Newton-Euler Equations Research Articles

Bond graph modeling and multi-body dynamics of a twin rotor system

The dynamics of a twin-rotor multi-input multi-output system, which is similar to that of a helicopter in many ways, is highly nonlinear in nature. In this article, a detailed dynamical model of twin-rotor multi-input multi-output system is developed and simulated by using bond graph approach. Nonlinear nature of the interface gain, thrust, and drag forces, and the stiffness of cable attached to support column joint are estimated. The rotors are modeled through the Newton–Euler equations. The bond graph model is created by using the generic sub-models and the same set of sub-models can be assembled differently to model many other similar systems such as tricopters and quadcopters. Inertial forces and moments, rotor thrust and drag forces, active and reactive motor torques, and direct current motor dynamics are considered in the model. The responses from the model are compared with the test data for validation.

Establishment and Simulation of Twelve-Degree-of-Freedom Model for UAV Parachute Recovery System

In the UAV parachute recovery process, the UAV and the parachute have always been in the state of dynamic balance, so it is difficult to deal with the constraint between them. In order to solve this problem, the UAV parachute recovery system was divided into three parts:the parachute, riser and UAV. The extension length of riser was obtained by the velocity relationships of the riser connection points. The riser tension was obtained by the product of the elastic coefficient and the extension length of the riser. And it was applied to the parachute and UAV systems respectively. Finally, based on the Newton-Euler equation, the 12-DOF model of UAV parachute recovery system was established, in which the unsteady aerodynamic model of the UAV from the forward flight to the steady descents was established based on the ONERA equation. The simulation and test results shows:the 12-DOF model is consistent with the results of the experimental data, which verifies the accuracy of the 12-DOF model. The 12-DOF model is more accurate than the past 6-DOF model. This model established in this paper can provide reference for the selection of parachute in the UAV parachute recovery system and the determination of the landing point of the UAV.

Effect of Eccentric Mass Distribution on the Motion of Spherical Particles in Shear Flows

Abstract A particle-resolved direct numerical simulation is performed on the motion of spherical particles with an eccentric internal mass distribution in lateral linear shear flow, which is oriented in the vertical direction and sheared in a horizontal direction. We examine the effect of mass eccentricity on the two-way interactions of particles with both laminar and turbulent shear flows. A spherical shell/hollow particle with an inner spherical core is focused on as a typical example of mass eccentric particles. The Navier–Stokes equations and the Newton–Euler equations are solved for the fluid phase and the particles, respectively. An immersed boundary method is adopted to represent the shell particle. The Newton–Euler equations are solved using the body-fixed coordinate system and four quaternion parameters, considering the deviation of the center of mass from the center of the spherical shell particle. Simulations are performed at a relatively low particle volume fraction of 0.4%. In turbulent flows, the Taylor-microscale Reynolds number reached about 49 at the end of the simulations. Numerical results show that shear-induced particle rotation is suppressed by the torque due to gravity. It is found that the lateral migration of mass eccentric particles becomes less vigorous in both laminar and turbulent flows since the effect of the Magnus lift force is also weakened for mass eccentric particles. It is also found that the evolution of fluid kinetic energy is significantly affected by the mass eccentricity of particles in laminar flows.

Interface-resolved direct numerical simulations of sediment transport in a turbulent oscillatory boundary layer

The flow within an oscillatory boundary layer, which approximates the flow generated by propagating sea waves of small amplitude close to the bottom, is simulated numerically by integrating Navier-Stokes and continuity equations. The bottom is made up of spherical particles, free to move, which mimic sediment grains. The approach allows to fully-resolve the flow around the particles and to evaluate the forces and torques that the fluid exerts on their surface. Then, the dynamics of sediments is explicitly computed by means of Newton-Euler equations. For the smallest value of the flow Reynolds number presently simulated, the flow regime turns out to fall in the intermittently turbulent regime such that turbulence appears when the free stream velocity is close to its largest values but the flow recovers a laminar like behaviour during the remaining phases of the cycle. For the largest value of the Reynolds number turbulence is significant almost during the whole flow cycle. The evaluation of the sediment transport rate allows to estimate the reliability of the empirical predictors commonly used to estimate the amount of sediments transported by the sea waves. For large values of the Shields parameter, the sediment flow rate during the accelerating phases does not differ from that observed during the decelerating phases. However, for relatively small values of the Shields parameter, the amount of moving particles depends not only on the bottom shear stress but also on flow acceleration. Moreover, the numerical results provide information on the role that turbulent eddies have on sediment dynamics.

