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Tendon-driven continuum robot kinematic models are frequently computationally expensive, inaccurate due to unmodeled effects, or both. In particular, unmodeled effects produce uncertainties that arise during the robot’s operation that lead to variability in the resulting geometry. We propose a novel solution to these issues through the development of a Gaussian mixture kinematic model. We train a mixture density network to output a Gaussian mixture model representation of the robot geometry given the current tendon displacements. This model computes a probability distribution that is more representative of the true distribution of geometries at a given configuration than a model that outputs a single geometry, while also reducing the computation time. We demonstrate uses of this model through both a trajectory optimization method that explicitly reasons about the workspace uncertainty to minimize the probability of collision and an inverse kinematics method that maximizes the likelihood of occupying a desired geometry.

In the conventional seesaw models of neutrino masses, leptogenesis occurs at a very high scale. Three approaches have been discussed in the literature to lower the scale of leptogenesis making them testable: mass degeneracy, hierarchy of couplings and three-body decays. We advocate yet another approach to a testable leptogenesis, whereby the decaying particles could go out of equilibrium at an accessible scale due to kinematics, although their couplings to the decay products are larger for generating a desired CP asymmetry. We demonstrate this new possibility for the testable leptogenesis in a two-Higgs doublet model where the neutrino masses originate from a one-loop diagram.

Comparisons of the positive and negative halves of the distributions of parity-odd event variables in particle-physics experimental data can provide sensitivity to sources of nonstandard parity violation. Such techniques benefit from lacking first-order dependence on simulations or theoretical models, but have hitherto lacked systematic means of enumerating all discoverable signals. To address that issue this paper seeks to construct sets of parity-odd event variables which may be proved to be able to reveal the existence of any Lorentz-invariant source of nonstandard parity violation which could be visible in data consisting of groups of real nonspace-like four-momenta exhibiting certain permutation symmetries.

The equilibrium of globular and galaxy clusters is analyzed using a gravitomagnetic (GM) model for a fluid in stationary, axially-symmetric motion. An oblique change of coordinates leads to a free-fall nonlinear force balance equation relating the GM flux function and the gravitational potential. An approximate internal solution of the force balance is obtained introducing trial functions in the form of a sedimentation equilibrium. The internal solution defines the tangential component of the GM field acting on the surface of the cluster. This GM component constitutes the boundary condition that must be used to obtain a self-consistent solution together with Gauss’ and Ampère’s laws. The complete solution is postponed for future work, but a simple application to the classic Coma Cluster problem indicates that the rotating velocity on the surface of the cluster is within the range of observed values, without introducing dark matter.

We support, with new fitting instruments and the analysis of more recent experimental data, the proposal of a relationship between the mass of a Supermassive Black Hole (SMBH) and the kinetic energy of random motions in the host elliptical galaxy. The first results obtained in a previous paper with 13 elliptical galaxies are now confirmed by the new data and an enlarged sample. We find M_BH ∝ (M_Gσ²/c²)^β with 0.8 ≤ β ≤ 1 depending on the different fitting methods and samples used. The meaningful case β = 1 is carefully analyzed. Furthermore, we test the robustness of our relationship, including in the sample also lenticular and spiral galaxies and we show that the result does not change. Finally, we find a stronger correlation between the mass of the galaxy and the corresponding velocity dispersion that allows us to connect our relationship to the M_BH ∝ σ^α law. With respect to this law, our relationship has the advantage of having a smaller scatter.

In this paper, we provide a new derivation of the Dirac equation which promptly generalizes to higher spins. We apply this idea to spin-half Elko dark matter.

We consider collision of two geodesic particles near the lightlike surface (black hole horizon or naked singularity) of such an axially symmetric rotating or static metric that the coefficient $g_{\varphi \varphi }\to 0$ on this surface. It is shown that the energy in the center of mass frame $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$ is indefinitely large even without fine-tuning of particles’ parameters. Kinematically, this is the collision between two rapid particles that approach the horizon almost with the speed of light but at different angles (or they align along the normal to the horizon too slowly). The latter is the reason why the relative velocity tends to that of light, hence to high $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$. Our approach is model-independent. It relies on general properties of geometry and is insensitive to the details of material source that supports the geometries of the type under consideration. For several particular models (the stringy black hole, the Brans–Dicke analogue of the Schwarzschild metric and the Janis–Newman–Winicour one) we recover the results found in literature previously.

