Search results for: direct and inverse kinematics

Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

Abstract:

This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: kinematics, degree of freedom, optimization, robot manipulator

Procedia PDF Downloads 467

Authors: J. G. Batista, L. J. de Bessa Neto, M. A. F. B. Lima, J. R. Leite, J. I. de Andrade Nunes

Abstract:

The robot manipulator is an equipment that stands out for two reasons: Firstly because of its characteristics of movement and reprogramming, resembling the arm; secondly, by adding several areas of knowledge of science and engineering. The present work shows the development of the prototype of a robotic manipulator driven by a Programmable Logic Controller (PLC), having two degrees of freedom, which allows the movement and displacement of mechanical parts, tools, and objects in general of small size, through an electronic system. The aim is to study direct and inverse kinematics of the robotic manipulator to describe the translation and rotation between two adjacent links of the robot through the Denavit-Hartenberg parameters. Currently, due to the many resources that microcomputer systems offer us, robotics is going through a period of continuous growth that will allow, in a short time, the development of intelligent robots with the capacity to perform operations that require flexibility, speed and precision.

Keywords: Denavit-Hartenberg, direct and inverse kinematics, microcontrollers, robotic manipulator

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Authors: Adel Mohsen

Abstract:

A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale

Abstract:

This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.

Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories

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Authors: Atilla Bayram

Abstract:

This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: computed force method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss

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Authors: V. K. Banga

Abstract:

Robots are now playing a very promising role in industries. Robots are commonly used in applications in repeated operations or where operation by human is either risky or not feasible. In most of the industrial applications, robotic arm manipulators are widely used. Robotic arm manipulator with two link or three link structures is commonly used due to their low degrees-of-freedom (DOF) movement. As the DOF of robotic arm increased, complexity increases. Instrumentation involved with robotics plays very important role in order to interact with outer environment. In this work, optimal control for movement of various DOFs of robotic arm using various soft computing techniques has been presented. We have discussed about different robotic structures having various DOF robotics arm movement. Further stress is on kinematics of the arm structures i.e. forward kinematics and inverse kinematics. Trajectory planning of robotic arms using soft computing techniques is demonstrating the flexibility of this technique. The performance is optimized for all possible input values and results in optimized movement as resultant output. In conclusion, soft computing has been playing very important role for achieving optimized movement of robotic arm. It also requires very limited knowledge of the system to implement soft computing techniques.

Keywords: artificial intelligence, kinematics, robotic arm, neural networks, fuzzy logic

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study aimed at developing an inverse heat transfer approach for predicting the time-varying freezing front and the temperature distribution of tumors during cryosurgery. Using a temperature probe pressed against the layer of tumor, the inverse approach is able to predict simultaneously the metabolic heat generation and the blood perfusion rate of the tumor. Once these parameters are predicted, the temperature-field and time-varying freezing fronts are determined with the direct model. The direct model rests on one-dimensional Pennes bioheat equation. The phase change problem is handled with the enthalpy method. The Levenberg-Marquardt Method (LMM) combined to the Broyden Method (BM) is used to solve the inverse model. The effect (a) of the thermal properties of the diseased tissues; (b) of the initial guesses for the unknown thermal properties; (c) of the data capture frequency; and (d) of the noise on the recorded temperatures is examined. It is shown that the proposed inverse approach remains accurate for all the cases investigated.

Keywords: cryosurgery, inverse heat transfer, Levenberg-Marquardt method, thermal properties, Pennes model, enthalpy method

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Tarek El-Derini, Ahmed El-Shenawy

Abstract:

This paper presents the hardware implemented and validation for a special system to assist the unprofessional users of car with back trailers. The system consists of two platforms; the front car platform (C) and the trailer platform (T). The main objective is to control the Trailer platform using the actuators found in the front platform (c). The mobility of the platform (C) is investigated and inverse and forward kinematics model is obtained for both platforms (C) and (T). The system is simulated using Matlab M-file and the simulation examples results illustrated the system performance. The system is constructed with a hardware setup for the front and trailer platform. The hardware experimental results and the simulated examples outputs showed the validation of the hardware setup.

