Discrete Time Transfer Matrix Method Research Articles

Comparison of the Dynamic Performance of Planar 3-DOF Parallel Manipulators

This paper presents a comprehensive comparison study on the dynamic performances of three planar 3-DOF parallel manipulators (PPMs): 3-RRR, 3-PRR, and 3-RPR. In this research work, the discrete time transfer matrix method (DT-TMM) is employed for developing dynamic models of the planar parallel manipulators. Numerical simulations using the virtual work principle and ADAMS 2016 software are performed to verify the DT-TMM dynamic model of PPMs. Numerous dynamic performance indices, including dynamic dexterity, the power requirement, energy transmission efficiency, and the joint force/torque margin, are proposed to compare the dynamic performance of three PPMs under the general circular and linear trajectories. The comprehensive analyses and comparisons show that: (1) the 3-RRR PPM has advantages in terms of a circular trajectory, offering the best dynamic dexterity performance, the smallest power requirement, and the second-highest energy transfer efficiency; (2) the 3-PRR PPM performs best in terms of a linear trajectory, offering the best dynamic dexterity, the smallest power requirement range, and the best drive performance; and (3) the 3-RPR PPM has the highest energy transfer efficiency and demonstrates better dynamic performance in a circular trajectory compared to a linear trajectory.

Efficient technique in computational dynamic modeling of a flexible manipulator with large deformation

In the flexible manipulators, the links could be modeled using rigid elements and torsional springs, and similarly, the flexibility in actuators could be represented with the equivalent springs. This study applies the discrete time transfer matrix method for the dynamic analysis of flexible manipulators with large deformations. On a first-priority basis, transfer matrices are determined, including all the flexible link/joint mechanism components. A single transfer matrix is established for prismatic and rotational actuators with equivalent springs to build the robotic transfer matrix library. On the second priority, to reduce the computation time, a novel algorithm is developed. In the proposed flexible link discretization, the first element of the flexible link is considered as a function of other elements. It is designed to build a mathematical model as closely as possible to the realistic model with fewer elements. It is presented that this modeling technique can employ discrete data extracted by the sensors. The simulation primarily focuses on developing flexible beam/joint models validated in ADAMS. Besides, the dynamic behavior of a flexible PR robot with external forces acting on the linkage system is analyzed and examined. The result shows that the proposed modeling method affords a low computational time while the manipulator control needs to manage fast responses.

Fluid-Structure Interaction Analysis of Aircraft Hydraulic Pipe with Complex Constraints Based on Discrete Time Transfer Matrix Method

Fluid-structure interaction (FSI) is prevalent in aircraft hydraulic pipes due to high-pressure fluid pulsation, complex pipe path routing and boundary constraints, which pose a serious threat to the safety and reliability of the aircraft hydraulic system. This paper focuses on the FSI response of aircraft hydraulic pipes with complex constraints. A comprehensive fourteen-equation model for describing the FSI of pipe conveying fluid with wide pressure and Reynolds number range is proposed. The excitation models and complex boundary constraints of liquid-filled pipes are established. Moreover, based on the transfer matrix method (TMM), combined with the time discreteness and analytical integral method, a discrete time transfer matrix method (DTTMM) for solving the FSI fourteen-equation model in time domain is presented. Then, the numerical solution and experiment of an ARJ21-700 aircraft hydraulic pipe with complex constraints is carried out with four working conditions. The obtained results verify the correctness of the proposed model and solution method, and reveal the universal laws of the FSI response about aircraft hydraulic pipes, which can also provide theoretical and experimental references for modeling, solutions and verification in the FSI analysis of pipe conveying fluid.