Ulnocarpal impaction syndrome is believed to be caused by abutment between the ulna and the ulnar carpus. We measured radiocarpal and midcarpal ranges of motion in 40 patients with ulnocarpal impaction syndrome by radiographic motion studies. The results showed that the radiocarpal and midcarpal ranges of motion were equally restricted in the affected wrist compared with the unaffected wrist. Therefore, motion of the radiocarpal joint and midcarpal joint contributed equally to total wrist motion bilaterally. No correlation between ulnar variance and the contribution of radiocarpal motion to overall wrist motion was found. Restriction of wrist motion in ulnocarpal impaction syndrome is not caused directly by abutment between the ulna and ulnar carpus, but a satisfactory explanation for restricted motion is still lacking.

With advances in imaging and computing technology the greater capacity to diagnose, plan and deliver care to patients with hand and wrist disorder is being realised. Work in our laboratory, has been able to identify certain specific rules that control wrist motion, and is a step on the pathway to creating a unified theory of carpal mechanics which will incorporate a kinetic biomechanical model. This will allow more precise anatomically based as well as quantitative diagnoses, but also an ability to test a proposed intervention in a “what if” scenario.

Purpose: Component position is critical in knee arthroplasty. We propose using a navigated knee axis (NKA) that is kinematically determined using a navigation system as an alignment reference, instead of defining the transepicondylar axis (TEA) with bony landmarks. This paper investigates whether this NKA should be computed over small arc segments versus over a full range of motion. Methods: Twelve unembalmed cadaver knees were tested. A navigation system computed the NKA for segments and for the full arc of motion in multiple planes. Results: The NKA computed near extension was different from the plane perpendicular to the mechanical axis (P > 0.005), while the NKA computed in flexion matched the TEA. Conclusion: The NKA determined from the full arc of motion was more reproducible and more closely estimated important knee parameters.

Pain is routinely implicated as a factor when considering impaired movement in injured populations. Movement velocity is often considered during the rehabilitation process; unfortunately our understanding of pain's impact on shoulder movement velocity in rotator cuff tear patients is less understood. Therefore, the purpose of this study was to test the hypothesis that there would be an increase in peak and mean shoulder elevation velocities following the decrease of shoulder pain in rotator cuff tear patients, regardless of tear size. Fifteen subjects with full-thickness rotator cuff tears (RCT) performed humeral elevation and lowering in three planes before and after receiving a lidocaine injection to relieve pain. Pain was assessed using a visual analog scale. Humeral elevation velocity data were collected using an electromagnetic tracking system. A significant reduction in pain (pre-injection 3.53 ± 1.99; post-injection 1.23 ± 1.43) resulted in significant increases in maximum and mean humeral elevation velocities. Mean shoulder elevation and lowering velocities increased 15.10 ± 2.45% while maximum shoulder movement velocities increased 12.77 ± 3.93%. Furthermore, no significant relationships were noted between tear size and movement velocity. These significant increases in movement velocity provide evidence to further support the notion that human motion can be inhibited by injury-associated pain, and that by reducing that pain through clinical interventions, human movement can be impacted in a positive fashion.