Interaction of rigid body motion and rarefied gas dynamics based on the BGK model

In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK model is solved by the semi-Lagrangian method suggested by Russo &amp; Filbet ^{[<span class="xref"><a href="#b22" ref-type="bibr">22</a></span>]}. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.

Dynamic Modeling and Residual Vibration Suppression of the Redundantly-Actuated Cable Driving Parallel Manipulator

An improved input shaping (IS) scheme was proposed for the redundantly actuated cable driving parallel robots (CDPRs) to suppress the residual vibration (RV). To make the design of the RV suppression convenient, the flexible displacements of the moving platform were taken as the generalized coordinates considering the axial deformation of cables, and rigid-flexible dynamic model of generalized redundantly actuated CDPRs was established with the Newton-Euler equation and the Newton's law. Then to cope with time-variant vibration frequencies of the CDPRs due to the variable lengths of cables, the technique that combined the one- to three-order zero vibration (ZV) IS with the particle swarm optimization (PSO) and the controller was proposed to suppress the RV. At last, to validate the effectiveness the proposed method, the simulations were carried out in a redundantly actuated CDPR that has six degree-of-freedom CDPR and seven driving cables with the proposed method, the results show that the RVs can be reduced significantly.

Variants of the Sliding Mode Control in Presence of External Disturbance for Quadrotor

In this paper, an Improved Integral Power Rate Exponential Reaching Law (IIPRERL) Sliding Mode Control strategy has been presented to cater to the chattering problem and stability issue with the focusing on to achieve minimum steady-state errors in the presence of matched disturbances for a quadrotor. Control strategies have been implemented on quadrotor which is 6 Degree of Freedom (DOF) underactuated model and it is derived via Newton-Euler(NE) equations. The main focus of this article is to design two flight control strategies for a quadrotor. Firstly, a novel IIPRERL-SMC is designed through Improved Integral Sliding Mode Control (II-SMC) via proper gain scheduling by system Eigenvalues. The control objective is to construct a controller such that would force the state trajectories to approach the sliding surface with an exponential policy. Meanwhile, a strong condition for reaching the law of sliding surface via Hurwitz stability has been introduced to the hovering of the quadrotor. Secondly, kinodynamic Rapidly Exploring Random Tree with Fixed Node (RRT*FN) which is an incremental sampling-based optimal algorithm has been implemented for online navigation and flight control of the quadrotor system. Online planning which is based on the offline one, is given on-board radar readings which gradually produces a smooth 3-D trajectory aiming at reaching a predetermined target in an unknown environment. The performance and stability of the quadrotor are completely examined by utilizing Lyapunov stability analysis. Simulations are presented to verify that the proposed scheme is effective with Hurwitz stability for both translational and rotational parts of the quadrotor.

Determination of Joint Load of Human Lower Limb by Using 2D Inverse Dynamics Modelling

The human lower limb is a major part of the human body that is exposed to high joint load during daily activities. Different lifestyles and cultural activities can affect the loading condition generated at the joint during motion. For instance, deep squatting is more frequently performed by Asians compared to Europeans e.g. kneeing on tatami among Japanese and sitting position during prayer among Muslims. The aim of this research is to determine the joint load of the human lower limb during the squat lifting movement by using inverse dynamics of 2-dimensional (2D) human lower limb model. The 2D inverse dynamics modelling was used to describe and compute all the joint force reactions from the known ground reaction and lower limb kinematics. In this study, 2D human lower limb model was analysed during the squat lifting movement. Inverse dynamics computation was performed using MATLAB programming based on Newton-Euler equations to determine the joint forces and moments. The joint loads at ankle, knee and hip joints for every knee flexion angle were obtained and the maximum forces at the ankle, knee and hip were 613.9, 614.1 and 596.1 N, respectively.