Modeling and Vibration Analysis of a 3-UPU Parallel Vibration Isolation Platform with Linear Motors Based on MS-DT-TMM

The dynamics and vibration characteristics of a 3-UPU parallel mechanism isolator are investigated by theoretical modeling, numerical simulation, and experimental study. The system consists of two platforms, three linear motors, and the Hook hinges. Firstly, the dynamical mathematical model of this vibration isolator is innovatively established and solved by using the discrete-time transfer matrix method of the multibody system (MS-DT-TMM). According to the modeling principle, the transfer matrix of each component is derived, including the upper and lower platforms, Hooke hinges, and linear motors. Then, the dynamical equation of the overall system is obtained by multiplying all transfer matrices. Secondly, the solution of equation is calculated through the setting of boundary conditions. The numerical simulation is carried out according to the known parameters. The dynamical and vibration analysis of the isolation platform is performed, involving the displacement and force characteristics of the branches. Furthermore, in view of the fact that the Hooke hinges and linear motors are simplified as spatial elastic hinges in modeling. The vibration suppression effect caused by adjusting spring stiffness and damping coefficient is discussed. The simulation results verified the correctness of the MS-DT-TMM method through the comparison with ADAMS simulation results. Finally, the prototype of the vibration isolator is constructed and assembled, and the vibration experiment is conducted. By testing the responses of the isolation device mounted on the vibration table, the natural frequency of the isolator is obtained. The purpose of this experiment is to avoid resonance when it is applied as a vibration isolator in the future. This paper provides a theoretical basis for the later vibration research and control scheme design of the 3-UPU parallel vibration isolation platform.

Multibody System Discrete Time Transfer Matrix Method for Nonlinear Shear Dynamic analysis of Immersed Tunnels

Shear seismic response analysis is critical for seismic design of immersed tunnels. According to the structural characters of immersed tunnels and shear dynamic response of their joints, a multibody dynamic model consisting of multi-rigid body, shear hinge, and viscous damping hinge is proposed for shear response analysis, in which the dynamic stiffness of the shear hinge is divided into two stages based on a threshold. Following the discrete time transfer matrix method for multibody system dynamics (MS-DT-TMM), the mechanical model and mathematical expression of each tunnel element is derived first and then assembled for the whole tunnel system. A solution procedure is proposed to solve the shear dynamic response of immersed tunnels using the proposed multibody system model. It is shown that the MS-DT-TMM has the same computational accuracy as the finite element method (FEM) and the modeling process is more efficient and flexible when compared to FEM. Although the MS-DT-TMM discussed herein is only applied to shear response analysis, it can easily be extended to analyze axial force and bending moment of immersed tunnels leading to a complete, rapid yet accurate enough seismic analysis of immersed tunnels suitable for engineering practices.

Computational efficient discrete time transfer matrix method for large deformation analysis of flexible manipulators

In this article, a large deformation analysis of a flexible manipulator is examined by using the discrete time transfer matrix method. Since this robotic analysis is very demanding in terms of both computation time and memory usage, the main goal is to reduce the computational complexity compared to the conventional algorithm. In this study, the proposed model is validated with Euler–Bernoulli beam and a corresponding ADAMS model. A planar robotic arm in the presence of links and joints flexibility is studied. It concludes that the theoretical formulation attributes for large flexible multibody systems and practical robotic application.

Integrating Dynamics into Design and Motion Optimization of a 3-PRR Planar Parallel Manipulator with Discrete Time Transfer Matrix Method

This paper presents a novel method of dynamic modeling and design optimization integrated with dynamics for parallel robot manipulators. Firstly, a computationally efficient modeling method, the discrete time transfer matrix method (DT-TMM), is proposed to establish the dynamic model of a 3-PRR planar parallel manipulator (PPM) for the first time. The numerical simulations are performed with both the proposed DT-TMM dynamic modeling and the ADAMS modeling. The applicability and effectiveness of DT-TMM in parallel manipulators are verified by comparing the numerical results. Secondly, the design parameters of the 3-PRR parallel manipulator are optimized using the kinematic performance indices, such as global workspace conditioning index (GWCI), global condition index (GCI), and global gradient index (GGI). Finally, a dynamic performance index, namely, driving force index (DFI), is proposed based on the established dynamic model. The described motion trajectory of the moving platform is placed into the optimized workspace and the initial position is determined to finalize the end-effector trajectory of the parallel manipulator by the further optimization with the integrated kinematic and dynamic performance indices. The novelty of this work includes (1) developing a new dynamic model method with high computation efficiency for parallel robot manipulators using DT-TMM and (2) proposing a new dynamic performance index and integrating the dynamic index into the motion and design optimization of parallel robot manipulators.