Purpose: We investigated the distribution of three-axis rotational directions of the tibiotalar joint in intact feet under axial loading and categorized them according to the combinations of the three-axis rotational directions of the tibiotalar joint as three-dimensional (3D) rotational patterns. Methods: The differences in rotational orientation of the talus relative to the tibia under unloaded and axial-loaded conditions were calculated from the 3D models of the tibiotalar joint that were reconstructed from magnetic resonance (MR) images in 27 intact male feet. Results: In the sagittal plane, the talus rotated into plantarflexion in 63% of the feet and into dorsiflexion in 30%. In the coronal plane, the talus rotated into inversion in 37% of the feet and into eversion in 33%. In the transverse plane, the talus rotated into adduction in 85% of the feet and into abduction in 4%. A total of 10 3D tibiotalar joint rotational patterns were observed under axial loading. There were no significant differences in the frequencies of the 10 tibiotalar joint rotational patterns (p > 0.05). Conclusions: The 3D tibiotalar joint rotational patterns under axial loading were consolidated into 10 directions, which provides insight into the subject-specific kinematics of the tibiotalar joint.

An estimated 3 million youth participate in youth baseball. The purpose of this review is to highlight musculoskeletal development and specific throwing-related injuries in youth baseball players, as well as the current knowledge of pitching biomechanics, which are closely intertwined with the both arm development and injuries. Methods: A systematic literature review was conducted to highlight musculoskeletal development, throwing-related injuries and pitching mechanics. Results: Youth athletes are actively going through skeletal maturation which includes the formation of new bone at the epiphyseal plate, increasing muscle mass and/or strength, and morphological changes in tendons and ligaments. These processes setup youth pitchers to sustain throwing injuries at their shoulder and elbow in ways that differ from their adult counterparts. Faulty pitching biomechanics may also cause throwing injuries. Deviation from proper mechanics at any point can cause injuries in the shoulder and elbow. Conclusion: Many musculoskeletal changes occur during the development of a youth baseball player. Some of these changes are beneficial for improving throwing performance, but also predispose the athlete to injury. Improper biomechanics may be related to the throwing-related injuries that are seen in youth baseball players.

Background: With cell phone use and ownership on the rise, daily circumstances often require individuals to divide attentional resources between walking and a cell phone-related task. This division of attention has been found to detrimentally effect task performance, making pedestrian cell phone usage an increasing safety concern. However, most studies have investigated the impact of dual-tasks on situational awareness and few have focused on tasks other than texting. Therefore, this study aimed to investigate the effect of various cell phone-related tasks on lower limb kinematics during walking.

Methods: Fourteen healthy, college-aged subjects completed gait analysis trials in five walking conditions, one single-task walking condition and four dual task conditions: Walk+Converse, Walk+Read (Simple), Walk+Read (Difficult), and Walk+Text. Subjects’ movements were recorded with a motion capture system and peak sagittal plane lower extremity joint angles, gait velocity, and stride length were calculated.

Results: Of the eight kinematic outcome measures analyzed, all but one revealed some significant (p < 0.05) differences between dual-task walking conditions. Gait velocity and stride length both decreased due to the addition of the dual tasking, with the magnitude of the reduction becoming more apparent with the increased difficulty of the cell phone-based task.

Conclusion: This study supports a fundamental change to gait kinematics in response to cell phone use while walking, with the magnitude of impact being directly related to the complexity of the secondary task. The significant changes to gait kinematics in complex dual-task situations could present a threat to balance.

Purpose: Most shoulder pathologies are associated with altered scapular kinematics which is mentioned as scapular dyskinesis. Scapular mobility, especially in upward rotation, measurement is essential for diagnosis and treatment. Easy-to-use, clinically applicable 2-dimensional (2-D) measurements would show excellent intra-tester reliability. To quantify intra-tester reliability for measuring scapular upward rotation in individuals with scapular dyskinesias, the landmark palpation with a video annotation tool was used.

Methods: Ten participants with scapular dyskinesis were recruited. Scapular upward rotation was measured at rest, 30°, 60°, 90°, and 120° of humeral elevation in the coronal plane both raising and lowering phases. Two trials were conducted for each arm position randomly, and an assessor took the pictures throughout. The video annotation tool (2-D Kinovia program) was used for measuring scapular upward rotation angles between days. The intra-tester reliability of scapular upward rotation was calculated.

Results: This measurement technique demonstrated excellent intra-tester reliability (ICC${}_{3,1}$ = 0.98), range 0.96–0.99, and standard error of measurement was less than 1°.

