Showing papers in "Multibody System Dynamics in 1998"

A New Approach for the Dynamic Analysis of Parallel Manipulators

Abstract: A new approach for the dynamic analysis of parallel manipulators is presented in this paper. This approach is based on the principle of virtual work. The approach is firstly illustrated using a simple example, namely, a planar four-bar linkage. Then, the dynamic analysis of a spatial six-degree-of-freedom parallel manipulator with prismatic actuators (Gough–Stewart platform) is performed. Finally, a numerical example is given in order to illustrate the results. The approach proposed here can be applied to any type of planar and spatial parallel mechanism and leads to faster computational algorithms than the classical Newton–Euler approach when applied to these mechanisms.

A Continuous Analysis Method for Planar Multibody Systems with Joint Clearance

Abstract: Clearance from manufacturing tolerances or wear is likely to degrade the dynamic performance of connected machine parts. When joint clearance is introduced, the dynamic response of the mechanical system is substantially changed, seen as high acceleration and force peaks and dissipation of energy. Looking at contact models, the simpler ones, such as the linear Kelvin–Voigt or the nonlinear Hertz model, are characterized by a set of parameters. These include material parameters, coefficient of restitution and possibly a coefficient of friction. The analysis models can be divided into two groups – continuous and dis-continuous, related to whether integration is carried out through the period of contact, or stopped and restarted after the impact. Based on the equations of motion for a multibody system of rigid bodies, it is suggested that the continuous analysis approach is combined with a contact force model to describe joint clearance in rotational joints. Performing simulations with this methodology allows not only to quantify the overall mechanism behaviour, but also in-depth analysis of the impact mechanics in the clearance joint. Experimental data from a double pendulum impacting a rigid plate is used to verify the suggested continuous analysis method.

Computational Schemes for Flexible, Nonlinear Multi-Body Systems

Abstract: This paper deals with the development of computational schemes for the dynamic analysis of flexible, nonlinear multi-body systems. The focus of the investigation is on the derivation of unconditionally stable time integration schemes for these types of problem. At first, schemes based on Galerkin and time discontinuous Galerkin approximations applied to the equations of motion written in the symmetric hyperbolic form are proposed. Though useful, these schemes require casting the equations of motion in the symmetric hyperbolic form, which is not always possible for multi-body applications. Next, unconditionally stable schemes are proposed that do not rely on the symmetric hyperbolic form. Both energy preserving and energy decaying schemes are derived that both provide unconditionally stable schemes for nonlinear multi-body systems. The formulation of beam and flexible joint elements, as well as of the kinematic constraints associated with universal and revolute joints. An automated time step selection procedure is also developed based on an energy related error measure that provides both local and global error levels. Several examples of simulation of realistic multi-body systems are presented which illustrate the efficiency and accuracy of the proposed schemes, and demonstrate the need for unconditional stability and high frequency numerical dissipation.

An Improved Formulation for Constrained Mechanical Systems

Abstract: This paper presents an investigation of the advantages of a new formulation in the study of mechanical systems with holonomic and nonholonomic constraints. The formulation, originally proposed for systems of constrained particles, provides an efficient and robust means of simulating general multibody systems in the presence of redundant, degenerate and intermittent constraints. The structure of the formulation also allows the use of a dynamics code for pure kinematics analysis with a simple substitution. In addition, the formulation separates applied and constraint forces explicitly allowing recovery of constraint forces by straightforward means. Several examples are given to demonstrate the effectiveness of the formulation in special circumstances.

Design Optimization of Multibody Systems by Sequential Approximation

Abstract: Design optimization of multibody systems is usually established by a direct coupling of multibody system analysis and mathematical programming algorithms. However, a direct coupling is hindered by the transient and computationally complex behavior of many multibody systems. In structural optimization often approximation concepts are used instead to interface numerical analysis and optimization. This paper shows that such an approach is valuable for the optimization of multibody systems as well. A design optimization tool has been developed for multibody systems that generates a sequence of approximate optimization problems. The approach is illustrated by three examples: an impact absorber, a slider-crank mechanism, and a stress-constrained four-bar mechanism. Furthermore, the consequences for an accurate and efficient accompanying design sensitivity analysis are discussed.

Kinematic and Dynamic Analyses of the Tripode Joint

Abstract: This paper is concerned with an application of multibody techniques to the dynamic analysis of the tripode joint. The purpose of the mathematical model developed is the computation of all the constraint forces. In fact, the results of this investigation are preliminary for a study on the influence of geometry and inertia design parameters on the noise and vibrations caused by the joint.

