The use of inertial measurement units (IMUs) to compute gait outputs such as the 3D lower limb kinematics is of huge potential, but no consensus on the procedures and algorithms exists. This study aimed at evaluating the validity of a 7-IMUs system against the optoelectronic system. Ten asymptomatic subjects were included. They wore IMUs on their feet, shanks, thighs and pelvis. The IMUs were embedded in clusters with reflective markers. Reference kinematics was computed from anatomical markers. Gait kinematics was obtained from accelerometer and gyroscope data after sensor orientation estimation and sensor-to-segment (S2S) calibration steps. The S2S calibration steps were also applied to the cluster data. IMU-based and cluster-based kinematics were compared to the reference through root mean square errors (RMSEs), centered RMSEs (after mean removal), correlation coefficients (CCs) and differences of amplitude. The mean RMSE and centered RMSE were respectively 7.5° and 4.0° for IMU-kinematics, and 7.9° and 3.8° for cluster-kinematics. Very good CCs were found in the sagittal plane for both IMUs and cluster-based kinematics at the hip, knee and ankle levels (CCs>0.85). The overall mean amplitude difference was about 7°. These results reflected good accordance of our system with the reference, especially in the sagittal plane, but the presence of offsets requires caution for clinical use.

Background: Water treadmill (WT) exercise is a popular modality for the training and rehabilitation of horses. However, evidence-based literature regarding the use of WT exercise, particularly using inclines, is lacking.Objectives: The aim of this study was to assess the effect of recurring inclined WT sessions on equine epaxial muscles development.Methods: Six horses completed 24 sessions of 15 minutes of WT activity over four weeks. Horses walked with water at mid-cannon level at a treadmill incline of 4%. Back traces were measured at three and seven centimetres ventral to the dorsal midline at T5, T9, T14 and T18, prior to the first session (W0) and weekly for 4 weeks (W1-4). Results: Overall the back traces demonstrated progressive increases in muscle development (p<0.05), starting at W2 up to W4. At three centimetres ventral to the dorsal midline the most to least significant increases in gross muscle development were at T18, T5, T9 and T14, respectively and when measured at seven centimetres ventrally, the most to least significant increases were demonstrated at T5, T18 and T14 . It was noted that increases in thoracic back profile musculature were mainly observed within two to four weeks of the WT intervention.Conclusions: It has been concluded that repeated WT exercise on an incline setting has a significant effect on the rate and size of growth of equine thoracic back profile musculature. Muscle hypertrophy due to resistance training in the WT starts at 2 weeks within the programme, and it progresses as exercise continues to be performed.

Teaching kinematic rotations is a daunting task for even some of the most advanced mathematical minds. However, envisioning and explaining the three-dimensional rotations can be highly simplified by changing the paradigm. This paradigm change allows for a high school student with a understanding of geometry to be able to not only develop the matrix but also explain the rotations at a collegiate level. The proposed method includes the assumption of a point (P) within the initial three-dimensional frame with axes (x ̂_i, y ̂_i, z ̂_i). It then utilizes a two-dimensional rotation view (2DRV) to measure how the coordinates of point P translate after the initial axis is rotated instead of using the established Euler's formula. The equations are used in matrix notation to develop a direction cosine matrix (DCM) for future equations. This method provides a high school student with an elementary and repeatable process to compose and explain kinematic rotations.

The injury rate in agility dogs is relatively high compared to the general population. No study to date has considered the biomechanical effects of the dog walk obstacle in agility trials, highlighting a research need. The aim of this study was to test for correlation between dog age, weight, speed, contact training method and agility experience and forelimb joint angulation and peak ground reaction forces (GRFs) over this obstacle. Dogs were filmed running across a Kennel Club (KC) standard dog walk whilst wearing reflective markers attached to specific anatomical points. A Tekscan Comformat and a Tekscan Walkway pressure mat were secured to the dog walk contact area and the ground at the end of the dog walk respectively. Joint angulation and peak forelimb GRFs were recorded and analysed. A key finding is that the way a dog will move across the obstacle changes depending on their level of experience, with experienced dogs showing increased flexion of the elbow joints and decreased extension of the carpus compared to inexperienced competitors. Higher speeds over the dog walk also resulted in significantly increased elbow joint flexion. Increased joint angulation and higher GRF’s are associated with a higher risk of injury.

Most schoolchildren carry schoolbags, of which a substantial proportion carry loads that exceed 15% of their body mass. Although the effects of loading have been investigated to varying degrees, the status of schoolbag loading and the acute affects thereof on gait and posture have not been thoroughly investigated within the South African context. A total of 60 participants in the 10-13-year age range volunteered for the present study. Significant differences were evident for relative load carriage (χ2(3) = 14.54, p &lt; .001), forefoot and heel forces (Mdiff = 17.05-34.86 N, p &lt; .001), force-ratios (Mdiff = 0.02, p = .029), and gait speed (Mdiff = -0.18 km/hr, p = .016).), but not for any postural angles (Mdiff = -3.37-6.08 deg, all p &gt; .052). Those who exceeded 15% BM were ~9 times more likely to report pain than those below 15% BM. The children in the current carried significantly heavier realtive loads (p &lt; .001) compared to similarly aged children from other countries. Loading leads to acute changes in posture and gait that are likely not meaningful. However, excessive loading (&gt;15% BM) leads to significantly higher perceptions and reporting of pain in 10-13 year-old children.

