Recursive Linearization of Multibody Dynamics and Application to Control Design

1990 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Control Design ◽  
Numerical Differentiation ◽  
Difficult Problem ◽  
Computational Method ◽  
Computational Error ◽  
Dynamics Modeling ◽  
Analytical Approximations

Abstract The non-linear equations of motion in multi-body dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.

Recursive Linearization of Multibody Dynamics and Application to Control Design

1994 ◽  
Vol 116 (2) ◽  
pp. 445-451 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Control Design ◽  
Numerical Differentiation ◽  
Difficult Problem ◽  
General Purpose ◽  
Computational Method ◽  
Computational Error ◽  
Dynamics Modeling ◽  
Analytical Approximations

The nonlinear equations of motion in multibody dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.

AI-VCR Computational Research on Visibility of 3D Materials Solids Reality Pictures

2010 ◽  
Vol 143-144 ◽  
pp. 592-597
Author(s):  
Qiu Sun Ye
Keyword(s):  
Difficult Problem ◽  
Computational Method ◽  
Computational Error ◽  
Computational Research ◽  
3D Solid

An optional spatial 3D material solid reality picture may be showed on a 2D showing plane, its surface is commonly consisted of too many sub-surfaces of the 3D solid reality picture in both dispersal and continuation. It was a difficult problem to express all exact visibilities of solids sub-surfaces; because of some numerals computational error properties of visibilities are always unknown. So far, we cannot choose but select a proper dispersal degree of materials sub-surfaces, an approaching function of an optional material sub-surfaces B-Rep (Bound Representation), and numerals computation without any perturbation motion, etc. A novel numeral computational method of expressing exact visibilities of 3D spatial materials solids reality pictures with intelligent properties of VCR is given in this paper.

A Closed-Form Dynamics of a Novel Fully Wrist Driven by Revolute Motors

2016 ◽  
Vol 32 (4) ◽  
pp. 479-490
Author(s):  
J. Enferadi ◽  
A. Shahi
Keyword(s):  
Closed Form ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Angular Displacement ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Spherical Robot ◽  
Dynamics Modeling ◽  
Dynamical Equations ◽  
Moving Platform

AbstractThis paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a novel spherical robot that is called a 3(RPSP)-S parallel manipulator. The proposed manipulator provides high rotational displacement of the moving platform for low angular displacement of the motors. The advised robot is suitable for repetitive oscillatory applications (for example, wrist and ankle rehabilitation and table of autopilot and gyroscope life test, etc.). First, we describe the structure of the proposed manipulator and solve the inverse kinematics problem of the manipulator. Next, based on the principle of virtual work, a methodology for deriving the dynamical equations of motion is developed. The elaborated approach shows that the inverse dynamics of the manipulator can be reduced to solving a system of three linear equations in three unknowns. Finally, a computational algorithm to solve the inverse dynamics of the manipulator is advised and several trajectories of the moving platform are simulated and verified by a special dynamics modeling commercial software (MSC ADAMS).

Multibody Dynamics Modeling of Sand Flow From a Hopper and Sand Pile Angle of Repose

2013 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Shahriar G. Ahmadi ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Multibody Dynamics ◽  
Flow Rate ◽  
Search Algorithm ◽  
Equations Of Motion ◽  
Friction Model ◽  
Angle Of Repose ◽  
Dynamics Modeling ◽  
Three Dimensional Model ◽  
Normal Contact ◽  
Sand Flow

An explicit time integration multibody dynamics code is used to create a three-dimensional model of sand. Sand is modeled using discrete cubical particles with appropriate normal contact force and tangential friction force models. The model is used to predict the sand angle of repose and flow rate during discharge from a conical hopper. A penalty technique is used to impose normal contact constraints (including particle-particle, particle-hopper and particle-ground contact). An asperity-based friction model is used to model friction. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. The governing equations of motion are solved along with contact constraint equations using a time-accurate explicit solution procedure. Parameter studies are performed in order to study the effects of the particle size and the orifice’s diameter of the hopper on the angle of repose and sand flow rate. The results of the simulations are validated using previously published experimental results.