Differential quadrature discrete time transfer matrix method for vibration mechanics

Transfer matrix method is a practical technology for vibration analysis of engineering mechanics. In this article, a new version of mixed differential quadrature discrete time transfer matrix method is presented for simulating vibrations. First, ordinary differential equations of the substructure or the element of a mechanical system are determined by classical mechanics rules or the finite element method. These ordinary differential equations can be transformed to a set of algebraic equations at some discrete time points by the application of a differential quadrature method. After extending the state vector of the transfer matrix method, new transfer equations and transfer matrices of the substructures (or elements) of a mechanical system are developed finally. Riccati transformation is used to improve the computational convergence of the method. Several numerical examples show that the proposed method can be regarded as an efficient tool for transient response analysis of vibration systems.

Dynamics analysis and wave compensation control design of ship’s seaborne supply by discrete time transfer matrix method of multibody system

Abstract Real-time dynamics analysis and control of ship's seaborne supply (SSS) operations under complex sea conditions is a research hotspot in the fields of marine and ship engineering, mechanics and control engineering. In this paper, the discrete time transfer matrix method of multibody system is proposed for dynamics modeling and analysis of a SSS system. This method solves the dynamics of system easily only by the low-order transfer equations, instead of the usual high-order global differential or differential-algebra equations of system; therefore, its computational efficiency is enhanced essentially. Then for improving the positioning precision and security of supply operations, a hybrid control system which is composed of three PD controllers and a fuzzy controller is designed to compensate the ship’s relative motion caused by sea waves. The formulas, dynamics algorithm and control design details are all presented. Some illustrative simulations show the proposed modeling method and control strategy are accurate and feasible, with low computational complexity and satisfying control performance.

Direct differentiation method for sensitivity analysis based on transfer matrix method for multibody systems

SummaryOn one hand, the new version of transfer matrix method for multibody systems (NV‐MSTMM), has been proposed by formulating transfer equations of elements in acceleration level instead of position level as in the original discrete time transfer matrix method of multibody systems to study multibody system dynamics. This new formulation avoids local linearization and allows using any integration algorithms. On the other hand, sensitivity analysis is an important way to improve the optimization efficiency of multibody system dynamics. In this paper, a totally novel direct differentiation method based on NV‐MSTMM for sensitivity analysis of multibody systems is developed. Based on direct differentiation method, sensitivity analysis matrix for each kind of element is established. By assembling transfer matrices and sensitivity analysis matrices based on differentiation law of multiplication, the sensitivity analysis equation of overall transfer equation is deduced. The computing procedure of the proposed method is also presented. All these improvements as well as three numerical examples show that the direct differentiation method based on NV‐MSTMM is suitable for optimizing the dynamic sensitivity in multi–rigid‐body systems.

Dynamics analysis and fuzzy anti-swing control design of overhead crane system based on Riccati discrete time transfer matrix method

This paper describes an efficient method called Riccati discrete time transfer matrix method of multibody system (MS-RDTTMM) for studying the dynamic modeling and anti-swing control design of a two-dimensional overhead crane system, which consists of a trolley, rope, load, and control subsystem. Regarding the rope as a series of rigid segments connected by hinges, a multibody model of the overhead crane system can be developed easily by using MS-RDTTMM. Then three separate fuzzy logic controllers are designed for positioning and anti-swing control. For improving the performance of the predesigned fuzzy control system, the genetic algorithm based on MS-RDTTMM is presented offline to tune the initial control parameters. Using the recursive transfer formula to describe the system dynamics, instead of the global dynamics equation in ordinary dynamics methods, the matrices involved in this method are always very small, and the computational cost of the dynamic analysis and control system optimization can be greatly reduced. The numerical verification is carried out to show the computational efficiency, numerical stability, and control performance of the proposed method.

