. The data was analyzed through Space Syntax Axial Line analysis to test the axis of the river. The findings of this study revealed that optimizing the axis of the river could direct much more active movement into the area. Consequently, it is concluded that the Bunus River should be integrated into the design of the cycling tracks and pedestrian paths that span over it, thus improving the connectivity of the pedestrian and social network in Kampong Bharu as a whole.

Study on mechanical properties and failure mode of single-fissure sandstone discs under bi-directional linear loading

The tensile failure of discontinuous geological rock masses in underground spaces is an enduring issue in geotechnical engineering. Understanding the mechanical behaviour and failure characteristics of cracked rock under tension is vital for the safe practice of underground projects. In this study, bi-directional linear load tests were conducted on single-fissure sandstone discs under different stress ratios i (axial stress P1: lateral stress P2) = 1:1, 2:1, 3:1, 4:1, and ∞:1, with crack inclination angles α = 0°, 30°, 45°, 60°, and 90°. The specimens’ deformation characteristics, acoustic emission features, and microfracture characteristics were recorded using the digital image correlation (DIC), PIC-2 acoustic emission(AE) system, and the scanning electron microscopic (SEM). The results showed that the strength at α = 0° was not significantly different from that of intact discs. The AE results and test results indicated that the peak load and initiation load decreased when increasing α and i, and the initiation load approached the peak load. In addition, when the stress ratio was small(i ∼ 1:1), the failure mode of the specimens was mainly controlled by the lateral stress P2. As i increased, the constraint of the lateral stress weakened, and the final failure mode of the specimens was primarily determined by the crack inclination angles. Furthermore, fracture trajectories between adjacent load points were shear cracks, fractures along the axial load line were tensile cracks, and the failure between the end of the fissure and the axial load point was a tensile-shear mixed crack with tensile failure as the dominant mode. DIC displacement vector analysis and SEM results confirmed these failure characteristics. The findings provide a reference for underground support structures' design and safety maintenance.

Functional alignment in total knee arthroplasty best achieves balanced gaps and minimal bone resections: an analysis comparing mechanical, kinematic and functional alignment strategies.

Key concepts in total knee arthroplasty include restoration of limb alignment and soft-tissue balance. Although differences in balance have been reported amongst mechanical alignment (MA), kinematic alignment (KA) and functional alignment (FA) techniques, it remains unclear whether there are differences in gap imbalance or resection thicknesses when comparing different constitutional alignment subgroups. MA (measured resection technique), KA (matched resections technique) and FA (technique based on the restricted KA boundaries) were compared in 116 consecutive patients undergoing 137 robotic-assisted cruciate-retaining total knee arthroplasties. The primary outcome was the proportion of balanced gaps (differential laxities ≤ 2mm) for extension, flexion, medial and lateral gap measurements. Manual pre-resection laxity measurements were obtained for MA and KA and manual post-resection measurements were obtained for FA in 10° and in 90° of knee flexion. Secondary outcomes were resection depths and implant alignment. All outcomes were analysed per constitutional coronal alignment and joint line obliquity subgroups. The proportions of balance in all four gap measurements were 54.7%, 66.4% and 96.5%, with MA, KA and FA, respectively. Across all constitutional alignment types, FA achieved the highest proportion of balance. MA resected the least amount of bone from the medial tibial plateau. KA had femoral components in most valgus and most internally rotated, tibial components in most varus and was the most bone-preserving for the posteromedial femoral condyle. FA had the most externally rotated femoral components and was most bone-preserving for the distal femoral resections. The study shows that implant alignment to the mechanical axis or joint line anatomy (equal resections) alone does not guarantee a balanced total knee arthroplasty. FA resulted in the highest proportion of balanced knees across all analysed subgroups. Future research will consider whether one alignment philosophy leads to superior outcomes for different constitutional alignment subgroups. Level II.

The Plumbline: A Novel Radiographic Tool for Assessment of Metatarsus Adductus with Hallux Valgus