Time Integration Incorporated Sensitivity Analysis With Generalized-α Method for Multibody Dynamics Systems

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Dynamic Loading ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Time Integration ◽  
Optimization Method ◽  
Sensitivity Analysis Method ◽  
System Equations ◽  
Consecutive Time

The topology optimization method is extended for the optimization of geometrically nonlinear, time-dependent multibody dynamics systems undergoing nonlinear responses. In particular, this paper focuses on sensitivity analysis methods for topology optimization of general multibody dynamics systems, which include large displacements and rotations and dynamic loading. The generalized-α method is employed to solve the multibody dynamics system equations of motion. The developed time integration incorporated sensitivity analysis method is based on a linear approximation of two consecutive time steps, such that the generalized-α method is only applied once in the time integration of the equations of motion. This approach significantly reduces the computational costs associated with sensitivity analysis. To show the effectiveness of the developed procedures, topology optimization of a ground structure embedded in a planar multibody dynamics system under dynamic loading is presented.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

scholarly journals INVESTIGATION OF THE DYNAMICS OF AN OVERHEAD CRANE LIFTING PROCESS IN A VERTICAL PLANE

Transport ◽  
2005 ◽  
Vol 20 (5) ◽  
pp. 176-180 ◽  
Author(s):  
Marijonas Bogdevičius ◽  
Aleksandr Vika
Keyword(s):  
Dynamic Behaviour ◽  
Equations Of Motion ◽  
Asynchronous Motor ◽  
Linear Equations ◽  
Vertical Plane ◽  
Overhead Crane ◽  
Dynamic Forces ◽  
Planet Gear ◽  
Linear Equations Of Motion ◽  
Non Linear Equations

The paper analyses the dynamic behaviour of supporting structure of an overhead crane during the operation of a hoisting mechanism. The crane is expected to operate with a hook and to carry 50 kN of weight. The electric hoist consists of an asynchronous motor with a magnetic brake, a two‐level planet gear, a load drum and an upper block. Non‐linear equations of motion of a crane hoisting mechanism are derived. Real dynamic forces and their influence on the hoisting crane behaviour are obtained. Numerical results of the crane are derived considering two hoisting regimes during the operation of the hoisting.

scholarly journals NON-RIGID KINEMATIC EXCITATION FOR MULTIPLY-SUPPORTED SYSTEM WITH HOMOGENEOUS DAMPING

2018 ◽  
Vol 14 (4) ◽  
pp. 152-157
Author(s):  
Alexander G. Tyapin
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Internal Damping ◽  
Static Response ◽  
Kinematic Excitation ◽  
Hand Part ◽  
Internal Forces ◽  
The Right ◽  
Damping Model

This paper continues the discussion of linear equations of motion. The author considers non-rigid kinematic excitation for multiply-supported system leading to the deformations in quasi-static response. It turns out that in the equation of motion written down for relative displacements (relative displacements are defined as absolute displacements minus quasi-static response) the contribution of the internal damping to the load in some cases may be zero (like it was for rigid kinematical excitation). For this effect the system under consideration must have homogeneous damping. It is the often case, though not always. Zero contribution of the internal damping to the load is different in origin for rigid and non-rigid kinematic excitation: in the former case nodal loads in the quasi-static response are zero for each element; in the latter case nodal loads in elements are non-zero, but in each node they are balanced giving zero resulting nodal loads. Thus, damping in the quasi-static response does not impact relative motion, but impacts the resulting internal forces. The implementation of the Rayleigh damping model for the right-hand part of the equation leads to the error (like for rigid kinematic excitation), as damping in the Rayleigh model is not really “internal”: due to the participation of mass matrix it works on rigid displacements, which is impossible for internal damping

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