This paper presents a simple model and explanation for the flat rotation curves of Spiral Galaxies without resorting to: (1) The introduction of Dark Matter, (2) a modification of Newton's 2nd law (MOND) or (3) a modification of Einstein's theory of General Relativity. The model that is developed involves a rotating baryonic disk (a rotating frame of reference with an "effective angular velocity" about its center surrounded by a rotating cloud of hydrogen (HI). The model also assumes that the measurements that are made on the rotating HI cloud are made from an earth based inertial frame of reference. The predictions of the model rely on the relationship between velocities as measured by earth based radio telescopes and the velocities as measured in the rotating frame. Calculations of the rotation curves of three galaxies are made using this model and compared with readily available experimental data

The teaching of the lunge technique in fencing is critical in the developmental age. The relations of anthropometrics with kinematics of lunge was studied only in adult fencers, and no study exist in young considering the different level of experience. Our aims were to assess, in young fencers, which factors, between the anthropometric and the kinematics, were mostly connected with lunge performance (speed and excursion) in different genders and expertise levels. Fifteen young fencers participated in this study. Lunge kinematics, anthropometric characteristics and force expressed in vertical jump tests were collected. Maximal lunge velocity resulted mainly correlated with the posterior knee’s extension ((r=0.56, p=0.031). The lunge distance and mean hip velocity were mostly correlated with fencers’ height (r=0.85, p=0.000 and r=0.76, p=0.001) and FFM (r=0.8, p=0.000 and r=0.73, p=0.002). Experts and non-experts show significant differences in fat free mass, area of upper arm, and of thighs (Effect Size = 1,27 – 1,33, p= 0,021-0,035). From our results it emerges that, in this age range, the analysed aspects of lunge performance are mainly correlated with participant’s anthropometry. Moreover, it is already possible in this age span, to find technical differences linked to the experience.

Calculating a minimum-time trajectory requires the solving of a boundary value problem resulting from invocation of necessary conditions of optimality to set up a set of ordinary differential equations to solve the trajectory between the initial position and desired ending position with set constraints on the path between the two. This manuscript expresses the minimum time optimum trajectory between a satellite in a geosynchronous orbit and a target set on earth’s surface utilizing a non-rotating earth centric coordinate system. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Simulation precision (validated by the quaternion normalization condition) reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the ubiquitous 321 “aerospace” rotation sequence and a 99.84% increase over the so-called 313 “orbital” rotation sequence. Utilizing the proposed optimal trajectory candidate yields a total flight time of 2 hours, 34 minutes and 46 seconds, or an average velocity of 3.85 kilometers per second, while impacting the target with a velocity of 11.54 kilometers per second.

Finding a suitable support is a key process in the life history of climbing plants. Climbers that find a suitable support have greater performance and fitness than those that remain prostrate. Numerous studies on climbing plant behavior have elucidated the mechanistic details of support searching and attachment. Far fewer studies have addressed the ecological significance of support-searching behavior and the factors that affect it. Among these, the diameter of supports influences their suitability for twining plants. When support diameter increases beyond some point climbing plants are unable to maintain tensional forces and therefore lose attachment to the trellis. Here we further investigate this issue by putting pea plants in the situation to choose between supports of different diameters while their movement was recorded by means of a three-dimensional motion analysis system. The results indicate that the way climbing plants move can vary depending on whether they are presented with one or two potential supports. Furthermore, when presented with a choice between a thin and a thick support, the plants showed a distinct preference for the former than the latter. The present findings shed further light on how climbers make decisions as far as support search is concerned, and provide evidence that plants adopt one of several alternative plastic responses in a way that optimally corresponds to environmental scenarios.

Climbing plants require an external support to grow vertically and enhance light acquisition. Climbers that find a suitable support have greater performance and fitness than those that remain prostrate. Support search is characterized by oscillatory movements (i.e., circumnutation), in which plants rotate around a central axis during their growth. Numerous studies have elucidated the mechanistic details of circumnutation, but how this phenomenon is controlled remains unclear. Here, we use supervised machine learning algorithms to generate models that learn to discriminate between the presence/absence of a support in the environment. Results indicate that there is a difference in the pattern of circumnutation, depending on the presence of a support, that can be learned and classified rather accurately. We also identify distinctive kinematic features that contribute to the classification tasks. Overall, machine learning approaches appear to be powerful tools for understanding the movement of plants.

The paper deals with the problems of direct kinematics related to a 2T6R robot, the direct kinematics of the plane mechanism of the robot. The direct kinematics of this proposed new robot help to study the movement, including the dynamic one, to determine the forces in the mechanism and to model the possible trajectories of the final effector point, thus determining the robot's working space and some of its multiple possible uses. Two totally different methods were used to verify the calculation relations, the results obtained by both methods being practically identical. The first method used is an original trigonometric method, and the second is an original geometrically analytical method.

This study examines the effects and durability of postural exercise on gait kinematics in people with intellectual and developmental disabilities (IDD). Thirty-four men with mild IDD were assigned to either the training group (n = 19) or the control group (n = 15). The TG performed the intervention over 8 weeks, 3 days/week, 1 h/day. The results indicated that the intervention program had a significant effect on some variables of gait. Also, in the TG between post-test and follow-up, there was no significant difference, which indicated that gait variables were maintained by the TG one month after the end of the program. This study provides evidence that postural exercises can be used as an effective intervention for improving gait in individuals with IDD.

The study is devoted to the issues of mathematical modeling and simulating the sport differential mechanism (DM) with controllable torque redistribution. The issue is caused by the elaboration of ADAS systems with the automated torque vectoring for transmissions of all-wheel-drive (AWD) vehicles and the inclusion of such devices in the combined autonomous vehicle trajectory control scheme. At the article's beginning, the use of devices for redistributing traction forces is reasoned by analyzing the curvilinear vehicle motion, where they could ensure the accuracy of vehicle steerability. The literature review highlights modern developments in the field of modeling and researching such DMs. Considering the vehicle turn with a minimum radius, the conditions corresponding to passing greater torque over the outrunning rear axle are determined. All the mechanism's components and loads acting between them are described in detail. To form an original method of mathematical description of the mechanism functioning, the system of differential equations, systems of kinematic and force connections are considered separately. The article details the mathematical approach to generalize the way for automating the equation compilation for rotational mechanical systems such as vehicle transmissions. In the simulation section, a Simulink model reflecting the functional components and calculation procedures is presented. A series of testing and simulations on the DM operation with forcible torque distribution is carried out. Modeling data are presented, and the analysis of simulation results is performed. In the completion, conclusions are made regarding the scope and use of this model and the prospects for further developing the method proposed to automate the formation of equation systems.

