Planar Motion Research Articles

Surface topography demonstrates gradual improvement in spinal range of motion in all three planes following posterior spinal fusion in adolescent idiopathic scoliosis.

After posterior spinal fusion (PSF) for adolescent idiopathic scoliosis (AIS), there is alteration in trunk range of motion (ROM) in the coronal, sagittal and axial planes. Previous studies have shown that ROM decreases with increased number of levels fused, which may affect the ROM between patients who undergo non-selective thoracic fusion (NSF) and selective thoracic fusion (STF) patient groups. This study sought to longitudinally evaluate the ROM of the trunk in patients with AIS who underwent posterior spinal fusion, using surface topography, comparing STF and NSF patient motion at multiple time points postoperatively. A retrospective review of data from a single-center prospective registry was conducted. Inclusion criteria required subjects to span 11-21 years of age at surgery, a diagnosis of AIS, and valid ROM measurements obtained via ST scanning. Axial, sagittal and coronal ROM was performed at six timepoints: preoperative, 6 weeks, 3, 6, 12, and 24 months postoperative. All patients had an upper instrumented vertebra (UIV) of T2, T3 or T4, and a lower instrumented vertebra (LIV) of T12, L1, L2 or L3. STF was defined as an LIV of T12 or L1, and NSF as LIV as L2 or L3. SRS22r was collected at all time points. Generalized estimation equation modeling across timepoints were conducted. 54 patients were evaluated: 40 patients in the NSF group (average preoperative Cobb angle of 56.4 ± 12.3°) and 14 in the STF group (average preoperative Cobb angle of 57.4° ± 6.7°). In the NSF group, ROM in the coronal and axial planes decreased significantly postoperatively and remained significantly decreased at 24 months postoperatively (25% decrease in the axial plane, 20% in the coronal plane). Sagittal ROM had significant decrease in ROM at all time points, but at 2 years postoperatively was no longer significant, although still 17% decreased. In the STF group, all three planes had significantly decreased initially but axial and coronal planes returned to baseline (no significant difference from preoperative values) at 24 months, while sagittal plane motion remained significantly diminished, although only by 4%. STF demonstrated no difference in SRS22r total, pain or self-image scores between preoperative and 2 years, while NSF had worse SRS22r total, pain, and self image scores at 2 years vs. preoperative values. When comparing NSF to STF, there was diminished axial, sagittal and coronal plane range of motion at 24 months postoperatively, but no differences in SRS22r total. The coronal, sagittal, and axial ROM as measured by ST demonstrated significant decreases from preoperative to postoperative following PSF; however, this deficit trends towards improvement over time. Our data demonstrates that at two years, NSF has poorer motion than STF patients in all three planes.

Replication of Coupled Movements of the Wrist: A Cadaveric Study of Total Wrist Arthroplasty.

The purpose of this study was to determine how well the active range of motion and the forces required to achieve motions are maintained following cadaveric implantation of the ball-and-socket style total wrist arthroplasty (TWA). An active wrist motion simulator was used to produce flexion, extension, radioulnar deviation, dart-thrower's motion, and circumduction in 14 fresh-frozen cadaveric wrists before and after TWA. Identical tendon displacements were applied to five major wrist flexors and extensors to control motion presurgery and postsurgery. Motion trials were recorded using biplanar video fluoroscopy and digitally reconstructed with 6 degrees of freedom using x-ray reconstruction of moving morphology. Wrist angles were subsequently measured with respect to an anatomically based radial coordinate system. Forces applied to the five actuated tendons were recorded by the simulator throughout all motion trials. Maximum wrist angles, dart-thrower's motion plane orientation, circumduction ellipse parameters, and peak tendon forces in pre-TWA and post-TWA conditions were compared. There were no significant differences in maximal flexion, extension, radial, or ulnar deviation angles when comparing preoperative anatomic wrists with the same wrist following implantation of the TWA. Orientation of dart-thrower's motion planes and circumduction ellipses with respect to the sagittal plane increased after cadaveric surgery, whereas the area of the circumduction ellipses remained similar. Tendon forces were similar in anatomic and TWA wrists apart from flexor forces, which decreased in flexion in TWA wrists. In our cadaveric setup, the TWA was able to recreate functional motion patterns without significantly increased tendon forces. The results of this study support the assertion that a ball-and-socket style TWA can provide a postoperative range of motion adequate to perform activities of daily living.