Computationally efficient dynamic modeling of robot manipulators with multiple flexible-links using acceleration-based discrete time transfer matrix method

Abstract This paper presents a novel and computationally efficient modeling method for the dynamics of flexible-link robot manipulators. In this method, a robot manipulator is decomposed into components/elements. The component/element dynamics is established using Newton–Euler equations, and then is linearized based on the acceleration-based state vector. The transfer matrices for each type of components/elements are developed, and used to establish the system equations of a flexible robot manipulator by concatenating the state vector from the base to the end-effector. With this strategy, the size of the final system dynamic equations does not increase with the number of joints or the number of link beam elements that each link is decomposed. The developed method intends to avoid the traditional computation of the global system dynamic equations that usually have large size for flexible robot manipulators, and only involves calculating and transferring component/element dynamic equations that have small size. The numerical simulations and experimental testing of flexible-link manipulators are conducted to validate the proposed methodologies.

Compliant dynamics of a rectilinear rear-independent system

The rectilinear rear-independent suspension investigated in this paper could remain the wheel alignment parameters invariable in theory. However, its dynamics is much more complex than that of the existing suspensions because of its redundant constraints in structure. Considering the elasticity of the rectilinear rear-independent suspension, a rigid-flexible half-car dynamic model is established for the first time based on the discrete time transfer matrix method. At the same time, a rigid half-car dynamic model is established as a comparison. The natural frequency characteristics and dynamic response of the rectilinear rear-independent suspension under random road excitations are analyzed and compared with those of rigid half-car dynamic model. The results reveal that the suspension system has apparent influence to the dynamics of vehicle. The wheel alignment parameters will fluctuate within a narrow range which is mainly determined by the rolling vibration of vehicle. And the suspension system could reduce and filter the road excitations with high frequency and small amplitude. This provides a good effect on the ride comfort of vehicle. Dynamics analysis of the rectilinear rear independent suspension reveals that the proposed modeling approach could deal with the dynamics of rigid-flexible multibody systems with redundant constraints effectively.

Research on the rigid-flexible multibody dynamics of concrete placing boom

Abstract A method is proposed for rigid-flexible multibody dynamic modeling of concrete placing booms, to improve the calculation efficiency and ensure the accuracy. Concrete placing booms consist of four types of substructures, according to the slender rods and the mechanism features. The transfer matrixes of substructures are derived based on the discrete time transfer matrix method. Then, the manipulator's overall transfer matrix is assembled and used for the numerical calculation. An experiment based on a test rig is performed to validate the proposed method, and a model based on ADAMS (short of MSC.ADAMS) is also established to compare the calculating efficiency of the proposed method.

A Rapid Gun Firing Correction Algorithm Using Discrete Time Transfer Matrix Method

To improve the next shot hit accuracy, a firing angle correction algorithm will be developed using the distance error computed between the impact and target coordinates to determine the launch azimuth and quadrant elevation angles for artillery projectiles. This correction method will be developed using the discrete time transfer matrix method of the projectile modified point mass model DTTMM-4DOF to improve correction method performance. To validate the proposed algorithm, a spin-stabilized 155mm-HE projectile flight trajectory will be used, assuming that wind magnitude and direction with the down range are changing as function of projectile altitude.

Force Analysis of the Anchor Chains and the Cable in the Crane-System with a Floating Base in Regular Waves

In order to analyze the force of the anchor chains and the cable in the crane-system with a floating base, firstly the system is simplified to two-rigid-body model and the anchor chains in the system are in symmetric layout; then the motion response of the system as well as the force of the anchor chains and the cable are solved by use of discrete time transfer matrix method, lastly the time history curves of motion of the system and the force of the anchor chains and the cable are obtained. The results of numerical simulation show that the roll motion has greater influences on the system comparing with sway and heave, the amplitudes of sway and heave are small. Furthermore, the force of the anchor chains are mainly caused by the roll motion while the force caused by sway and heave are relatively small.