Dynamics Modeling and Analysis of a Novel Constraint Metamorphic Reversible Plough

To meet the requirements of different farming objects, this paper presents a novel constraint metamorphic reversible plough (CMRP) which has four distinct working phases and the feature of underactuation, and its prototype has been manufactured for practical testing purposes. Firstly, the kinematics of the mechanism in each phase are studied systematically with the closed-loop vector method, including displacement, velocity, and acceleration analysis. Considering the underactuated characteristics of the mechanism in the source phase, its dynamic models in the source phase are further established by the Lagrange equation. Based on the theory that velocity and acceleration are the same in an extremely brief period, the motion laws of the slider in the source phase can be obtained. To obtain the constraint force/torque acting on the crucial joints in each phase, the dynamic model of the CMRP is established by the Newton–Euler equation. Furthermore, the initial position of the CMRP with a flexible prismatic joint can be determined using the static balance equation. Finally, the obtained kinematic and dynamic models of the CMRP in each phase are verified, respectively, through comparing the simulation results in SolidWorks and Matlab software, and the experiment with the prototype is conducted. The CMRP proposed in this study provides a feasible technical scheme for improving the capability of reversible plough over unknown and complex terrains.

Design and analysis of a scissors double-ring truss deployable mechanism for space antennas

Space deployable mechanism plays an important role in the orbital deployment and stable support of the antenna reflection surface, which is an important component for the spacecraft radar antenna. In order to improve the structural stiffness of the ring truss deployable antenna mechanism when it has a large diameter, a scissors double-ring truss deployable mechanism is proposed in this paper. First, structure analysis of general ring truss deployable antenna and construction of the scissors double-ring truss deployable mechanism are conducted, and the whole mechanism is decomposed to a plurality of mechanism units. Then, degree of freedom (DOF) of the scissors double-ring truss deployable mechanism is analyzed based on screw theory, the result showed that it has only one DOF. Furthermore, based on screw theory, kinematic characteristics of the scissors double-ring truss deployable mechanism are examined, velocities and accelerations of the components in the mechanism are obtained, as well as the Jacobian matrixes. Finally, based on Newton-Euler equation and the principle of virtual work, a dynamic model of the whole mechanism is established, numerical calculation and simulation verification are carried out, and the results verified the correctness of the theoretical analysis. The scissors double-ring truss deployable mechanism proposed in this paper can be well applied in the field of space antennas, and the theoretical analysis method based on screw theory used in this paper can provide insights into other spatial deployable mechanisms.

A dynamic model for underwater robotic fish with a servo actuated pectoral fin

The main objective of this work is to mimic and model pectoral fins based locomotion mechanisms observed in various labriform fishes like box-fish, angel fish, etc. accounting the previous problems using rigid joint connection for fins. The hydrodynamic forces acting on the pectoral fin are evaluated for a quasi-static state using blade element approach while taking into account the added mass. Implementing Newton–Euler equations, the kinematics and the dynamics of a free-swimming robot-fish are obtained. Thus, an analytical model is derived to calculate net forces and torques generated throughout the gait. Apart from a parametric study, simulations are performed to predict various output parameters like thrust, acceleration and swimming speed for some specific locomotion. For experimental validation, a rigid fish-like-body is fabricated with a pair of fins attached symmetrically on lateral sides of the body. Each fin is actuated using three servo-motors in [Ry Rz Ry] configurations to exhibit both the rowing and flapping gaits. A micro-controller is deployed to control the actuators by generating pulse-width modulation and read inertial sensors (a gyroscope and an accelerometer mounted at the centroid of the body) using I2C protocol. In addition, a Bluetooth module is also attached to it for communicating the sensor’s readouts to a computer (running MATLAB script). To achieve some specific motions of rowing gait, the fins are actuated appropriately while the robot is freely submerged underwater and the sensor’s data are recorded in real-time for parallel observations. Based on video motion analysis and the sensed data, the values of acceleration are calculated and compared with the theoretical values predicted by the model.

Fluid Structure Interaction of Buoyant Bodies with Free Surface Flows: Computational Modelling and Experimental Validation

In this paper we present a computational model for the fluid structure interaction of a buoyant rigid body immersed in a free surface flow. The presence of a free surface and its interaction with buoyant bodies make the problem very challenging. In fact, with light (compared to the fluid) or very flexible structures, fluid forces generate large displacements or accelerations of the solid and this enhances the artificial added mass effect. Such a problem is relevant in particular in naval and ocean engineering and for wave energy harvesting, where a correct prediction of the hydrodynamic loading exerted by the fluid on buoyant structures is crucial. To this aim, we develop and validate a tightly coupled algorithm that is able to deal with large structural displacement and impulsive acceleration typical, for instance, of water entry problems. The free surface flow is modeled through the volume of fluid model, the finite volume method is utilized is to discretize the flow and solid motion is described by the Newton-Euler equations. Fluid structure interaction is modeled through a Dirichlet-Newmann partitioned approach and tight coupling is achieved by utilizing a fixed-point iterative procedure. As most experimental data available in literature are limited to the first instants after the water impact, for larger hydrodynamic forces, we specifically designed a set of dedicated experiments on the water impact of a buoyant cylinder, to validate the proposed methodology in a more general framework. Finally, to demonstrate that the proposed numerical model could be used for a wide range of engineering problems related to FSI in multiphase flows, we tested the proposed numerical model for the simulation of a floating body.