Relationship between muscle activation and sagittal knee joint biomechanics in patients with patellofemoral pain syndrome: a cross-sectional study

BackgroundPatellofemoral pain syndrome (PFPS) is one of the most common conditions affecting the knee joint, yet its pathomechanics remain unclear. The aim of this study was to investigate changes in muscle activation and gait patterns and to analyze the relationship between muscle activation and kinetic gait patterns in patients with PFPS.MethodsThis study included 31 patients with PFPS and 28 healthy volunteers without any symptoms. The sagittal plane motion of the knee joint, representing primary movement of the knee joint, was evaluated to identify changes in gait patterns. Electromyography (EMG) was used to measure muscle activation of vastus medialis (VM), vastus lateralis (VL), semitendinosus (ST), and gastrocnemius (GCM) muscles during gait analysis. Biomechanical features were analyzed during the three phases of the gait cycle; weight acceptance (WA), single limb support (SLS), and swing limb advancement (SLA) (0 ~ 12%, 13 ~ 50%, and 51 ~ 100% of the gait cycle, respectively).ResultsThe average knee extension moment (KEM) during WA was lower in the patient group and no significant differences were observed in the knee flexion angle (KFA). With respect to muscle activation, the patient group showed significantly higher muscle activation of the ST muscle in all phases. As the absolute value of the moment increased, the activation of the VM, VL, and ST muscles increased more rapidly in the patient group, especially when KEM was under −1% body weight × height (Bw × Ht) or over 5% Bw × Ht.ConclusionsPatients with PFPS exhibit elevated muscle activation, particularly in response to changes in the knee extension moment, which is likely a compensatory mechanism to manage knee joint loading during gait. These results highlight altered neuromuscular adaptations in PFPS, suggesting targeted therapies may help improve functional outcomes.Level of evidence III, cross-sectional study

Fate of the Mandible in Class III Patients Subjected to Bimaxillary Surgery with a New 3D Planning Reference

Class III patients have classically been managed through monomaxillary techniques, mainly involving mandibular setback movements. More recently, according to the upper incisor to soft tissue plane (UI-STP) or Barcelona Line (BL) planning protocol, bimaxillary procedures for upper maxilla advancement and reduced mandibular setback have been recommended in order to secure better aesthetic outcomes and avoid upper airway constriction. The present study describes the jaw movements in the sagittal plane performed in class III patients subjected to bimaxillary surgery following the BL protocol. A retrospective evaluation was performed on 124 class III patients subjected to bimaxillary surgery. All subjects underwent upper maxilla advancement. A total of 112 patients received mandible advancement movement (90.3%), nine received mandibular setback (7.25%), and the mandible underwent no movement along the sagittal dimension in the three remaining patients (2.4%). Mandibular advancement was significantly the most frequent treatment option. The presented results suggest that when the BL planning protocol is used as an aesthetic and functional reference, class III occlusion appears mostly related to maxillary sagittal hypoplasia instead of mandible hyperplasia, so bimaxillary advancement surgery should be considered as one of the first-choice procedures for the treatment of these patients.

Emission of Protonated Riboflavin Induced by Inhibition of Out-of-plane Vibration in a Rigid Polymer Network.

Chromophores incorporated into rigid polymer matrices may exhibit novel photophysical properties distinct from those in liquid solutions. In this work, we explored the decay path of the second ππ* state (2ππ*) of riboflavin in poly(vinyl alcohol) (PVA) solutions and films with various acidities. Highly efficient internal conversion from 2ππ* to the lowest ππ* state (1ππ*) induced by slight in-plane motion is demonstrated in all PVA solutions and films, irrespective of environmental acidity and rigidification. Ground-state protonation of riboflavin occurs in the highly acidic PVA film, and this cationic species emits fluorescence around 460 nm, in contrast to the ultrafast nonradiative relaxation in aqueous solution. The emission is demonstrated to originate from the 2ππ* state rather than the 1ππ* state. The 2ππ*-1ππ* internal conversion of protonated riboflavin is demonstrated to be induced by out-of-plane motion and impeded in a rigid PVA network, resulting in the anti-Kasha fluorescence.