Investigation on Spin-Stabilized Projectile Trajectory Observability Based on Flight Stability

To accurately estimate the projectile ballistic trajectory, where the real impact point can not be identified in case of indirect firing, a 3D tracking radar with Doppler is used during the first portion of projectile trajectory to estimate the projectile attitude and angular motion during flight, and hence; compute the impact point using a nonlinear six-degree-of-freedom 6-DOF trajectory model. A numerical study is done to investigate the effect of the flight stability of a 105mm artillery projectile on the length of Doppler radar data needed to accurately estimate the projectile impact point. A discrete time transfer matrix method DTTM-4DOF is used to estimate the in-flight projectile angular motion using Doppler radar measurements. Simulated Doppler radar data are generated using the 6-DOF model including the projectile initial disturbance problem.

A dynamic model of mobile concrete pump boom based on discrete time transfer matrix method

Mobile concrete pump boom is typical multibody large-scale motion manipulator. Due to posture constantly change in working process, kinematic rule and dynamic characteristic are difficult to solve. A dynamics model of a mobile concrete pump boom is established based on discrete time transfer matrix method (DTTMM). The boom system is divided into sub-structure A and substructure B. Sub-structure A is composed by the 1st boom and hydraulic actuator as well as the support. And substructure B is consists of the other three booms and corresponding hydraulic actuators. In the model, the booms and links are regarded as rigid elements and the hydraulic cylinders are equivalent to spring-damper. The booms are driven by the controllable hydraulic actuators. The overall dynamic equation and transfer matrix of the model can be assembled by sub-structures A and B. To get a precise result, step size and integration parameters are studied then. Next the tip displacement is calculated and compared with the result of ADAMS software. The displacement and rotation angle curves of the proposed method fit well with the ADAMS model. Besides it is convenient in modeling and saves time. So it is suitable for mobile concrete pump boom real-time monitoring and dynamic analysis. All of these provide reference to boom optimize and engineering application of such mechanisms.

Discrete Time Transfer Matrix Method for Projectile Trajectory Prediction

AbstractDue to the importance of the ballistic trajectory computation including the estimation of launch point and impact point problems, a fast and accurate model is needed to increase the weapon precession. A discrete time transfer matrix method is developed and presented in this paper to compute the trajectory for both fin- and spin-stabilized artillery projectiles. This method is based on discretizing the projectile continuous nonlinear system into a set of linear equations using a second-order Taylor series. These equations are collected into one transfer matrix which can be used in trajectory prediction with high computation speed by evaluating a set of algebraic equations instead of integrating differential equations. Results demonstrate that the presented formulation agrees very well with those obtained numerically using the well-known nonlinear 6-degree-of-freedom model.

Discrete Time Transfer Matrix Method for Launch Dynamics Modeling and Cosimulation of Self-Propelled Artillery System

In many industrial applications, complex mechanical systems can often be described by multibody systems (MBS) that interact with electrical, flowing, elastic structures, and other subsystems. Efficient, precise dynamic analysis for such coupled mechanical systems has become a research focus in the field of MBS dynamics. In this paper, a coupled self-propelled artillery system (SPAS) is examined as an example, and the discrete time transfer matrix method of MBS and multirate time integration algorithm are used to study the dynamics and cosimulation of coupled mechanical systems. The global error and computational stability of the proposed method are discussed. Finally, the dynamic simulation of a SPAS is given to validate the method. This method does not need the global dynamic equations and has a low-order system matrix, and, therefore, exhibits high computational efficiency. The proposed method has advantages for dynamic design of complex mechanical systems and can be extended to other coupled systems in a straightforward manner.