Keywords: kinematics, modeling, robot, MATLAB

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

Abstract:

Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Y. T. Tsai, Jin H. Huang

Abstract:

The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

Keywords: inverse problem, cone effective area, loudspeaker, nonlinear conjugate gradient method

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Authors: Faisal Yousafzai, Murad-ul-Islam Khan, Kar Ping Shum

Abstract:

We introduce the concept of partially inverse AG**-groupoids which is almost parallel to the concepts of E-inversive semigroups and E-inversive E-semigroups. Some characterization problems are provided on partially inverse AG**-groupoids. We give necessary and sufficient conditions for a partially inverse AG**-subgroupoid E to be a rectangular band. Furthermore, we determine the unitary congruence η on a partially inverse AG**-groupoid and show that each partially inverse AG**-groupoid possesses an idempotent separating congruence μ. We also study anti-separative commutative image of a locally associative AG**-groupoid. Finally, we give the concept of completely N-inverse AG**-groupoid and characterize a maximum idempotent separating congruence.

Keywords: AG**-groupoids, congruences, inverses, rectangular band

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Authors: Yu Menshikov

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In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solution are analyzed. Several methods for remove the influence of uncontrollable inaccuracy have been suggested.

Keywords: inverse problems, filtration, uncontrollable inaccuracy

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Authors: Sangbaek Park, Seungju Lee, Soo-Won Chae

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Unstable shoes are known to strengthen lower extremity muscles and improve gait ability and to change the user’s gait pattern. The change in gait pattern affects human body enormously because the walking is repetitive and steady locomotion in daily life. It is possible to estimate the joint motion including joint moment, force and inertia effect using kinematic and kinetic analysis. However, the change of internal stress at the articular cartilage has not been possible to estimate. The purpose of this research is to evaluate the internal stress of human body during gait with unstable shoes. In this study, FE analysis was combined with motion capture experiment to obtain the boundary condition and loading condition during walking. Motion capture experiments were performed with a participant during walking with normal shoes and with unstable shoes. Inverse kinematics and inverse kinetic analysis was performed with OpenSim. The joint angle and muscle forces were estimated as results of inverse kinematics and kinetics analysis. A detailed finite element (FE) lower extremity model was constructed. The joint coordinate system was added to the FE model and the joint coordinate system was coincided with OpenSim model’s coordinate system. Finally, the joint angles at each phase of gait were used to transform the FE model’s posture according to actual posture from motion capture. The FE model was transformed into the postures of three major phases (1st peak of ground reaction force, mid stance and 2nd peak of ground reaction force). The direction and magnitude of muscle force were estimated by OpenSim and were applied to the FE model’s attachment point of each muscle. Then FE analysis was performed to compare the stress at knee cartilage during gait with normal shoes and unstable shoes.

Keywords: finite element analysis, gait analysis, human model, motion capture

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: D. Maneetham, L. Sivhour

Abstract:

Robotic arm manipulators are widely used to accomplish many kinds of tasks. SCORBOT-ER 4u is a 5-degree of freedom (DOF) vertical articulated educational robotic arm, and all joints are revolute. It is specifically designed to perform pick and place task with its gripper. The pick and place task consists of consideration of the end effector coordinate of the robotic arm and the desired position coordinate in its workspace. This paper describes about forward kinematics modeling and analysis of the robotic end effector motion through joint space. The kinematics problems are defined by the transformation from the Cartesian space to the joint space. Denavit-Hartenberg (D-H) model is used in order to model the robotic links and joints with 4x4 homogeneous matrix. The forward kinematics model is also developed and simulated in MATLAB. The mathematical model is validated by using robotic toolbox in MATLAB. By using this method, it may be applicable to get the end effector coordinate of this robotic arm and other similar types to this arm. The software development of SCORBOT-ER 4u is also described here. PC-and EtherCAT based control technology from BECKHOFF is used to control the arm to express the pick and place task.