Integration of neuromuscular control for multidirectional horizontal planar reaching movements in a portable upper limb exoskeleton for enhanced stroke rehabilitation.

Globally, the prevalence of stroke is significant and increasing annually. This growth has led to a demand for rehabilitation services that far exceeds the supply, leaving many stroke survivors without adequate rehabilitative care. In response to this challenge, this study introduces a portable exoskeleton system that integrates neural control mechanisms governing human arm movements. This design leverages neuroplasticity principles to simulate natural movements, aiming to reactivate and strengthen neuromuscular connections and thus enhance rehabilitation outcomes. A tailored musculoskeletal model of the human arm and an associated cost function were developed to accurately replicate the planar motion trajectories of a healthy human arm across 32 directions. The application of a Proportional-Derivative (PD) controller enables precise tracking of these trajectories by the exoskeleton. Individual testing has demonstrated high consistency between the exoskeleton-driven motion paths and the simulated trajectories, especially in trajectory accuracy along the X and Y axes. These findings support the efficacy of integrating advanced neural control strategies with practical exoskeleton designs in stroke rehabilitation.

Three-dimensional scapular kinematics during commonly used rehabilitation exercises in patients 12 weeks after Reversed Shoulder Arthroplasty.

Reversed shoulder arthroplasty (rTSA) is often used to restore functionality in patients with joint arthropathy and dysfunctional rotator cuff. As rTSA changes the biomechanical properties of the shoulder, an altered movement pattern of arm and scapula is to be expected. Previous studies focused on changes of the scapulohumeral rhythm during functional elevation tasks. To our knowledge, no study exists examining scapular kinematics during rehabilitation exercises in a patient population with rTSA. Therefore, this study aimed to analyze 3-dimensional scapular kinematics during 3 commonly used rehabilitation exercises, 12 weeks after rTSA surgery. It was hypothesized that scapular kinematics would be different between the horizontal and the vertical plane. Secondly, differences in scapular kinematics in the vertical plane, between the open and closed chain were hypothesized. In this cross-sectional study, 48 patients (55 shoulders) aged 69 ± 7.4 years participated. Scapular kinematics in terms of anterior/posterior tilt, external/internal rotation and upward/downward rotation were registered during 3 rehabilitation exercises. Exercises varied based on the plane (horizontal or vertical) and the modality (closed or open chain). Data were analyzed using Statistical Parametric Mapping (SPM). Post-hoc pairwise analysis within SPM (SPM(t)) revealed no significant differences among the exercises regarding posterior tilt. During vertical plane exercises (Standing Wall Slide 120° (WS), Standing reach 120° (REACH)), the scapula was more upwardly rotated for most of the time (14.93% - 74.63%, p<0.001) than during the exercise in the horizontal plane (Seated Bench Slide (BS)). No statistically significant differences were found between the vertical open chain (REACH) and the vertical closed chain exercise (WS). For the internal /external rotation, significant differences were found between the horizontal (BS) and the vertical plane (WS, REACH) (0% - 100%, p<0.001), and between the open (REACH) and closed chain (WS) vertical exercises (3.0% - 91.5%, p<0.001), with more external rotation when performing the movement in the vertical plane, and in the closed chain compared to respectively the horizontal plane and the open chain. Scapular kinematics during rehabilitation exercises after rTSA differ, depending on the plane and modality of the exercise. Insight into the impact of changing the plane (horizontal /vertical), and training in open versus closed chain, may assist physical therapists in the choice of exercises.