Analysis of plesiosaur swim dynamics by means of a digital 3D armature (wireframe “skeleton”) of a pliosauromorph (“Ava”) demonstrates that: 1, plesiosaurs used all four flippers for primary propulsion; 2, plesiosaurs utilized all four flippers simultaneously; 3, respective pairs of flippers of Plesiosauridae, front and rear, traveled through distinctive, separate planes of motion, and; 4, the ability to utilize all four paddles simultaneously allowed these largely predatory marine reptiles to achieve a significant increase in acceleration and speed, which, in turn, contributed to their sustained dominance during the Mesozoic.

This paper introduces an alternative method to design the path following controller of an under-actuated spherical mobile robot, which has a single pendulum structure its inside as a driving mechanism. The mechanism has an under-actuated problem; two inputs for the roll and pitch but no direct input for the yaw. In order to overcome this problem, the proposed method defines a virtual reference input for the heading direction. The virtual reference input works as a control input since it can be arbitrarily designed just like the reference input of a conventional system. The control scheme using the defined virtual reference input achieves the stabilization and path following control of the under-actuated spherical mobile robot without any additional control technique. The stability of the proposed control scheme is guaranteed by Lyapunov stability analysis, and simulation results are given to demonstrate its performance.

We propose a deep reinforcement learning based manipulator path tracking method to solve the computationally difficult and non-unique problem of manipulator path tracking methods based on inverse kinematics. By transforming the path tracking task into a sequence decision problem, our method adopts an end-to-end learning method for closed-loop control and avoids the process of finding the inverse solution. We first explored the feasibility of the deep reinforcement learning method in the path tracking of the manipulator. After verifying the feasibility, the path tracking of the multi-degree-of-freedom(multi-DOF) manipulator was realized by combining the maximum entropy deep reinforcement learning algorithm. The experimental results show that our method has a good effect on the path tracking of the manipulator, which not only avoids the process of finding the inverse kinematics solution, but also requires no dynamic model. Therefore, we believe that our method has great significance in the study of manipulator path tracking.

When dealing with galactic dynamics, or more specifically, with galactic rotation curves, one basic assumption is always taken: the frame of reference relative to which the rotational velocities are given is assumed to be inertial. In other words, fictitious forces are assumed to vanish relative to the observational frame of a given galaxy. It might be interesting, however, to explore the outcomes of dropping that assumption; that is, to search for signatures of non-inertial behavior in the observed data. In this work, we show that the very discrepancy in galaxy rotation curves could be attributed to non-inertial effects. We derive a model for spiral galaxies that takes into account the possible influence of fictitious forces and find that the additional terms in the new model, due to fictitious forces, closely resemble dark halo profiles. Following this result, we apply the new model to a wide sample of galaxies, spanning a large range of luminosities and radii. It turns out that the new model accurately reproduces the structures of the rotation curves and provides very good fittings to the data.

The remote monitoring of clinical parameters plays a fundamental role in different situations, like pandemic health emergencies and post-surgery conditions. In these situations, the patients might be impeded in their movements and it could be difficult to have a specific health monitoring. In recent years, technological advancements in smartphones have opened up new possibilities in this landscape. The present work aims to propose a new method for respiratory kinematics monitoring via smartphone sensors. In particular, a specific application was developed to register Inertial Movement Unit (IMU) sensors data from the smartphone for respiratory kinematics measurement and to guide the user through a specific acquisition session. The session was defined to allow for the monitoring of the respiratory movement in five prescribed positions. The application and the sequence were successfully tested on a given population of 77 healthy volunteers. The resulting accelerometers and gyroscope signals were processed to evaluate the significance of differences according to participants sex, vector components and smartphone positioning and, finally, to estimate the respiratory rate. The emerged statistical differences revealed the significance of information in the different acquisition positions.

In the context of Kalman filters, the predicted error covariance matrix $\mathbf{P}_{k+1}$ and measurement noise covariance matrix $\mathbf{R}$ are used to represent the uncertainty of state variables and measurement noise, respectively. However, in real-world situations, these matrices may vary with time due to measurement faults. To address this issue in CubeSat attitude estimation, an adaptive extended Kalman filter has been proposed that can dynamically estimate the predicted error covariance matrix and measurement noise covariance matrix using an expectation-maximization approach. Simulation experiments have shown that this algorithm outperforms existing methods in terms of attitude estimation accuracy, particularly in sunlit and shadowed phases of the orbit, with the same filtering parameters and initial conditions.

Parallel manipulators with multiple end-effectors bring us interesting advantages over conventional parallel manipulators such as improved manipulability, workspace and avoidance of singularities. In this work the kinematics of a five-bar planar parallel manipulator equipped with two end-effectors is approached by means of the theory of screws. As an intermediate step the displacement analysis of the robot is also investigated. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that regard the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) plays a central role. In order to exemplify the method of kinematic analysis, a case study is included. Furthermore, the numerical results obtained by means of the theory of screws are confirmed with the aid of special software like ADAMS.^TM

Background: This systematic review aimed to provide a comprehensive overview of the effects of Functional Electrical Stimulation (FES) on gait characteristics in healthy individuals. Methods: Six electronic databases (PubMed, Embase, Epistemonikos, PEDro, COCHRANE Library, Scopus) were searched for studies evaluating the effects of FES on spatiotemporal, kinematic and kinetic gait parameters in healthy individuals. Two examiners evaluated the eligibility and quality of included studies using the PEDro scale. Results: A total of 15 studies met the inclusion criteria. Findings from the literature reveal that FES can be used to modify lower-limb joint kinematics, i.e., to increase or reduce the range of motion of hip, knee and ankle joints. In addition, FES can be used to alter kinetics parameters, including ground reaction forces, center of pressure trajectory, or knee joint reaction force. As a consequence of these kinetics and kinematics changes, FES can lead to changes in spatiotemporal gait parameters, such as gait speed, step cadence, and stance duration. Conclusion: The findings of this review improve our understanding of the effects of FES on gait biomechanics in healthy individuals, and highlight the potential of this technology as a training or assistive solution for improving gait performance in this population.