Category: Bunion; Midfoot/Forefoot Introduction/Purpose: Metatarsus adductus (MTA) is a complex multiplanar deformity of the foot which has a 30% reported approximate radiographic incidence in patients with symptomatic hallux valgus (HV). Various radiographic angles have been proposed for the assessment of MTA, but these measurements can be complex with a broad range of interrater reliability. We propose a simplistic radiographic assessment method termed the ‘plumbline’ to identify the presence of MTA and to ascertain if enough physical space is available to align the first metatarsal to the longitudinal foot axis via an isolated 1st ray procedure, or if necessary, through a combined approach which also addresses the lesser metatarsals. This method provides a visual reference to determine if a physical blockade to 1st ray correction is present. Methods: The plumbline is assessed on standard weight-bearing AP radiographs. Neutral foot positioning is key as a pronated or supinated clinical position of the foot will impact the alignment of this and other radiographic angular relationships. A transverse midfoot axis line is drawn by identifying and linking two individual points marked at the calcaneocuboid joint and the talonavicular joint. A third point is marked at the distal lateral apex of the medial cuneiform at the first tarsometatarsal joint. A 90° line is subtended from the transverse midfoot axis line, crosses the third point, and extends distally to the 2nd metatarsal head. A positive radiographic plumbline occurs when this line intersects the 2nd metatarsal indicating the need to correct the adducted lesser metatarsal position prior to addressing HV. A negative plumbline remains tangential to the 2nd metatarsal and indicates an isolated HV correction is possible. Results: The metatarsus adductus angle (MAA) measured via Sgarlato's method (SA), and the plumbline were recorded in patients (N=20) scheduled for HV surgery. Initially the cohort was subdivided into subjects deemed to have a normal MAA (SA &lt; 15°; N=10) and an abnormal MAA (SA&gt;15°; N=10). A mean pre-operative MAA measurement of 8.1° (SD 2.3; range 5, 12.1) and 26.5° (SD 4.5; range 19.2, 33.7) were found in these respective subsets. All subjects (100%) with an MAA &lt; 15° (N=10) were found to have a negative plumbline radiographically and subjects (100%) with a MAA &gt;15° (N=10) presented with a positive plumbline. The plumbline findings identified when an isolated HV correction would have been possible or impeded based upon 2nd metatarsal position, thus driving the surgical decision making algorithm. Conclusion: The plumbline is used to determine when concomitant MTA and HV correction is beneficial without the need to measure other more traditional radiographic angular relationships. It is a quick and simple method of evaluating the proximity of the metatarsal segments to determine if the first metatarsal is amenable to reduction in isolation or if correction will be limited due to a 2nd metatarsal bone blockade. The visual simplicity of the measurement can also aid in patient education and surgeon satisfaction when describing the surgical approach to this complex three-dimensional anatomic pathology.

Can the reduction quality of distal humeral transphyseal fractures be determined using reference measurements on conventional radiography?

Our objective was to compare the radiological outcomes of transphyseal fractures treated using closed reduction and percutaneous fixation, without arthrography, with those of supracondylar humerus fractures treated using the same method within a similar age group. Additionally, we aimed to assess the efficacy of the reference points in the lateral and anteroposterior radiographs utilized for the evaluation of reduction. The study included patients aged 0-3 years who underwent surgery for supracondylar and transphyseal fractures between 2013 and 2022. All the patients were diagnosed using anteroposterior (AP) and lateral elbow X-rays. No arthrographic intervention was used either in the diagnosis or treatment phase. On the AP X-rays, we assessed the alignment between the humeral shaft line and the ulnar long axis line to determine the positioning of the distal humeral physis segment in relation to the humerus. Additionally, we evaluated the relationship between the anterior cortex line of the humerus and the coronoid process on lateral radiographs. At the final follow-up visit, Flynn criteria were used for functional assessment. The study comprised 24 patients with supracondylar humerus fractures and 24 patients with transphyseal fractures. In the early post-operative radiographs, the humero-ulnar angle measured 6.43° (-7° - 16.6°) in the supracondylar group and 9.8° (-4.3° - 25.3°) in the transphyseal group (p = 0.087). The distance between the coronoid and the anterior humeral line was 9.19 mm (4.27 - 16.08) for the supracondylar fracture group and 8.05 mm (3.29 - 14.85) for the transphyseal fracture group (p = 0.513). The current study's findings suggest that both the humero-ulnar angle and the distance between the coronoid and the anterior humeral line are valuable indicators for assessing the quality of reduction in transphyseal distal humerus fractures.

P90. Evaluation of the odontoid-coronal vertical axis line in coronal alignment in a symptomatic cohort

P90. Evaluation of the odontoid-coronal vertical axis line in coronal alignment in a symptomatic cohort