Steady and dynamic load measurements over a generic submarine hull form with various appendage configurations

Experimental studies for the steady and dynamic loads over a generic submarine hull form ( SUBOFF) with various appendage configurations in submerged motion was investigated through scaled model tests in the High Speed Towing Tank facility at Naval Science &amp; Technological Laboratory, India. Steady load measurements were performed for a range of angles of incidence in angle of attack (± 35°) and drift (0° to 35°) including control surface deflections (± 20°). Measurements for dynamic loads were performed in both vertical and horizontal plane of motion for oscillating frequencies ranging from 0.21 to 0.55 Hz. The studies were carried out for four different configurations of SUBOFF comprising of bare hull, bare hull with sail, bare hull with control fins and fully appended hull. The aim of the present study for the load measurements is to gather steady and dynamic force/moment data, estimate hydrodynamic coefficients, validate and extend such data over a wide range of operation scenarios experienced by a submarine including high angle of incidence. The particulars of the SUBOFF model, experimental facility and measurement technique, test results for load measurements and estimated hydrodynamic coefficients are highlighted in the paper. The measurements data generated from the above studies will greatly complement the current research on hydrodynamic load characteristics for submerged bodies both computationally and experimentally.

Pneumatically Actuated Rehabilitation Equipment for the Sagittal and Frontal Plane Movements of the Neck Joint

The timely reintegration into their daily routine of patients suffering from work-related musculoskeletal disorders is a priority in medical rehabilitation. This can be accomplished by means of certain procedures and adequate medical rehabilitation equipment. Starting from these considerations this paper proposes an original constructive solution of a rehabilitation device designed for the passive mobilization of the neck joint in the sagittal and frontal plane. The constructive solution that is put forward uses a pneumatic muscle as the actuation element, ensuring the adaptability of the equipment to the particular pain tolerance of each patient. The construction and dimensioning calculations of the equipment are presented, followed by the determination of the torsional rigidity and compliance permitted by the system. Based on the results the paper concludes with recommendations for the optimum deployment of the rehabilitation equipment.

Analytical Treatise on Endo-Atmospheric Fuel-Optimal Rocket Landings

While there is a strong current interest in and an increasing body of the latest numerical work on fuel-optimal powered descent inside an atmosphere, little recent analytical understanding of the problem has been reported. This paper analyzes the endo-atmospheric fuel-optimal rocket landing problem in three-dimensional motion. The necessary conditions for the problem that account for both propulsive and aerodynamic forces are derived. They include the full set of costate equations and the optimality conditions of the body attitude in terms of the angle of attack and sideslip angle. In contrast to a long-standing assumption of coordinated flight in the literature, it is shown that in general coordinated flight is not optimal if sideslip modulation is allowed. Special cases, such as small-angle and in-plane motion, are analyzed and harmonized with the previous results that are well known in the literature. The analytical conditions derived in this paper can also serve as independent verification for numerical solutions obtained by direct methods in optimal control or can be exploited for trajectory-design purposes.

Human in vivo talocrural contributions to ankle joint complex kinematics during walking, running, and hopping.

The human ankle joint complex, consisting of calcaneus, talus, and tibia, is often simplified as a single functional ankle joint, neglecting the motion of the talus. Understanding the individual contributions of the talus and calcaneus is crucial for comprehending ankle joint complex function in healthy populations, and alterations in function that may exist in clinical conditions. To achieve accurate bone kinematics, high-resolution biplanar videoradiography was used with participants engaged in walking and running (n=9) and hopping (n=9) with no overlap in participants. The rotation axes for the calcaneus and talus were analysed relative to the tibia over the ankle joint dorsi-/plantar flexion phases. Contributions of the talocrural joint to overall ankle joint complex function were measured by comparing the range of motion (talus relative to calcaneus). Most of the sagittal plane motion in the ankle joint complex (80%) occurred in the talocrural joint, with the subtalar joint contributing 20%. Rotation of the calcaneus about the tibia dominated frontal and transverse plane motion during hopping. Although surprisingly large ranges of talus motion were also observed in these planes (>5deg), indicating notable inter-subject variability and that the talocrural joint is not a simple hinge joint. The study highlights the importance of directly quantifying talus motion to understand ankle joint complex function. The results showed opposing talus and calcaneus movements for many participants during different locomotor tasks, which may influence the magnitude and distribution of subtalar joint loading. In addition, the large out-of-sagittal plane movements and inter-subject variability in talus and calcaneus motion may further emphasize the need for personalised models to investigate treatments for ankle pathologies.