Bionic robotic hand can perform many movements similar to human hand. But there is still a significant gap in manipulation between robot and human hand. It is necessary to understand the finger kinematics and motion patterns of human hand to improve the performance of robotic hand. This study aimed to comprehensively investigate normal hand motion patterns by evaluating the kinematics of hand grip and release in healthy individuals. The data corresponding to rapid grip and release were collected from the dominant hand of 22 healthy people by sensory glove. The kinematics of 14 finger joints were analyzed, including the dynamic range of motion (ROM), peak velocity, joint sequence and finger sequence. The results show that the proximal interphalangeal (PIP) joint had a largest dynamic ROM than metacarpophalangeal (MCP) and distal interphalangeal (DIP) joints. Besides, the PIP joint had the highest peak velocity, both in flexion and extension. For joint sequence, the PIP joint moved prior to the DIP or MCP joints during flexion, while extension started in DIP or MCP joints, followed by PIP joint. Regarding the finger sequence, the thumb started to move before four fingers, and stopped moving after the fingers during both grip and release. This study explored the normal motion patterns in hand grip and release, which provided kinematic reference for the design of robotic hand and thus contribute to its development.

Understanding neck pain is an important societal issue. Kinematic data from sensors may help to gain insight on the pathophysiological mechanisms associated with neck pain through a quantitative sensorimotor assessment of one patient. The objective of this study was to evaluate the potential usefulness of artificial intelligence with several Machine Learning (ML) algorithms in assessing neck sensorimotor performance. Angular velocity and acceleration measured by an inertial sensor placed on the forehead during the DidRen laser test in thirty-eight acute and subacute non-specific neck pain (ANSP) patients were compared to forty-two healthy control participants (HCP). Seven supervised ML algorithms were chosen for the predictions. The most informative kinematic features were computed using Sequential Feature Selection methods. The best performing algorithm is the Linear Support Vector Machine with an accuracy of 82% and Area Under Curve of 84%. The best discriminative kinematic feature between ANSP patients and HCP is the first quartile of head pitch angular velocity. This study has shown that supervised ML algorithms could be used to classify ANSP patients and identify discriminatory kinematic features potentially useful for the clinicians in the assessment and monitoring of the neck sensorimotor performance in ANSP patients.

In-depth research on the rehabilitation mechanism and motion characteristics of a rehabilitation training robot based on 4-UPUS parallel mechanism. The overall design and the working principle of each key component are explained, and the robot rehabilitation scheme is described. The static analysis and modal analysis of the robot bearing structure are carried out to verify whether the static mechanical characteristics of the mechanism meet the application requirements under working conditions.A simplified mathematical model of the six-bar linkage mechanism is established, and the kinematics of the mechanism is solved by the geometric analysis method. The motion characteristic diagram of each key point is obtained through simulation calculation. Establish the motion model of the parallel mechanism, and discuss the working space and motion performance analysis of the mechanism. The forward solution analysis of the mechanism position is carried out by using the numerical analysis method, and the three-dimensional graphics of the attitude angle and linear displacement of the reachable working space are obtained.Taking the UPUS single branch chain as the analysis object, the single open chain analysis method is used to solve the kinematics image of the corresponding surface in the working space of the mechanism, which verifies the correctness of the kinematics theoretical solution and the feasibility of simulation.The research results show that the 4-UPUS parallel mechanism rehabilitation training robot can cooperate with the ankle joint for rehabilitation training. It makes up for the single movement of the current lower limb rehabilitation robot and the unsatisfactory rehabilitation effect, and provides a reference for the practical application of the subsequent ankle joint rehabilitation robot system.

The paper presents an innovative hexapod walking robot built with 3-UPU parallel mechanism. In the robot, the parallel mechanism is used as both an actuator to generate walking and also a connecting body to connect two groups of three legs, thus enables the robot to walk with simple gait by very few motors. In the paper, the forward and inverse kinematics solutions are obtained. The workspace of the parallel mechanism is analyzed using limit boundary search method. The walking stability of the robot is analyzed, which yields the robot’s maximum step length. The gait planning of the hexapod walking robot is studied for walking on both flat and uneven terrains. The new robot, combining the advantages of parallel robot and walking robot, has a large carrying capacity, strong passing ability, flexible turning ability, and simple gait control for its deployment for uneven terrain.

Plants characterized by a soft or weak steam, such as climbing plants, need to find a potential support (e.g., wooden trunk) to reach greater light exposure. Since Darwin’s research on climbing plants, several studies on their searching and attachment behaviors have demonstrated their unique ability to process different support features to modulate their movements accordingly. Nevertheless, the strategies underlying this ability are yet to be uncovered. The present research tries to fill this gap by investigating how the interaction between above- (i.e., stem, tendril, …) and belowground (i.e., the root system) plant organs influence the kinematics of the approach-to-grasp movement. With three-dimensional (3D) kinematical analysis, we characterized the movement of pea plants (Pisum sativum L.) towards a support with different thicknesses above and belowground (i.e., thin below, thick aboveground, or the opposite). As a control condition, the plants were presented to supports with the same thickness below- and aboveground (i.e., either entirely thin or thick). The results suggest an integration between the information from below- and aboveground for driving the reach-to-grasp behavior of the aerial plant organs. Information about the support conveyed by the root system seems particularly important to fulfil the end-goal of the movement.

This study aims to explore the possibility of estimating a multitude of kinematic and dynamic quantities using subject-specific musculoskeletal models in real-time. The framework was designed to operate with marker-based and inertial measurement units enabling extensions far beyond dedicated motion capture laboratories. We present the technical details for calculating the kinematics, generalized forces, muscle forces, joint reaction loads, and predicting ground reaction wrenches during walking. Emphasis was given to reduce computational latency while maintaining accuracy as compared to the offline counterpart. Notably, we highlight the influence of adequate filtering and differentiation under noisy conditions and its importance for consequent dynamic calculations. Real-time estimates of the joint moments, muscle forces, and reaction loads closely resemble OpenSim's offline analyses. Model-based estimation of ground reaction wrenches demonstrates that even a small error can negatively affect other estimated quantities. An application of the developed system is demonstrated in the context of rehabilitation and gait retraining. We expect that such a system will find numerous applications in laboratory settings and outdoor conditions with the advent of predicting or sensing environment interactions. Therefore, we hope that this open-source framework will be a significant milestone for solving this grand challenge.