Experimental study on damage mechanism of blood vessel by cavitation bubbles

Ultrasound-induced cavitation in blood vessels is a common scenario in medical procedures. This paper focuses on understanding the mechanism of microscopic damage to vessel walls caused by the evolution of cavitation bubbles within the vessels. In this study, cavitation bubbles were generated using the low-voltage discharge method in 0.9% sodium chloride saline, and vessel models with wall thicknesses ranging from 0.7 mm to 2 mm were made using a 3D laminating process. The interaction between cavitation bubbles and vessel models with different wall thicknesses was observed using a combination of high-speed photography. Results show that cavitation bubble morphology and collapse time increased and then stabilized as the vessel wall thickness increased. When the cavitation bubble was located in vessel axial line, pair of opposing micro-jets were formed along the axis of the vessel, and the peak of micro-jet velocity decreased with increasing wall thickness. However, when the cavitation bubble deviated from the vessel model center, no micro-jet towards the vessel model wall was observed. Further analysis of the vessel wall deformation under varying distances from the cavitation bubble to the vessel wall revealed that the magnitude of vessel wall stretch due to the cavitation bubble expansion was greater than that of the contraction. A comparative analysis of the interaction of between the cavitation bubble and different forms of elastic membranes showed that the oscillation period of the cavitation bubble under the influence of elastic vessel model was lower than the elastic membrane. Furthermore, the degree of deformation of elastic vessel models under the expansion of the cavitation bubble was smaller than that of elastic membranes, whereas the degree of deformation of elastic vessel models in the contraction phase of the cavitation bubble was larger than that of elastic membranes. These new findings provide important theoretical insights into the microscopic mechanisms of blood vessel potential damage caused by ultrasound-induced cavitation bubble, as well as cavitation in pipelines in hydrodynamic systems.

A comparison of two wave energy converters’ power performance and mooring fatigue characteristics – One WEC vs many WECs in a wave park with interaction effects

The production of renewable energy is key to satisfying the increasing demand for energy without further increasing pollution. Harnessing ocean energy from waves has attracted attention due to its high energy density. This study compares two generations of floating heaving point absorber WEC, WaveEL 3.0 and WaveEL 4.0, regarding their power performance and mooring line fatigue characteristics, which are essential in, e.g., LCoE calculations. The main differences between the two WECs are the principal dimensions and minor differences in their geometries. The DNV software SESAM was used for simulations and analyses of these WECs in terms of buoy heave motion resonances for maximising energy harvesting, motion characteristics, mooring line forces, fatigue of mooring lines, and hydrodynamic power production. The first part of the study presents results from simulations of unit WEC in the frequency domain and in the time domain for regular wave and irregular sea state conditions. A verification of the two WECs’ motion responses and axial mooring line forces is made against measurement data from a full-scale installation. In the second part of the study, the influence of interaction effects is investigated when the WECs are installed in wave parks. The wave park simulations used a fully-coupled non-linear method in SESAM that calculates the motions of the WECs and the mooring line forces simultaneously in the time domain. The amount of fatigue damage accumulated in the mooring lines was calculated using a relative tension-based fatigue analysis method and the rainflow counting method. Several factors that influence the power performance of the wave park and the accumulated fatigue damage of the mooring lines, for example, the WEC distance of the wave park, the sea state conditions, and the direction of incoming waves, are simulated and discussed. The study's main conclusion is that WaveEL 4.0, which has a longer tube than WaveEL 3.0, absorbs more hydrodynamic energy due to larger heave motions and more efficient power production. At the same time, the accumulated fatigue damage in the moorings is lower compared to WaveEL 3.0 if the distance between the WECs in the wave park is not too short. Its motions in the horizontal plane are larger, which may require a larger distance between the WEC units in a wave park to avoid losing efficiency due to hydrodynamic interaction effects.

Anatomical study of the distal course of the posterior tibial artery: A cadaver study.

This study aimed to describe the course, branches, and variances of the posterior tibial artery, which provides the arterial supply of the plantar surface of the foot, starting from the tarsal tunnel level to provide descriptive information for all surgical interventions, diagnostic radiological procedures, and promising endovascular therapies in the tarsal region. In this study, a dissection of 48 feet was performed on 25 formalin-fixed cadavers (19 males and 6 females). Surgical instruments and a digital caliper were used for dissection and measurements, and the critical structures were recorded by a Canon 250D camera to be illustrated later. All parameters were significantly longer in male cadavers compared to females. According to the correlation analysis, while there was a significant and robust correlation between the axial line and pternion-deep plantar arch (R=.830, P .05), a moderate correlation was found between the axial line and sphyrion-bifurcation (R=.575; P < .05), axial line and deep plantar arch-2nd interdigital commissure (R=.457; P < .05), and sphyrion-bifurcation and pternion-deep plantar arch (R=.480; P < .05). Variation in any branch of the posterior tibial artery was observed in 27 of the 48 studied sides. In our study, the branching and variability of posterior tibial artery on the plantar surface of the foot were described in detail with the determined parameters. In conditions that cause tissue and function loss and require reconstruction, such as diabetes mellitus and atherosclerosis, the most critical factor in increasing treatment success is a better understanding of the region's anatomy.

