In this paper, the obstacles to solve three-dimensional motion problems using two-dimensional Newton-Euler analyses are presented and examined. The three-dimensional motion analysis method used in industry and medicine is based on a robotic approach and is based on the mathematics of matrix analysis. This approach requires a deep understanding of matrix mathematics and controlling the accuracy of its performance at each stage, which has its own complexities. The aim of this paper is to apply two-dimensional methods for analyzing problems that are inherently three-dimensional and require spatial geometric vector analyses. The main method proposed in this paper to solve the major problem of three-dimensional analyses is to use a two-dimensional image of the member length instead of using the full length of the member in calculations, especially when calculating the moment of inertia of three-dimensional objects on a plane. This research is a type of mathematical analysis and proves the similarity of the results between two-dimensional and three-dimensional approaches in the analysis of three-dimensional problems. The analysis tool in this study is the INVERSE DYNAMICS method. The assumption of dynamic determinism governs the analysis, that is, for each unknown variable, an equation between the variables in the problem is necessary. This is important in most problems assuming that the spatiotemporal data of the movement of each member and at least one end or joint in the mechanism are known. The results obtained in this paper show that it is possible to calculate the moment of inertia of three-dimensional objects moving in space using two-dimensional kinematic analyses. The advantages and disadvantages of both three-dimensional and two-dimensional methods are mentioned in this research. The use of two-dimensional methods in the analysis of three-dimensional objects moving in space provides a better understanding of the movement and monitoring the results. Also, with this approach, researchers can monitor the accuracy of the results and the spatiotemporal trend of kinematic variables and prevent and avoid computational errors and mathematical modeling in describing three-dimensional movements.

In this paper, an online neural INVERSE controller is used to deal with actuator faults. In such a way that the INVERSE of the nonlinear induction furnace system (IFS) is used as a fault-tolerant controller (FTC) so that it can cover the fault of the actuator. The design is such that an online neural network is used to model the NIFC, the three-layer neural network is ‎converted into a four-layer RBF neural network, and the last ‎layer is the ‎nonlinear IFS, and this layer is It is unchangeable and the ‎controller and the system are connected and finally ‎form a four-layer neural network. So, an intelligent INVERSE ‎model of the IFS is used as  FTC to cover the actuator fault of ‎the ‎nonlinear IFC. This controller design is done in two ways: in the ‎first part, five inputs are used for training the neural network, ‎one of which is the neural network training error, but in the ‎second part, in addition to the five inputs of the first part, the ‎derivative of the error is used. And the error integral has also ‎been used in neural network training and the advantage of the ‎second plan is to reduce overshoot. Finally, a fault actuator is ‎applied to the ‎nonlinear IFS in the 10th to the 30th second,  ‎despite the presence of the intelligent FTC, this defect is ‎covered in less than one second, and the system continues to ‎function normally despite the operator's defect in this interval ‎of time.‎

Forecasting the forces of the linear actuators with the aim of designating proportionate motors and or structural design of the motion system in flight simulators is of the considerable importance. In this paper, INVERSE dynamic analysis of the 6 degrees of freedom Stewart – Gough motion system, using Newton-Euler formulation approach consisting linear actuator components and moving platform DYNAMICS with application prospects to flight simulators is illustrated. The developed INVERSE DYNAMICS simulation software of the motion system is provided by the output results of the general nonlinear INVERSE kinematical based motion cueing system for computing the static and dynamic actuating forces in typical surge – pitch maneuver. Compared simulation results clearly indicate a significant disproportionate difference between the static and dynamic loads for the prototypical maneuver. Thereupon true attention on predicting the dynamic forces associated with the proposed INVERSE kinematics in structural design and or designating linear actuator is emphasized.

The main purpose of this paper is to derive the INVERSE dynamic equation of motion of n-rigid robotic manipulator that mounted on a mobile platform, systematically. To avoid the Lagrange multipliers associated with the nonholonomic constraints the approach of Gibbs-Appell formulation in recursive form is adopted. For modeling the system completely and precisely the dynamic interactions between the manipulator and the mobile platform as well as both nonholonomic constraints associated with the no-slipping and the no-skidding conditions are also included. In order to reduce the computational complexity, all the mathematical operations are done by only 3×3 and 3×1 matrices. Also, all dynamic characteristics of a link are expressed in the same link local coordinate system. Finally, a computational simulation for a manipulator with five revolute joints that mounted on a mobile platform is presented to show the ability of this algorithm in generating the equation of motion of mobile robotic manipulators with high degree of freedom.

Considering frictional, inertial and machining forces, the authors have presented an enhanced analysis of a hexapod table as used in milling machines. The Newton-Euler analysis of hexapod’s components has been implemented by a simulation program developed by the authors in MATLAB environment and the results have been verified by those of others. The impact of various loads involved in machining operation carried out on a milling machine equipped with hexapod table has been presented in the paper. This provides a potential machine tool designer with guidelines on the importance of these loads and helps him give appropriate weights to them.

Background: Competitive sailing requires efforts pertinent to physiological limitations and coordination between different parts of the body. Such coordination depends on the torques applied by muscles to the joints. Objective: This study aims to simulate the motion and provide a control law for the joint torques in order to track the desired motion paths. Material and Methods: In this analytical study, an INVERSE DYNAMICS based control is employed in order to simulate the motion by tracking the desired movement trajectories. First, the DYNAMICS equations are obtained using Lagrange method for 5 degrees of freedom (5 DOF) model. In the following, a robust control scheme with INVERSE DYNAMICS method based on the Proportional-Integral-Derivative (PID) approach is employed to track the desired joint angles obtained from the experiment. Results: The simulation results demonstrate the performance of the proposed control method. Low settling times are achieved for the entire joint, which is appropriate in comparison with the time period of each cycle (3. 75 s). Also, the maximum torques required to be applied to the joints are in physiological range. Conclusion: This study provided an appropriate model for the analysis of human movement in rowing sport. The model can also be cited in terms of basic biological theories in addition to practical computational uses in biomechanical engineering. Accordingly, the generated control signals can help to improve the interactive body movements during paddling and in designing robotic arms for automatic rowing.

Inspired by the muscle arrangement of the octopus and skeleton of the snakes, a wire‐driven serpentine robot arm has been simulated and constructed in this article. The robot links which are connected via flexible beam act as the snake backbone. Instead of using motors at each joint, four sets of wire are employed as octopus muscles to drive the robot arm. For the spatial INVERSE kinematics, after determining the generalized coordinates of the system, governing algebraic equations of the system including constraint equations of the joints and cables and favorable movements have been determined. For displacement analysis, these equations have been solved using the Newton‐Raphson method. Using this method robot workspace has also been determined. For the INVERSE DYNAMICS of the robot, cables tension force has been considered as external forces. Using Embedding technique with specified constraint matrix, mass matrix and acceleration vectors that are determined from INVERSE kinematics, cables tension force and torque of motors are specified. To validate the snake robot model, a prototype has been built and programmed for some circular and arcuate routs. Travelled pass by end effector have been obtained. Comparing the results with the desired path, accuracy of the designed robot has been investigated.

In many infeasible linear programs it is important to construct it to a feasible problem with a minimum parameters changing corresponding to a given nonnegative vector. This paper defines a new INVERSE problem, called “INVERSE feasible problem”. For a given infeasible polyhedron and an n-vector x0 a minimum perturbation on the parameters can be applied and then a feasible polyhedron is concluded.