Automatic control to any of robot manipulators, some kind of issues are being observed. A numerical method for solution generation to the inverse kinematics problem of redundant robotic manipulators is presented to obtain the smoothest algorithm as possible, leading to a robust iterative method. After the primary objective of the reachability of end-effectors to the target point is achieved, the aim is set to resolve the redundant degrees of freedom of redundant manipulator. This method is numerically stable since it converges to the correct answer with virtually any initial approximation, and it is not sensitive to the singular configurations of the manipulator. In addition, this technique is computationally effective and able to apply for serial manipulators with any DOF applications. A planar 3R-DOF serial link redundant manipulator is considered as exemplar problem for solving. Also, the continuum approach for resolving more complex structure with variable DoF is illustrated here and their brief applicability to support surgeries and adaptive use of artificial linkage moments is also calculated.

The three-pronged sliding universal coupling is a new kind of three-pronged coupling. To study its kinematic and dynamic characteristics, directional cosine matrices are utilized as tools to analyze the coordinate systems by establishing simplified geometric models and corresponding motions. Through the analysis of the motions of the input and output shafts and employing the method of single-force element, a set of equilibrium equations for the forces acting on the output shaft and the input shaft are formulated for solution analysis. The research indicates that during the rotation process, there exists a small angular difference between the input shaft and the intermediate shaft, demonstrating the quasi-constant angular velocity characteristics of the new tripod sliding universal coupling. The curves of the forces and torques acting on each component of the coupling approximate sinusoidal curves. The optimal operating angle range for the new tripod universal coupling is at angle , during which the system exhibits good transmission and mechanical performance.

In volleyball, the jump serve is a fundamental and crucial skill that is one of the most commonly used serving techniques. This study aimed to examine the kinematic differences between straight line (SL) and diagonal line (DL) in volleyball jump serves by focusing on torso and attack arm joint motions. Three-dimensional coordinate data were captured using a motion capture system (200 Hz) in 14 right-handed male professional volleyball players who performed SL and DL jump serves. This result suggests that the pelvis and torso backward rotation angles during the arm-clocking phase were smaller when performing DL serves. During ball contact, the servers exhibited greater forward rotation angles of the pelvis and torso to control the upper body facing the diagonal direction of the target zone. In addition, lowering the forward tilt angle of the trunk helped the servers maintain body balance in the air and increased their wrist flexion angle, preventing the ball from flying out of bounds when performing DL. These findings highlight the importance of controlling pelvic and torso rotations in the transverse plane when adjusting for different serving lines. These insights can guide volleyball athletes and coaches in refining their serving techniques.

The overhead squat movement engages various bodily structures, and its interaction with three-dimensional elastic resistance along the kinetic chain approach remains insufficiently comprehended. This study aimed to describe the scapular kinematics during an overhead squat with the forearm in a supination exercise against an ER and clarify the therapeutic potential of this exercise on scapular rehabilitation. Using an electromagnetic tracking system, we recorded the three-dimensional shoulder kinematics of 19 male participants across seven humeral elevation positions. These positions were captured at 15-degree intervals, spanning from 30 to 120 degrees. The results indicated notable distinctions in scapular upward rotation [F(1,17)=6.09, p=0.024] and scapular posterior tilt [F(1,17)=6.04, p=0.025] between the phases. Furthermore, the interactions revealed significant differences in resistance and phases during humeral elevation for scapular upward/downward rotation [F(3.77,62.48)=7.99, p&lt;0.001], scapular internal/external rotation [F(2.98, 50.64, p&lt;0.001)], and scapular tilt [F(2.58, 43.81)=4.76, p=0.008]. The findings demonstrated that increasing resistance through elastic resistance played a pivotal role in enhancing scapular stability throughout the humerus elevation motion. This underscores the potential of the overhead squat movement as a valuable tool for both shoulder assessment and treatment.

Humans can recombine thousands of different facial expressions. This variability is due to the ability to voluntarily or involuntarily modulate emotional expressions, which, in turn, depends on the existence of two anatomically separate pathways. The Voluntary (VP) and Involuntary (IP) pathways mediate the production of posed and spontaneous facial expressions, respectively, and might also affect the left and right sides of the face differently. This is a neglected aspect in the emotion literature, where posed expressions instead of genuine expressions are often used as stimuli. Two experiments with different induction methods were specifically designed to inves-tigate the unfolding of spontaneous and posed facial expressions of happiness along the facial vertical axis (left, right) with a high-definition 3D optoelectronic system. The results showed that spontaneous expressions were distinguished from posed facial movements as revealed by relia-ble spatial and speed key kinematic patterns in both experiments. Moreover, VP activation pro-duced a lateralization effect: compared with the felt smile, the posed smile involved an initial acceleration of the left corner of the mouth, while an early deceleration of the right corner oc-curred in the second phase of the movement, after the velocity peak.

In a previous paper, the authors dealt with the current showstoppers for morphing systems and with the reasons that have inhibited their commercial applicability. In this work, the authors ex-press a critical vision of the current status of the proposed architectures and the needs that should be accomplished to make them viable for installation onboard of commercial aircraft. The distinc-tion is essential because military and civil issues and necessities are very different, and both the solutions and difficulties to be overcome are widely diverse. Yet, still remaining in the civil seg-ment, there can be other differences, depending on the size of the aircraft, from large jets to com-muters or general aviation, in turn classifiable in tourism, acrobatic, ultralight and so on, each with their own peculiarities. Therefore, the paper wants to try to trace a common technology de-nominator, if possible, and envisage a future perspective of actual applications.