Keywords: forward kinematics, D-H model, robotic toolbox, PC- and EtherCAT-based control

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Authors: Seungwon Baek, Haeseok Jeong, Haehyun Lee, Woojin Park

Abstract:

The main purpose of this study was to compare obese people to the non-obese in terms of joint kinematics in lower-limb body. The height of chairs was also considered as a design factor. Obese people had a difficulty in sit-to-stand (STS) tasks compared to the non-obese people. High chair heights can make STS task easy and it helps the obese to be more comfortable with STS task in particular. Subjects were instructed to wear inertial measurement unit (IMU) sensors. They perform STS task using chairs of different heights. Joint kinematics and subjective ratings of discomfort were measured. Knee angles of the obese group were greater than that of the non-obese group in normal type. No significant difference in joint kinematics was found in high chair. Interaction effect was found between obesity and height of chair. The results verified the previous research that had suggested a biomechanical model of STS movement. The results can be applied to occupational design for the obese.

Keywords: biomechanics, electromyography, joint kinematics, obesity, sitting, sit-to-stand

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Authors: Abdon Choque-Rivero

Abstract:

The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice when the coefficients are real valued. The inverse problem of recovery of the coefficients from various data sets containing the so-called transmission eigenvalues is analyzed. The Marchenko method is utilized to solve the corresponding inverse problem.

Keywords: inverse scattering, discrete system, transmission eigenvalues, Marchenko method

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Djamel Remache, Serge Dos Santos, Michael Cliez, Michel Gratton, Patrick Chabrand, Jean-Marie Rossi, Jean-Louis Milan

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Skin tissue is an inhomogeneous and anisotropic material. Uniaxial tensile testing is one of the primary testing techniques for the mechanical characterization of skin at large scales. In order to predict the mechanical behavior of materials, the direct or inverse analytical approaches are often used. However, in case of an inhomogeneous and anisotropic material as skin tissue, analytical approaches are not able to provide solutions. The numerical simulation is thus necessary. In this work, the uniaxial tensile test and the FEM (finite element method) based inverse method were used to identify the anisotropic mechanical properties of porcine skin tissue. The uniaxial tensile experiments were performed using Instron 8800 tensile machine®. The uniaxial tensile test was simulated with FEM, and then the inverse optimization approach (or the inverse calibration) was used for the identification of mechanical properties of the samples. Experimentally results were compared to finite element solutions. The results showed that the finite element model predictions of the mechanical behavior of the tested skin samples were well correlated with experimental results.

Keywords: mechanical skin tissue behavior, uniaxial tensile test, finite element analysis, inverse optimization approach

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Authors: Soujanya Pasumarthi

Abstract:

Inverse docking is a relatively new technique that has been used to identify potential receptor targets of small molecules. Our docking software package MDock is well suited for such an application as it is both computationally efficient, yet simultaneously shows adequate results in binding affinity predictions and enrichment tests. As a validation study, we present the first stage results of an inverse-docking study which seeks to identify potential direct targets of PRIMA-1. PRIMA-1 is well known for its ability to restore mutant p53's tumor suppressor function, leading to apoptosis in several types of cancer cells. For this reason, we believe that potential direct targets of PRIMA-1 identified in silico should be experimentally screened for their ability to inhibitcancer cell growth. The highest-ranked human protein of our PRIMA-1 docking results is oxidosqualene cyclase (OSC), which is part of the cholesterol synthetic pathway. The results of two followup experiments which treat OSC as a possible anti-cancer target are promising. We show that both PRIMA-1 and Ro 48-8071, a known potent OSC inhibitor, significantly reduce theviability of BT-474 breast cancer cells relative to normal mammary cells. In addition, like PRIMA-1, we find that Ro 48-8071 results in increased binding of mutant p53 to DNA in BT- 474cells (which highly express p53). For the first time, Ro 48-8071 is shown as a potent agent in killing human breast cancer cells. The potential of OSC as a new target for developing anticancer therapies is worth further investigation.