Analytical ray-tracing of synchrotron emission around accreting black holes

Polarimetric images of accreting black holes encode important information about laws of strong gravity and relativistic motions of matter. Recent advancements in instrumentation have enabled such studies of two objects: the supermassive black holes M87* and Sagittarius A*. Light coming from these sources is produced by a synchrotron mechanism whose polarization is directly linked to magnetic field lines, and propagates toward the observer in a curved spacetime. We studied the distortions of the gas image by employing the analytical ray-tracing technique for polarized light ARTPOL, which is adapted for the case of synchrotron emission. We derived analytical expressions for fast conversion of the intensity or flux, polarization degree, and polarization angle from the local coordinates to those of the observer. We placed an emphasis on the nonzero matter elevation above the equatorial plane and noncircular matter motions. Applications of the developed formalism include static polarimetric imaging of the black hole vicinity and dynamic polarimetric signatures of matter close to the compact object.

Can we reliably assess spine movement quality in clinics? A comparison of systems to evaluate reliability of spine movement quality in a healthy population

Inertial measurement units (IMUs) have the potential to facilitate a large influx of spine movement and neuromuscular control data to stratify low back pain (LBP) diagnosis and care; however, uncertainties related to validity and reliability are preventing widespread use and acceptance. This study evaluated the concurrent validity of Xsens DOT IMUs relative to gold-standard optical motion capture equipment, and compared within- and between-day reliability of both systems to track spine range of motion (ROM) and movement quality (MQ) by evaluating intraclass correlation coefficients (ICC), standard error of measurement (SEM), coefficient of variation (CV), and minimum detectable difference (MDD). ROM was evaluated during planar ROM movements, and local dynamic stability (LDS; λmax), mean absolute relative phase (MARP) and deviation phase (DP) were estimated from repetitive trunk flexion at 3 speeds, in 15 healthy controls. Results show no statistically significant differences between systems for all metrics, and ICCs ≥ 0.86; therefore, validity was confirmed for tracking primary axis ROM and MQ. IMU data revealed that absolute (C7, T12, and S1) and relative (thoracic, lumbar, and total) ROM was the most reliable metric, followed by λmax, DP, and MARP. Reliability was similar between systems, suggesting that the poorer between-day reliability (higher SEM and CV, lower ICC) observed is attributable to movement variability and sensor placement rather than equipment error. MDDs provide thresholds to researchers and clinicians for identifying change in MQ. Further standardization of evaluated movements/metrics, and patient subgrouping are suggested to improve reliability assessments and refine MDDs in future work.

Sensitivity-Based Distributed NMPC: Experimental Results for a Levitating Planar Motion System

Sensitivity-Based Distributed NMPC: Experimental Results for a Levitating Planar Motion System

Evaluation of Material Selection for Small Wind Turbine Blades Using the TOPSIS Method