First, this paper broaches the epistemological status of scientific tenets and approaches: phenomenological (descriptive only), well-founded (solid first principles, conducive to deep understanding), provisional (can be falsified if universal and verified if existential), and imaginary (fictitious entities or processes, conducive to empirically unsupported beliefs). The ΛCDM “concordance model” involves such beliefs: the emanation of the universe out of a non-physical stage, cosmic inflation (invented ad hoc), Λ (fictitious energy), and exotic dark matter. Big Bang cosmology further faces conceptual and pragmatic problems in delimiting what expands from what does not. The problems dissolve after untying inertia from space. The cosmology that emerges appears immediately compatible with the considered observations and the ‘perfect cosmological principle’. Waves and field perturbations that propagate at c expand exponentially with distance (a gravitational effect). The cosmic web of galaxies does not. Potential -Φ varies as H/(cz) instead of 1/r. Inertial forces arise from the gravitational action of the rest of the universe. Due to dilatation, they are reduced disproportionately at low accelerations. A cut-off value a₀ = 0.168 cH is deduced. This explains the successful description of galaxy rotation curves by MoND. A fully elaborated physical theory is still pending. Wider implications are briefly discussed.

Elucidating the nature of dark matter in galactic systems remains one of the important unsolved mysteries of modern cosmology. As a thought experiment, we consider a galaxy model where the light radiating outward from stellar objects produces a gravitational effect larger than Einstein's theory of gravity predicts. Using computer simulations, we observe that this assumption allows the basic rotation curve profiles observed in both dwarf and late-type spiral galaxies to be recreated. It is important to highlight that a separate mass model describing the dark matter halo is not needed or used. This toy model may also lead to insights about the nature of dark energy. If the gravitational effects in the universe are currently dominated by radiated light as this toy model may suggest, the cosmic scale factor would be closely linked to the time-history and spatial distribution of star formation and death rates. An accelerating universe may simply be a manifestation of star death rates exceeding star formation rates in the current epoch.

Natural systems of units $\{U_i\}$ need to be overhauled to include the dimensionless coupling constants $\{\upalpha_{U_i}\}$ of the natural forces. Otherwise, they cannot quantify all forces of nature in a unified manner. Thus, each force must furnish a system of units with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts $\{ G, \upalpha_G \}$, thus it cannot account for gravitation. The cosmological system discounts $\{ \slashed{h}, \upalpha_\slashed{h} \}$, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, $\upalpha_G$ is the gravitational coupling constant and $\upalpha_\slashed{h}$ is Dirac's fine-structure constant. The speed of light $c$ and the impedance of free space $Z_0$ are resistive properties imposed by the vacuum itself, thus they must be present in all systems of units. The upgraded Planck system with fundamental units $${\rm UPS} \,:=\,\{ c, Z_0, G, \upalpha_G, \slashed{h}, \upalpha_\slashed{h}, \,\dots\,\!\},$$ describes all physical scales in the universe---it is nature's system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics, and some of which have been designated as mere coincidences. Based on the UPS results, that relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed/measured physical properties are coincidental in this universe. Furthermore, we derive from first principles Koide's $K=2/3$ enigmatic constant and additional analogous quark and vector boson constants. These are formal mathematical proofs that justify a posteriori the use of geometric means in deriving the quark/boson mass ladder. This ladder allows us to also calculate the Higgs couplings to the vector bosons and the Weinberg angle in terms of only $K$.

In the present paper, based on the ideas of Algerian physicist M.E. Hassani, the generalized Hassani spatio-temporal transformations in real Hilbert space are introduced. The original transformations, introduced by M.E. Hassani, are the particular cases of the transformations, introduced in this paper. It is proven that the classes of generalized Hassani transforms do not form a group of operators in the general case. Further, using these generalized Hassani transformations as well as the theory of changeable sets and universal kinematics, the mathematically strict models of Hassani kinematics are constructed and the performance of the relativity principle in these models is discussed.

Wire-driven hyper-redundant continuum manipulators are gaining more popularity and finding more applications in industry and in minimally invasive surgery. Unlike traditional rigid link manipulators, continuum robots with a flexible backbone structure are able to work in a highly constrained workspace and in an unstructured environment. However, in spite of a possible wide range of reachability, continuum manipulators have some issues related to payload capacity, accuracy and control. Therefore, in this research, we propose a novel hyper-redundant continuum robot with a passive sliding disc mechanism to improve payload capacity and accuracy. To prove the sliding mechanism concept, we demonstrate a comparison analysis with a conventional non-sliding continuum robot arm in a payload test, a bending test and a reachability test. Moreover, with this novel design, we are proposing robot kinematics and kinetic formulation and simulation results to validate the effectiveness of the sliding disc mechanism.

Since large articulated vehicles have uncertainties in trailer articulation angle as well as dynamic complexity, it is not easy to accurately establish a reliable motion plan. In this paper, two geometric path plans constructed based on the empirical rules of driving experts are presented so that articulated vehicles can automatically perform perpendicular parking on a reverse path. By analyzing the empirical parking methods of professional drivers, these path plans were constructed by appropriately combining several standardized simple basic motions to facilitate implementation in real vehicles. In addition, path plans included appropriate complementary motions to effectively respond to uncertainties arising from articulation angles, etc. The complementary motions developed in this study are based on the results of qualitative analysis on the behavior of articulated vehicles. The usefulness of the proposed articulated vehicle parking method has been proven through hundreds of experimental tests using a 1:10 ratio model automated vehicle.

For technical or medical applications, the knowledge of the exact kinematics of the human hand is key to utilizing its capability to handle and manipulate objects and to communicate with other humans or machines. The optimal relationship between the number of measurement parameters, measurement accuracy as well as complexity, usability and cost of the measuring systems is hard to find. Biomechanic assumptions, the concepts of a biomechatronic system and the mechatronic design process as well as commercially available components are used to develop a sensorized glove. The proposed wearable can measure 14 of 15 angular values of a simplified hand model introduced in this paper. Additionally, five contact pressure values at the fingertips and inertial data of the whole hand with a degree of freedom of six are gathered. Due to the modular design and a hand size examination based on anthropometric parameters, the concept of the wearable is applicable for a large variety of hand sizes and adaptable to different use cases. Validations show a combined root-mean-square error of 0.99° to 2.38° for the measurement of all joint angles at one finger, surpassing the human perception threshold and the current state of the art in science and technology for comparable systems.