Keywords: inverse docking, in silico screening, protein-ligand interactions, molecular docking

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Authors: Ella Bowles, Alexandra Hughes, Clara Karton, T. Blaine Hoshizaki

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As a fast-paced and physical game, body contact is an inevitable component in professional men's ice hockey. Despite efforts and advancements in material engineering to create safer equipment, brain trauma continues to persist and burden hockey players. Head and body contact occur in many ways and vary in terms of impact characteristics including the inbound velocity, force, direction, location, and compliance of the surfaces, which in turn influence head dynamics and brain injury outcomes including concussions. It has been reported that glass and board impacts account for approximately 40% of diagnosed concussions. This type of impact often involves the body (i.e., shoulder) contacting the surface prior to head contact, which may influence the head’s dynamic response by interrupting the head’s initial trajectory.  However, the effect of body-first contact during head impacts is not well understood. The purpose of this research is to compare the head’s kinematic response during direct and non-direct (body-first) head-to-glass impacts representative of ice hockey events. Analysis was performed under varying impact conditions of neck stiffness and impact velocity as they have been shown to influence the resulting head dynamics. Data was collected by video analysis of the 2016-17 NHL season and event reconstructions were performed using a Hybrid III headform, an unbiased neck with tension springs (uONSA), and a high-speed impactor. Direct and non-direct impacts were analyzed at three common velocities (3.0, 5.0, 7.0 m/s), and three neck stiffnesses representing low (25%), medium (75%), and high (100%) contraction. Reconstructions representing non-direct head-to-glass impacts used a shoulder bumper as the first point of contact followed by the head’s contact with the glass. The same method and equipment were used to replicate the direct head impacts, where the head made initial contact with the glass. The dynamic response of the head, specifically the peak resultant linear and rotational acceleration, was collected for each impact and compared between direct and non-direct contact under each condition. The results show that non-direct impacts created an initial head acceleration resulting from shoulder contact, preceding a secondary acceleration response from head contact with the glass. Compared to direct head impacts, non-direct impacts consistently resulted in lower linear and rotational acceleration of the head under all neck stiffness and velocity conditions with an average decrease of 32.56 g and 689.33 rad/s2. However, the linear acceleration produced from shoulder contact in non-direct impacts resulted in a higher response compared to direct impacts with low neck stiffness at 5 m/s (55.2g and 41.2g, respectively) and 7 m/s (76.1g and 73.4g, respectively), and medium neck stiffness at 5 m/s (55.4g and 43.9g, respectively ) and 7 m/s (94.4g and 69.5g, respectively. These findings show that non-direct impacts produce complex scenarios that are further influenced by interaction with neck stiffness and velocity. This research provides an understanding of the fundamentals of body-first impacts. With this basis, an understanding of the implications of body-first head-impacts to better distinguish trauma based on events, and adapt protocols, evaluations, technologies, and equipment accordingly.

Keywords: body-first, concussion, direct, hockey, kinematics

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Authors: Nafiseh Ebrahimi, Amir Jafari

Abstract:

The study of humanoid character is of great interest to researchers in the field of robotics and biomechanics. One might want to know the forces and torques required to move a limb from an initial position to the desired destination position. Inverse dynamics is a helpful method to compute the force and torques for an articulated body limb. It enables us to know the joint torques required to rotate a link between two positions. Our goal in this study was to control a human-like articulated manipulator for a specific task of path tracking. For this purpose, the human arm was modeled with a three-link planar manipulator activated by Hill muscle model. Applying a proportional controller, values of force and torques applied to the joints were calculated by inverse dynamics, and then joints and muscle forces trajectories were computed and presented. To be more accurate to say, the kinematics of the muscle-joint space was formulated by which we defined the relationship between the muscle lengths and the geometry of the links and joints. Secondary, the kinematic of the links was introduced to calculate the position of the end-effector in terms of geometry. Then, we considered the modeling of Hill muscle dynamics, and after calculation of joint torques, finally, we applied them to the dynamics of the three-link manipulator obtained from the inverse dynamics to calculate the joint states, find and control the location of manipulator’s end-effector. The results show that the human arm model was successfully controlled to take the designated path of an ellipse precisely.