Conclusions: The findings demonstrated that using this technique to measure scapular upward rotation was reliable in subjects with scapular dyskinesis.

A new algorithm is developed to solve the collision avoidance problem for a host ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. The objective of the collision avoidance maneuver is to maximize with respect to the state and control history the timewise minimum distance between a host ship and an intruder ship. Two limiting cases are considered: (i) the intruder ship is uncooperative and keeps its course unchanged during the encounter; (ii) the intruder ship is cooperative. In both cases, a differential game formulation is avoided and the collision avoidance problem is formulated as a maximin problem of optimal control.

Four problems are investigated and their solutions compared: Problems P1 and P2 deal with uncooperative collision avoidance, while Problems P3 and P4 deal with cooperative collision avoidance.

Numerical results show that the optimal control histories always involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values.

A well-known combinatorial algorithm can decide generic rigidity in the plane by determining if the graph is of Pollaczek–Geiringer–Laman type. Methods from matroid theory have been used to prove other interesting results, again under the assumption of generic configurations. However, configurations arising in applications may not be generic. We present Theorem 4.2 and its corresponding Algorithm 1 which decide if a configuration is $𝜀$-locally rigid, a notion we define. A configuration which is $𝜀$-locally rigid may be locally rigid or flexible, but any continuous deformations remain within a sphere of radius $𝜀$ in configuration space. Deciding $𝜀$-local rigidity is possible for configurations which are smooth or singular, generic or non-generic. We also present Algorithms 2 and 3 which use numerical algebraic geometry to compute a discrete-time sample of a continuous flex, providing useful visual information for the scientist.

The purpose of this paper was to investigate the anatomical location of the main axes of rotation of the knee, that is the axes of flexion-extension and longitudinal rotation. We compared 4 hypotheses on the correlation between the axis of flexion-extension and the femoral anatomy and 4 hypotheses on the correlation between the axis of longitudinal rotation and the tibial anatomy in 6 normal human knees. The methods used for the study were:. digitization by an electrogoniometer; computer reconstruction of motion and bone geometry, and an original geometrical interpolation to identify axes location. Our results suggest that: (a) the axis of flexion-extension lies in a cone spanned by the transepicondylar line and the so called FFc line;¹⁹ (b) the axis of longitudinal rotation can be represented by a line parallel to the tibial anatomical axis intersecting the flexion axis in a fixed point of the medial compartment.

With progress of modern technology, manually-propelled wheelchairs are still of importance for individuals with mobility impairments. The repeated wheelchair propulsion and strenuous daily activities cause high loads and thus injuries on the upper extremity joints. Over the past few years, a considerable number of studies have been made on biomechanical analysis of wheelchair propulsion and wheelchair-related activities. Thorough investigation of biomechanics during wheelchair propulsion enhances comprehension of mechanism of injuries and provides information to improve wheelchair design and fitting. Numerous investigations have been made to demonstrate factors which cause low effectiveness of force application and inefficiency of movements. Emphasis was also placed on developing analytical models to simulate wheelchair propulsion.

The reliable knowledge that model-based three-dimensional (3D) fluoroscopy can provide about in vivo joints kinematics is essential to diagnose orthopedic pathologies, develop new prosthesis, and evaluate clinical procedures. To exploit 3D fluoroscopy for the analysis of elbow kinematics, its use was evaluated considering a single model for the forearm or two different models for the ulna and radius. Active elbow flexion-extension and prono-supination motor tasks of a healthy male subject were acquired by means of fluoroscopy. The 3D bone models were automatically aligned to the relevant projections. The pose estimation algorithm sought the tangency condition of the projection rays with the model surface, minimizing a cost function and exploiting an adaptive distance map. Five iterative guided alignments were performed to avoid the final convergence to a local minimum. The results highlighted the critical alignment of the ulna/radius model, particularly when prono-supination is performed. From the physiological motion patterns and given the values of the cost function, 3D fluoroscopy was proven to be applicable to the analysis of the elbow kinematics when single bone models for the ulna and radius are used.