When creating a wind turbine blade, the material choice is crucial. Small wind turbine blades can be made out of a variety of materials, including wood, metals, carbon fibre reinforced polymers, natural fibre reinforced polymers, glass fibre reinforced polymers, and nanocomposites. Low density, high strength, and a long fatigue life are three attributes that must be present in the material used to create turbine blades. The substance is additionally made to tolerate high aerodynamic drag, fatigue loads, and impacts from the environment including dust particulate collecting and humidity. The material used to make the turbine blades should have the aforementioned essential qualities, including low density, high strength, and long fatigue life. Additionally, the material is made to endure high aerodynamic drag, fatigue loads, and environmental effects including dust particle collection and moisture materials. In order to capture energy from moving air masses, rotor blade designs rely on the principles of lift or drag. The lift blade design generates a force that lifts the object perpendicular to the plane of motion using the same principle that allows aeroplanes, kites, and birds to fly. Low density, high strength, fatigue resistance, and damage tolerance are requirements for materials used to make wind turbine blades. Composite materials, or materials with an elevated component content, are used extensively in the construction of the blades. Top Rank by Similarity to the Ideal Solution (TOPSIS), a multi-criteria evaluation technique, makes use of numerous factors. The alternative must be the furthest away of the beneficial ideal solution (BIS) &amp; the negative ideal solution (NIS) in order to be chosen. Topsis is built on this principle. The geometric gap between each choice and the most favourable option—that is, the option with the greatest score for each criterion—is calculated after a collection of alternatives is evaluated and the scores for all criteria are normalised. An analytical hierarchical process, the direct prioritisation approach, and other techniques can be utilised to calculate the value requirements according to the TOPSIS method. By using TOPSIS, parameters are thought to be steadily rising or decreasing. Alternate Parameters taken as Wood, Aluminium, epoxy based Carbon FRP (CFRPEP), epoxy based Glass FRP (GFRPEP), polypropylene based Glass FRP with (GFRPPP), epoxy based Cotton-Glass FRP (CGFRPEP), polypropylene based Cotton-Glass FRP (CGFRPPP), epoxy based FlaxGlass FRP (FGFRPEP), and epoxy based Sisal-Glass FRP with (SGFRPEP), plastic. Evaluation Parameters taken a Tensile Strength (MPa), Production Rate, Flexural Strength (MPa), Corrosion resistance, Blade Cost (USD), Setup Cost (USD), Density (kg/m^ {3}). From the result it is seen that epoxy based Carbon FRP (CFRPEP) got the first rank and Aluminium has the lowest rank. The first ranking epoxy based Carbon FRP (CFRPEP) is obtained with the lowest quality of Aluminium

Geometrically modulated contact forces enable hula hoop levitation

Mechanical systems with moving points of contact-including rolling, sliding, and impacts-are common in engineering applications and everyday experiences. The challenges in analyzing such systems are compounded when an object dynamically explores the complex surface shape of a moving structure, as arises in familiar but poorly understood contexts such as hula hooping. We study this activity as a unique form of mechanical levitation against gravity and identify the conditions required for the stable suspension of an object rolling around a gyrating body. We combine robotic experiments involving hoops twirling on surfaces of various geometries and a model that links the motions and shape to the contact forces generated. The in-plane motions of the hoop involve synchronization to the body gyration that is shown to require damping and sufficiently high launching speed. Further, vertical equilibrium is achieved only for bodies with "hips" or a critical slope of the surface, while stability requires an hourglass shape with a "waist" and whose curvature exceeds a critical value. Analysis of the model reveals dimensionless factors that successfully organize and unify observations across a wide range of geometries and kinematics. By revealing and explaining the mechanics of hula hoop levitation, these results motivate strategies for motion control via geometry-dependent contact forces and for accurately predicting the resulting equilibria and their stability.

The Structural Design, Kinematics, and Workspace Analysis of a Novel Rod-Cable Hybrid Cable-Driven Parallel Robot.

This study presents a novel rod-cable hybrid planar cable-driven parallel robot inspired by the biological synergy of bones and muscles. The design integrates rigid rods and flexible cables to enhance structural stability and precision in motion control. The rods emulate bones, providing foundational support, while the cables mimic muscles, driving motion through coordinated tension. This design enables planar motions with three degrees of freedom, and a structural configuration that mitigates sagging and vibration for improved stability and accuracy by introducing rigid structure. The study develops detailed kinematic models, including Jacobian analysis for motion control, and evaluates the workspace using geometric and Monte Carlo methods.

A Nonlinear Time Series Analysis on the Effect of Foot Injury on Gait Dynamics

The effects of foot injuries regarding bilateral asymmetry and gait dynamics are still poorly understood. Previous work discussed rehabilitation, postural control, and asymmetry, with the models being mainly validated for upper body translations and no or minimal assessment on rotation. The aim of this study was to assess the effect of foot injury on gait dynamics. For this, a wearable sensors system for data collection of the key variables of the of human movement was considered. The dynamics of motion – recorded in the plane of motion using a laser sensor – was assessed using a new projective method which considers the axial rotations, translation, and in-plane rotation patterns for normal human gait vs. simulated gait pathologies. A nonlinear timeseries analysis, along with a Poincare map, phase space, time delay, Lyapunov exponents, and false nearest neighbors (FNN) method have been considered in order to convey the periodicity of the data collected for a healthy individual with and without a simulated injury. The Lyapunov exponents which quantity the degree of separation of nearby trajectories are used to differentiate between the chaotic and non-chaotic behavior. The positive sign of the largest Lyapunov exponents for all data indicated “the exponential separation of nearby trajectories as time evolves”, that is, the chaotic behavior of the system.