Keywords: arm manipulator, hill muscle model, six-muscle model, three-link lodel

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Authors: Saleh Kasiri Bidhendi, Shiva Tashakori

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With the increasing application of six-wheel robots in various industries, including agriculture and environmental monitoring, there is a growing demand for efficient and reliable control systems that can improve manoeuvrability and at the same time reduce energy consumption. Moving on uneven terrains, various factors such as obstacles or soil heterogeneity can cause the robot to slip. There is limited research addressing this issue. Although the robot is supposed to track a predetermined path, sudden lateral deviation necessitates path planning. To further address this issue, explicit steering is added by activating actuators on steerable wheels, while the SMC controller still commands differential traction forces on all wheels. This integration improves energy efficiency and obstacle traversability while maintaining the merits of skid-steering, such as tight turning manoeuvrability. However, achieving the desired steer angles presents certain challenges. Inverse kinematics was initially employed to achieve the needed steering angles from the desired position, but this approach led to excessive steering without yawing the body. Switching to desired velocity values instead of position limited over-steering but caused zero lateral velocity on horizontal paths, which was problematic for unforeseen skidding. To overcome this, a proportional controller has been employed, using lateral error as its input and providing a proportional yaw angle as output, the P-controller contributes to modifying the steering angles. The controller's robustness has been verified through sensitivity analyses under critical speeds and turning radius conditions. Our findings offer valuable insights into designing more efficient steering controls for rocker-bogie mechanisms in challenging situations, emphasizing the importance of reducing energy¬ consumption.

Keywords: six-wheel robots, inverse kinematics, integrated steering, path following, manoeuvrability, energy efficiency, uneven terrains

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

Abstract:

A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Ahmad Moussavi

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In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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Authors: Saeed Ilbeigi, Bart Van Gheluwe

Abstract:

The purpose of this study was to identify the three-dimensional kinematics of the sprint start during the start phase of the sprint. The purpose of this study was to identify the three-dimensional kinematics of the sprint start during the start phase of the sprint. Moreover, the effect of anthropometrical factors such as skeletal muscle mass, thigh girth, and calf girth also were considered on the kinematics of the sprint start. Among all young sprinters involved in the national Belgium league, sixty sprinters (boys: 14.7 ± 1.8 years and girls: 14.8±1.5 years) were randomly selected. The kinematics data of the sprint start were collected with a Vicon® 620 motion analysis system equipped with 12 infrared cameras running at 250 Hz and running the Vicon Data Station software. For statistical analysis, T-tests and ANOVA׳s with Scheffé post hoc test were used and the significant level was set as p≤0.05. The results showed that the angular positions of the lower joints of the young sprinters in the set position were comparable with adult figures from literature, however, with a greater range of joint extension. The most significant difference between boys and girls was found in the set position, where the boys presented a more dorsiflexed ankle. No further gender effect was observed during the leaving the blocks and contact phase. The sprinters with a higher age, skeletal muscle mass, thigh girth, and calf girth displayed a better angular position of the lower joints (e.g. ankle, knee, hip) in the set position, a more optimal angular position for the foot and knee for absorbing impact forces at foot contact and finally a higher range of flexion/extension motion to produce force and power when leaving the blocks.