Predicting ground reaction forces (GRFs) and ground reaction moments (GRMs) through a biomechanical model-based approach offers advantages for biomechanical analysis, particularly in situations where the application of a statistical model is limited by insufficient training data. However, the current prediction method is unsuitable for clinical applications due to its long computational time. The present study developed a new optical motion capture (OMC)-based method to predict GRFs, GRMs, and joint torques. The proposed approach performed the estimation process by distributing external forces, as determined by the equation of motion, between the left and right feet based on foot deformations, thereby predicting the GRFs and GRMs without relying on machine learning or optimization techniques. We investigated the prediction accuracy during walking by comparing a conventional analysis using a force plate with the OMC results. The comparison revealed excellent or strong correlations between the prediction and measurement for all GRFs, GRMs, and lower limb joint torques. The proposed method, which provides practical estimation with low computational cost, facilitates efficient biomechanical analysis and rapid feedback of analysis results, thereby increasing its applicability for kinetics estimation in clinical settings.

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment aims at the determinations of the correction coefficients of the mathematical model. The dot grid target is measured and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analysed. Uncertainties are evaluated with implementation of the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centres, K-means clustering, etc., are the same for both two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of lateral stage of confocal microscope is meaningful and practicable.

The article presents the original derivation method of transformations for kinematics with a universal reference system. This method allows to derive transformations that meet the results of the Michelson-Morley and Kennedy-Thorndike experiments only in some frame of reference, e.g. in laboratories moving in relation to a universal frame of reference with small speeds. The obtained transformations are the basis for the derivation of the new physical theory, which has been called the Special Theory of Ether. The generalized transformations can be expressed by relative speeds (26)-(27) or by the parameter δ (v) (37)-(38). Based on conclusions of the Michelson-Morley’s and Kennedy-Thorndike’s experiments, the parameter δ (v) was determined. This allows the transformations to take a special form (81)-(82), which is consistent with experiments in which velocity of light is measured. On the basis of obtained transformations, the formulas for summing speed and relative speed were also determined. The entire article includes only original research conducted by its author.

Industrial manipulators and parallel robots are often used for tasks like drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows to completely remove the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient-descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection.

The article presents formal proof that the Special Theory of Relativity is wrong, that is, the interpretation of the mathematics on which STR is based, proposed by Einstein is incorrect. The article shows that there are infinitely many kinematics in which one-way speed of light is always equal to c. The kinematics of Special Theory of Relativity (STR) is only one of those infinitely many kinematics. It presents that mathematics on which STR kinematics is based can be interpreted differently and this leads to other conclusions on the properties of this kinematics. In this article, the whole class of linear transformations of time and coordinate was derived. Transformations were derived on the assumption that conclusions from Michelson-Morley’s and Kennedy-Thorndikea’s experiments are met for the observer from each inertial frame of reference, i.e. that the mean velocity of light in the vacuum flowing along the way back and forth is constant. It was also assumed that there is at least one inertial frame of reference, in which the velocity of light in a vacuum in each direction has the same value c, and the space is isotropic for observers from this distinguished inertial frame of reference (universal frame of reference). Derived transformations allow for building many different kinematics according to Michelson-Morley’s and Kennedy-Thorndikea’s experiments. The class of transformations derived in the study is a generalization of transformations derived in the paper [10], which consists in enabling non-zero values of parameter e(v). The idea of such a generalization derives from the person, who gave me this extended transformations class for analysis and publication.

Eight amniote genera (representing four clades) became aquatic during the Permian. The four clades were mesosaurids, tangasaurids, the neodiapsid Claudiosaurus, and the procolophonid Barasaurus. Two of eight genera survived the end-Permian mass extinction, but did not last long into the Mesozoic. A previously undescribed specimen of Claudiosaurus germaini, preserved in a lacustrine concretion from the Sakamena Formation, Madagascar, bears seventeen vertebrae that has been split along an approximate horizontal plane to reveal sections of neural canal casted in white calcite. Enlargement of the neural canal in the sacral region of this specimen of Claudiosaurus (vertebral segments 22-26) is more similar to that of Tupinambis (segments 24-28) than it is to Testudo (segments 16-23). Claudiosaurus skeletal anatomy provides evidence for swim propulsion by both hind limbs and by undulation of a dorsal-ventrally flattened tail. Evidence for the latter includes elongate transverse processes on distal tail vertebrae. Other Permian aquatic reptile genera (Mesosaurus, Hovasaurus, Barasaurus) used snake-like side-to-side tail undulation, whereas Claudiosaurus used cetacean-like up-down tail undulation in the vertical plane. It seems unlikely that any of these animals were particularly fast swimmers.

The progress in markerless technologies is bringing clinicians tools to rapidly evaluate tests such as Timed Up and Go (TUG) without compromising the time of the assessment, yet it raises questions about the potential trade-off in accuracy compared to traditional marker-based systems, suggesting that the precision of these evaluations is not yet conclusively established. The OpenCap system is an easy tool to process 3D kinematics with two iPhone cameras placed in front of the subject. Previous research has primarily focused on walking and movement towards the cameras with the subject facing the cameras (WF) and thus has been unable to disentangle the differences in the movement directions. We have compared the OpenCap system with a standard marker-based system for both walking directions. In OpenCap, we found significantly worse results capturing walking facing away from the cameras (RW). Compared to the marker-based system, our findings indicate troubles measuring kinematic parameters but provide good accuracy in measuring spatial-temporal parameters. These insights pave the way for refining markerless assessment technologies, potentially enhancing their utility in clinical settings.