Method for detecting pipeline spatial attitude using point cloud alignment

This paper introduces a new method for detecting the spatial attitude of pipeline welding based on point cloud registration. The method aligns the measured point cloud of the pipeline with the CAD model point cloud using point cloud registration and guides the pipeline adjustment accordingly. This automated measurement method has resolved the inefficiencies and potential for rework that can arise from manual instrument operation during pipeline pose detection, and has subsequently improved detection efficiency and accuracy. In addition, we propose a coarse registration algorithm based on the axial line of pipeline point clouds to help facilitate the alignment process. We conducted simulation experiments using 3D CAD models, which demonstrated that our coarse registration algorithm outperformed the other three compared methods in terms of accuracy. The simulation experiments also proved that the absolute value of the overall method's relative error was less than 0.1%.

Spatial Oscillations of a Pipeline with Vibrating Supports

Spatial oscillations of a section of a pipeline with a liquid contained in it during the translational vibrational movements of the supports are investigated. Oscillations of both supports occur with equal amplitudes, frequencies and phases. Pipe deformations associated with the exit of its axis from the bending plane are assumed to be small. The interactions of internal constant pressure and changes in the curvature of the axial line, longitudinal and circumferential deformations of the pipe are taken into account. Its flexural-rotational vibrations are described by a system of two non-linear differential equations. By applying the Bubnov-Galerkin method, this system is reduced to the Cauchy problem, which is then solved numerically by the Runge-Kutta method. In the case of small bending and angular motions of the pipe, a comparison of the analytical and numerical solutions is given. An analysis is given of periodic and non-periodic oscillations of steel, titanium and composite pipes, for which, in particular, frequency spectra and Poincare mappings are constructed.

CT scan analysis of implant mating comparing APA versus TEA in simultaneous bilateral TKA: One technique per knee

BackgroundThe optimal landmark for setting femoral component rotation in primary TKA remains a debate. This study compares the Anterior-Posterior Axis (APA) versus the Transepicondylar Axis (TEA) in patients undergoing simultaneous bilateral TKA, where one reference line was randomized to each knee. Implant mating was assessed via post-operative CT scans. MethodThe study included 32 patients with osteoarthritis in both knees with similar varus deformities. All patients underwent the same surgical procedure on both knees, aside from the selected femoral rotation axis line: APA randomized to one side and TEA to the contralateral. Post-operative CT scans were performed in extension to assess in-vivo mating. ResultsCT scan analysis showed mean rotation of the femoral implant externally rotated relative to the radiographic TEA with no significant difference between the APA and TEA groups (p = 0.28). Tibial implant rotation was also externally rotated to the radiographic TEA with no significant difference (p = 0.59). Femoral-tibial implant mating showed a mean external rotation of the tibia relative to the femur in both groups: 0.86 ± 4.0° external rotation in the APA group and 0.23 ± 3.7° external rotation in the TEA group. There was no significant difference between groups (p = 0.52). The range of mating mismatch was 15° in the APA group and 16.5° in the TEA group. ConclusionsWhen using a measured resection, posterior referencing technique, post-operative femoral-tibial implant mating measured by CT scan showed no superiority comparing the APA method versus the TEA method.Level OF EVIDENCE: 2Randomized prospective study.

Determination of the tibial axis using the tibial anterior border for total knee arthroplasty

Purpose: We investigated whether the anterior border of the tibia is parallel to the tibial axis, and which position of the anterior border should be used as a landmark of the tibial axis in total knee arthroplasty. Methods: Ninety-one patients prior to total knee arthroplasty were evaluated. Electrocardiogram electrodes were placed along the anterior border at 5 cm (A), 10 cm (B), and 15 cm (C) distal to the tibial tuberosity, and an anteroposterior X-ray image was taken. The angles of the AC, AB, and BC lines on the tibial bone axis line were measured. Results: The mean angles of the AC, AB, and BC lines to the tibial bone axis line were, respectively, 1.09, 2.22, and −0.02. The percentages within −3° to +3° were 86.8, 64.8, and 92.3, respectively. Conclusions: A line connecting a point 10–15 cm distal to the tibial tuberosity can serve as a reference line for total knee arthroplasty.

Points with rotational ellipsoids of inertia, envelopes of hyperplanes which equally fit the system of points in [formula omitted], and ellipsoidal billiards

For a given system of material points in Rk which represents a sample of a full rank, we study the points for which the ellipsoid of inertia is rotational. Using an initial information about such points with a rotational ellipsoid of inertia along the line of the major axis of the central ellipsoid of inertia, we construct a pencil of confocal quadrics with the following property: all the hyperplanes for which the hyperplanar moments of inertia for the given system of points are equal, are tangent to one of the quadrics from the pencil of quadrics. We close the loop by applying the confocal pencil of quadrics to get a full description of the points with rotational hyperplanar ellipsoids of inertia. We indicate relationships of the obtained results with integrable billiards within quadrics and PCA.