Keywords: anthropometry, kinematics, sprint start, young elite sprinters

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Authors: Isobel M. Thompson, Dorian Audot, Dominic Hudson, Martin Warner, Joseph Banks

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Underwater fly kick is an essential skill in swimming, which can have a considerable impact upon overall race performance in competition, especially in sprint events. Reduced wave drags acting upon the body under the surface means that the underwater fly kick will potentially be the fastest the swimmer is travelling throughout the race. It is therefore critical to understand fly kicking techniques and determining biomechanical factors involved in the performance. Most previous studies assessing fly kick kinematics have focused on two-dimensional analysis; therefore, the three-dimensional elements of the underwater fly kick techniques are not well understood. Those studies that have investigated fly kicking techniques using three-dimensional methodologies have not reported full three-dimensional kinematics for the techniques observed, choosing to focus on one or two joints. There has not been a direct comparison completed on the results obtained using two-dimensional and three-dimensional analysis, and how these different approaches might affect the interpretation of subsequent results. The aim of this research is to quantify the differences in kinematics observed in underwater fly kicks obtained from both two and three-dimensional analyses of the same test conditions. In order to achieve this, a six-camera underwater Qualisys system was used to develop an experimental methodology suitable for assessing the kinematics of swimmer’s starts and turns. The cameras, capturing at a frequency of 100Hz, were arranged along the side of the pool spaced equally up to 20m creating a capture volume of 7m x 2m x 1.5m. Within the measurement volume, error levels were estimated at 0.8%. Prior to pool trials, participants completed a landside calibration in order to define joint center locations, as certain markers became occluded once the swimmer assumed the underwater fly kick position in the pool. Thirty-four reflective markers were placed on key anatomical landmarks, 9 of which were then removed for the pool-based trials. The fly-kick swimming conditions included in the analysis are as follows: maximum effort prone, 100m pace prone, 200m pace prone, 400m pace prone, and maximum pace supine. All trials were completed from a push start to 15m to ensure consistent kick cycles were captured. Both two-dimensional and three-dimensional kinematics are calculated from joint locations, and the results are compared. Key variables reported include kick frequency and kick amplitude, as well as full angular kinematics of the lower body. Key differences in these variables obtained from two-dimensional and three-dimensional analysis are identified. Internal rotation (up to 15º) and external rotation (up to -28º) were observed using three-dimensional methods. Abduction (5º) and adduction (15º) were also reported. These motions are not observed in the two-dimensional analysis. Results also give an indication of different techniques adopted by swimmers at various paces and orientations. The results of this research provide evidence of the strengths of both two dimensional and three dimensional motion capture methods in underwater fly kick, highlighting limitations which could affect the interpretation of results from both methods.

Keywords: swimming, underwater fly kick, performance, motion capture

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Authors: Jianhua Zhou, Yuwen Zhang

Abstract:

A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.

Keywords: conduction, inverse problems, conjugated gradient method, laser

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Authors: Balgaisha Mukanova, Natalya Glazyrina, Sergey Glazyrin

Abstract:

The formulated problem of optimization of the technological process of water treatment for thermal power plants is considered in this article. The problem is of multiparametric nature. To optimize the process, namely, reduce the amount of waste water, a new technology was developed to reuse such water. A mathematical model of the technology of wastewater reuse was developed. Optimization parameters were determined. The model consists of a material balance equation, an equation describing the kinetics of ion exchange for the non-equilibrium case and an equation for the ion exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion exchange. A direct problem of calculating the impurity concentration at the outlet of the water treatment plant was numerically solved. The direct problem was approximated by an implicit point-to-point computation difference scheme. The inverse problem was formulated as relates to determination of the parameters of the mathematical model of the water treatment plant operating in non-equilibrium conditions. The formulated inverse problem was solved. Following the results of calculation the time of start of the filter regeneration process was determined, as well as the period of regeneration process and the amount of regeneration and wash water. Multi-parameter optimization of water treatment process for thermal power plants allowed decreasing the amount of wastewater by 15%.

Keywords: direct problem, multiparametric optimization, optimization parameters, water treatment

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