The dynamic behaviour of a machine tool (MT) directly influences the machining performances. The adoption of lightweight structures may reduce the effects of undesired vibrations and increasing the workpiece quality. This paper aims to present and compare a set of hybrid materials that may be excellent candidate to fabricate the MT moving parts. The selected materials have high dynamic characteristics and capacity to damp mechanical vibrations. In this way, starting by the kinematic model of a milling machine that highlights the main critical factors, this study paper evaluates a number of prototypes made of Al Foam sandwiches (AFS), Al Corrugated sandwiches (ACS) and materials reinforced by carbon fibres (CFRP). A set of prototypes has been fabricated, represented the Z-axis ram of a commercial milling machine. The static and dynamical properties have been evaluated by using both FE simulations and experimental tests. The obtained results show that the proposed structures may be a valid alternative to the conventional materials of MT moving parts, increasing machining performances. In particular, the AFS prototype highlighted a damping coefficient that is 20 times greater than a conventional ram (e.g. steel). The CFRP structure is able to satisfy the machining requirements with a reduced weight of 48.5%, while the ACS prototype showed a good trade-off between stiffness and damping.

The term `motor control´ encompasses a wide range of mechanisms thought to be implicated in the organization of movements. Their study, like that of any other scientific field, must use specific notions to get to grips with them. This review is therefore organized along a series of notions that are frequently used in motor control, and we will discuss them with particular emphasis on neurological conditions, which may disrupt normal motor functioning. We will start with a short description of the roles of space and time, in which movements take place. Subsequently we will deal with kinematics and kinetics (dynamics) of movements. Then, we will list the inputs to motoneurons (MNs), which, in different forms, convey signals from the central nervous system (CNS) to skeletal muscles and muscle spindles, including central pattern generators (CPGs), sensory inputs and supraspinal descending fiber systems. Some helpers in movement organization will be introduced, such as internal models and neuronal network models. A relatively brief section on sensory-motor learning will follow because learning abilities are required to endow the sensory-motor system with flexibility and adaptability. The major emphasis is placed on neurological processes, which result from genetic modifications, autoimmune diseases, neurodegenerative diseases, infections in the nervous system as well as vascular and traumatic lesions. These neurological diseases lead to a variety of impairments and symptoms, particularly movement derangements including cerebellar ataxia, spasticity, and (other) movement disorders such as Parkinson’s syndromes. The conclusion is that there is no unique top controller that controls ´motor control`.

Background. Pose estimation based on deep learning has been expected to be a breakthrough method to increase the accuracy of clinical photographic evaluation and to decrease interobserver errors. The purpose is to quantify pose estimation from photography of patients with adolescent idiopathic scoliosis (AIS) using open-source software packages and determine correlations between parameters obtained by radiography and photography. Methods. We included 12 consecutive patients with AIS treated with spinal correction surgery. Photographs were taken preoperatively using a tripod-mounted camera (iPhone 13Pro) on an X-ray tube head. To assess photographic parameters obtained by photography, we defined 17 points to analyze posture and define parameters. Results. In the sagittal plane, there was a significant correlation between the radiographic trunk tilt angle and the photographic sagittal trunk tilt angle of the shoulder–hip and ear–hip. In the coronal plane, there was a significant correlation between the radiographic clavicle angle and the photographic shoulder height angle, and the radiographic C7–CSVL and the photographic coronal trunk tilt angle. Conclusions. Posture analysis by photography using popular mobile devices has clinical utility for improving and promoting the screening and early detection of AIS because it is simple, without patient exposure to X-ray radiation.

The human ankle is a complex joint, most commonly represented as talocrural and subtalar axes. It is difficult to locate and take in vivo measurements of the ankle joint. There are no instruments for patients lying on a bed or the floor; that can be used in outdoor or remote sites. We have developed a "Turmell-meter" to address these issues. We started with the study of ankle anatomy and anthropometry, then we used the product of exponentials’ formula to visualize the movements. Furthermore, we built a prototype using human proportions and statistics. For pose estimation, we used a trilateration method by applying tetrahedral geometry. Additionally, we computed the axis direction by fitting 3D circles, plotting the manifold and chart as an ankle joint model. We presented the results of simulations, a prototype comprising 45 parts, specifically designed draw-wire sensors, and electronics. Finally, we tested the device by capturing positions and fitting them into the bi-axial ankle model as a Riemannian manifold. The Turmell-meter is intended to be a hardware platform for human ankle joint axis estimation, it is adjustable and has an easy setup. The proposed model has the properties of a chart in a geometric manifold, we provided the details

A particular challenge in the conceptual design of direct-from orbit delivery systems is the seemingly well-known kinematics retain fallacies whose efficacies are reduced over great distances. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. One of two ubiquitous sequences of three rotations used to construct the DCM involves first a rotation around the inertial z-axis, then intermediate y-axis, then finally about the body’s x-axis; a sequence commonly called the “aerospace sequence” or the a “3-2-1 rotation sequence”. The second ubiquitous sequence is the so-called “orbital sequence” or “3-1-3 rotation sequence” with rotations about the inertial z axis first, then about the intermediate x-axis, then finally about the body z-axis. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Six degrees of freedom of vehicle motion were simulated starting in orbit with a given thrust and commanded maneuver. The simulation performs all twelve possible rotation sequences (transforming inertial coordinates to body coordinates) with comparison by computational burden and error representing rotations about body axes (roll, pitch, and yaw respectively). Simulation precision is validated using the quaternion normalization condition indicating near machine precision (0.9\times{10}^{-15}) and reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the so-called 321 rotation and a 99.84% increase over the so-called 313 rotation.

The study of emission, propagation, and reflection of balls in Newtonian mechanics, employing the laws of conservation of momentum and energy when the mass of balls converges to zero, concludes that the kinematics of light is like that of massless balls. The kinematics of light explains why light speed is the constant in each inertial frame in which the light source and reflective mirror are at rest, why the laws of physics have the same form in each inertial frame, and why any experiment in an inertial frame cannot prove the motion of that the other inertial frame. The theory of special relativity misapplies symmetry observed in phenomena to two inertial frames; therefore, it duplicates a physics phenomenon from one inertial frame, considered stationary, into another. Moreover, Lorentz’s transformation offers light speed at the constant in the moving and opposite direction of the inertial frame but is variable in any other direction. Therefore, the theory of special relativity rejects itself with these unacceptable conclusions.