Modeling and Mechanical Analysis of Snake Robots on Cylinders

Abstract The narrow and redundant body of the snake robot makes it suitable for the inspection of complex bar structures, such as truss or tree structures. One of the key issues affecting the efficient motion of snake robots in complex bar structures is the development of mechanical models of snake robots on cylinders. In other words, the relationship between the payload and structural and performance parameters of the snake robot is still difficult to clarify. In this paper, the problem is approached with the Newton–Euler equations and the convex optimal method. Firstly, from the kinematic point of view, the optimal attitude of the snake robot wrapped around the cylinder is found. Next, the snake robot is modeled on the cylinder and transformed into a convex optimization problem. Then, the relationship between the payload of the snake robot on the cylinder and the geometric and attitude parameters of the body of snake robots is analyzed. Finally, the discussion for the optimal winding attitude and some advices for the design of the snake robot are proposed. This study is helpful toward the optimal design of snake robots, including geometry parameters and motor determination.

Mathematical Modelling, Simulation and Application of Full Flight Helicopter Simulator

In Aviation, Flight simulators are highly technological devices which are especially used to create the highly-accurate and zero-risk training environment for orientation, emergency, refresher, combat readiness & maintenance / testing pilot training. Full Flight Simulators are the simulators including a cockpit exactly like the real cockpit, visual system which is very close adapting the outside world images, a main simulation software which simulates the aerodynamic flight performance and the disruptive effects of helicopter. In this study, mathematical modelling of AS-532 Cougar helicopter by using Newton-Euler equation. Matlab-Simulink is used for demonstration of simulation results. Comparison of real simulator values and simulation results are enclosed.

Finite-time Attitude Tracking Control Method of Microsatellite Based on Adaptive Robustness and Neural Network Approximation

Abstract Aiming at the attitude tracking control of microsatellites, a finite-time attitude tracking control method based on adaptive robustness and neural network approximation is proposed. Specifically, based on quaternion and Newton-Euler equation, the model of microsatellite attitude tracking control is established. Then, a terminal sliding surface is proposed. All terms except control torque are regarded as total disturbance, which is estimated by three groups of adaptive variables and approximated by Chebyshev neural network. Adaptive robustness and neural network approximation are combined by a switching function and the controller is designed based on it. After that, the finite-time stability of the controller is proved by finite-time Lyapunov stability theorem. Finally, the numerical simulations are carried out and have verified the correctness and effectiveness of the method, which indicates that the controller has quick convergence speed and excellent control precision.

Dynamic Modeling, Simulation, and Experimental Verification of a Wafer Handling SCARA Robot With Decoupling Servo Control

In this paper, we propose a novel coordinated control method based on decoupling servo control to design a 4-DOF direct-drive SCARA robot for wafer handling purpose. As the basis of decoupling servo control, the dynamic model of the SCARA robot is obtained with two methods, the Newton-Euler equation, and Lagrangian equation. The validity of this SCARA dynamic equation is confirmed by these two methods. Due to disturbance and model uncertainty, three PD plus robust controllers are individually applied to three axes of the SCARA robot, together with decoupling control on three physically dynamically highly coupled robotic arms. The inverse dynamics of the SCARA robot is analyzed by feedback linearization, and the experimental results show that above PD plus robust controllers and decoupling control reduce the position tracking error effectively. Performance meets with the high speed and high precision requirements in the wafer handling process. The experimental data shows that the decoupling control algorithm makes the SCARA robot performance improved a lot. The position errors during dynamic tracking movement and the static errors are reduced by 4 to 20 times.