Type synthesis, analysis, and prototyping of 4R1H mechanisms

Abstract The article introduces a novel class of 4R1H mechanisms, where 4R indicates four revolute joints and 1H indicates one helical joint. The paper starts with the type synthesis of these mechanisms, which involves combining two kinematic chains with planar and cylindrical motion types into a single closed-loop kinematic chain. If we fix any link in such a chain, we get a workable mechanism. The synthesis procedure considers two options for the relative arrangement of these two kinematic chains. Adding an H joint to the kinematic chain allows us to design mechanisms whose output link performs spatial motion. Using the proposed synthesis procedure, we develop a family of 4R1H mechanisms. Next, we choose one mechanism as a representative example and consider its mobility, singularity, kinematic, and dynamic analysis. Using screw theory, we confirm the mechanism has one degree of freedom and determine its singular configurations. Kinematic analysis provides closed-form expressions to calculate displacements, velocities, and accelerations of all the mechanism links. Dynamic analysis uses these results to compute the motor torque required for one motion cycle. To verify the suggested analytical algorithms and obtained results, we use computer-aided design tools, which allow us to develop virtual and physical prototypes.

Real-time 3D MR guided radiation therapy through orthogonal MR imaging and manifold learning.

In magnetic resonance image (MRI)-guided radiotherapy (MRgRT), 2D rapid imaging is commonly used to track moving targets with high temporal frequency to minimize gating latency. However, anatomical motion is not constrained to 2D, and a portion of the target may be missed during treatment if 3D motion is not evaluated. While some MRgRT systems attempt to capture 3D motion by sequentially tracking motion in 2D orthogonal imaging planes, this approach assesses 3D motion via independent 2D measurements at alternating instances, lacking a simultaneous 3D motion assessment in both imaging planes. We hypothesized that a motion model could be derived from prior 2D orthogonal imaging to estimate 3D motion in both planes simultaneously. We present a manifold learning technique to estimate 3D motion from 2D orthogonal imaging. Five healthy volunteers were scanned under an IRB-approved protocol using a 3.0 T Siemens Skyra simulator. Images of the liver dome were acquired during free breathing (FB) with a 2.6mm × 2.6mm in-plane resolution for approximately 10min in alternating sagittal and coronal planes at ∼5 frames per second. The motion model was derived using a combined manifold learning and alignment approach based on locally linear embedding (LLE). The model utilized the spatially overlapping MRI signal shared by both imaging planes to group together images that had similar signals, enabling motion estimation in both planes simultaneously. The model's motion estimates were compared to the ground truth motion derived in each newly acquired image using deformable registration. A simulated target was defined on the dome of the liver and used to evaluate model performance. The Dice similarity coefficient and distance between the model-tracked and image-tracked contour centroids were evaluated. Motion modeling error was estimated in the orthogonal plane by back-propagating the motion to the currently imaged plane and by interpolating the motion between image acquisitions where ground truth motion was available. The motion observed in the healthy volunteer studies ranged from 12.6 to 38.7mm. On average, the model demonstrated sub-millimeter precision and>0.95 Dice coefficient compared to the ground truth motion observed in the currently imaged plane. The average Dice coefficient and centroid distance between the model-tracked and ground truth target contours were 0.96±0.03 and 0.26mm±0.27mm respectively across all volunteer studies. The out-of-plane centroid motion error was estimated to be 0.85mm±1.07mm and 1.26mm±1.38mm using the back-propagation (BP) and interpolation error estimation methods. The healthy volunteer studies indicate promising results using the proposed motion modeling technique. Out-of-plane modeling error was estimated to be higher but still demonstrated sub-voxel motion accuracy.