Kinematic Characteristics and Dynamics Analysis of an Overconstrained Scissors Double-Hoop Truss Deployable Antenna Mechanism Based on Screw Theory

Large diameter space deployable antenna is the key equipment for communication and data transmission between spacecraft and base stations on earth. Based on the overconstrained scissors mechanism, a double-hoop truss deployable antenna mechanism is constructed in this paper, which can be used as the antenna support mechanism for satellites and other spacecraft, and its kinematic characteristics and dynamics are analyzed based on screw theory. First, the configuration and the overconstrained features of the double-hoop truss deployable mechanism are analyzed with the truss mechanism divided into a plurality of mechanism units. The geometric conditions for the double-hoop form are also investigated with the consideration of joint size effects. Then, based on the screw theory, the degree of freedom (DOF) of the mechanism is analyzed, showing that this mechanism has only one DOF. Next, the velocity and acceleration of the components in the mechanism are examined. Through the screw and screw derivatives operation, the velocities and accelerations of the components and the Jacobian matrixes are obtained. Finally, a dynamic model of the double-hoop truss deployable mechanism is established based on the Newton-Euler equation and the principle of virtual work, and this model is verified by the numerical calculation and simulation verification. The overconstrained scissors double-hoop truss deployable antenna mechanism proposed in this paper has a good application prospect in the field of space deployable antennas, and the theoretical analysis method in this paper can provide insights into other complex spatial deployable mechanisms.

Design, stiffness analysis and experimental study of a cable-driven parallel 3D printer

Although additive manufacturing (AM) has been developed rapidly and become an absolutely necessary tool for reducing the cycle and cost of new product development, the mechanical structures of most 3D printers based on Fused Deposition Modeling (FDM) technology are still traditional serial or parallel mechanisms with rigid components. In this paper, a novel cable-driven parallel 3D printer (CDPP) is developed. Compared with the traditional rigid mechanisms, CDPP has the advantages of larger workspace, higher payload-to-weight ratio, easier modularity and reconfigurability. A cable-driven module with three translational degrees of freedom and a follow-up tensioning module with a spring are adopted for positioning. Firstly, the inverse kinematics of the CDPP is derived considering the cable length constraint. The inverse dynamics model of the CDPP is established based on the Newton–Euler equation and the kinematics. Secondly, the system stiffness of the CDPP and stiffness along three coordinate axes are derived, respectively. The system static stiffness with respect to the stiffness constant of the spring and the coordinates of the moving platform are obtained. Finally, the experiments are performed based on numerical simulation. The results of experiments without executing extrusion demonstrate the simulation results about the static stiffness. The feasibility of the CDPP is verified via the experiments while executing extrusion.

A rigorous proof for the equivalence of the projective Newton–Euler equations and the Lagrange equations of second kind for spatial rigid multibody systems

It is well known that the projective Newton–Euler equation and the Lagrange equation of second kind lead to the same result when deriving the dynamical equations of motion for holonomic rigid multibody systems. It can be shown that both approaches follow from the principles of d’Alembert or Jourdain. However, as to the author’s knowledge, no direct rigorous proof for the equivalence of these approaches is given in literature so far when it comes to spatial systems of rigid bodies. In this paper, we present a novel proof that directly addresses the projective Newton–Euler equation and the Lagrange equation of second kind without the detour via variational principles. The proof is mainly based on vector and matrix manipulations and elementary concepts of differential geometry. Although the mathematical framework is thereby kept simple, the argumentation is considerably more complex compared to the case of planar systems of rigid bodies or spatial systems of particles. An illustrative example is presented.

A NUMERICAL AND EXPERIMENTAL ANALYSIS OF THE DYNAMIC STABILITY OF HYDRAULIC EXCAVATORS

The paper presents the results of a numerical and experimental analysis of the dynamic stability of hydraulic excavators. The analysis has employed the software developed on the basis of a defined general dynamic mathematical model of an excavator grounded in Newton-Euler equations as well as the measured quantities of the excavator operating state in exploitation conditions. The defined model is used to model the members of the excavator kinematic chain using rigid bodies while the actuators (hydraulic cylinders and hydraulic motors) of the excavator drive mechanisms are modeled with elastically dampened elements. The elastically dampened characteristics of the actuators are defined with regard to the size of the actuator as well as to the compressibility and temperature of the hydraulic oil used in the excavator hydrostatic drive system. To illustrate the analysis, the paper provides the results of the analysis of the dynamic stability of a 16000 kg tracked excavator equipped with a manipulator digging bucket of 0.6 m3 in capacity.