Dynamic Analysis Tool for Legged Robots

Abstract: The paper introduces a systematic approach for dealing with legged robot mechanism analysis. First, we briefly summarize basic mathematical tools for studying the dynamics of these multi-loop and parallel mechanisms using a unified spatial formulation which is useful for computer algorithms. The dynamic behavior analysis is based on two stages. The first one deals with establishing the equations of motion of the whole mechanism including legs tip impact effects and allowing us to solve the direct and inverse dynamic problems. The second concerns the feet–ground interaction aspect which is one of the major problem in the context of dynamic simulation for walking devices. We focus on the phenomenon of contact by introducing a general model for dynamic simulation of contacts between a walking robot and ground. This model considers a force distribution and uses an analytical form for each force depending only on the known state of the robot system. Finally, some simulation results of biped robot are given. The simulation includes all phenomena that may occur during the locomotion cycle: impact, transition from impact to contact, contact during support with static friction, transition from static to sliding friction and sliding friction.

Modeling and Solution of Some Mechanical Problems on Lie Groups

Abstract: We apply Munthe-Kaas and Crouch–Grossman methods in the solution of some mechanical problems. These methods are quite new, and they exploit intrinsic properties of the manifolds defined by the mechanical problems, thus ensuring that the numerical solution obey underlying constraints. A brief introduction to the methods is presented, and numerical simulations show some of the properties they possess. We also discuss error estimation and stepsize selection for some of these methods.

Tolerance Optimization for Mechanisms with Lubricated Joints

Abstract: This paper addresses an analytical approach to tolerance optimization for planar mechanisms with lubricated joints based on mechanical error analysis. The mobility method is applied to consider the lubrication effects at joints and planar mechanisms are stochastically defined by using the clearance vector model for mechanical error analysis. The uncertainties considered in the analysis are tolerances on link lengths and radial clearances and these are selected as design variables. To show the validity of the proposed method for mechanical error analysis, it is applied to two examples, and the results obtained are compared with those of Monte Carlo simulations. Based on the mechanical error analysis, tolerance optimizations are applied to the examples.

Efficient dynamic constraints for animating articulated figures.

Abstract: This paper presents an efficient dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A non-trivial extension of Featherstone's O(n) recursive forward dynamics algorithm is derived which allows enforcing one or more constraints on the animated figures. We demonstrate how the constraint force evaluation algorithm we have developed makes it possible to simulate collisions between articulated figures, to compute the results of impulsive forces, to enforce joint limits, to model closed kinematic loops, and to robustly control motion at interactive rates. Particular care has been taken to make the algorithm not only fast, but also easy to implement and use. To better illustrate how the constraint force evaluation algorithm works, we provide pseudocode for its major components. Additionally, we analyze its computational complexity and finally we present examples demonstrating how our system has been used to generate interactive, physically correct complex motion with small user effort.

Chain Vibration and Dynamic Stress in Three-Dimensional Multibody Tracked Vehicles

Abstract: A three-dimensional computational finite element procedure for the vibration and dynamic stress analysis of the track link chains of off-road vehicles is presented in this paper. The numerical procedure developed in this investigation integrates classical constrained multibody dynamics methods with finite element capabilities. The nonlinear equations of motion of the three-dimensional tracked vehicle model in which the track link s are considered flexible bodies, are obtained using the floating frame of reference formulation. Three-dimensional contact force models are used to describe the interaction of the track chain links with the vehicle components and the ground. The dynamic equations of motion are first presented in terms of a coupled set of reference and elastic coordinates of the track links. Assuming that the structural flexibility of the track links does not have a significant effect on their overall rigid body motion as well as the vehicle dynamics, a partially linearized set of differential equations of motion of the track links is obtained. The equations associated with the rigid body motion are used to predict the generalized contact, inertia, and constraint forces associated with the deformation degrees of freedom of the track links. These forces are introduced to the track link flexibility equations which are used to calculate the deformations of the links resulting from the vehicle motion. A detailed three-dimensional finite element model of the track link is developed and utilized to predict the natural frequencies and mode shapes. The terms that represent the rigid body inertia, centrifugal and Coriolis forces in the equations of motion associated with the elastic coordinates of the track link are described in detail. A computational procedure for determining the generalized constraint forces associated with the elastic coordinates of the deformable chain links is presented. The finite element model is then used to determine the deformations of the track links resulting from the contact, inertia, and constraint forces. The results of the dynamic stress analysis of the track links are presented and the differences between these results and the results obtained by using the static stress analysis are demonstrated.

An Efficient Implementation of the Recursive Approach to Flexible Multibody Dynamics

Abstract: This paper deals with the efficient extension of the recursive formalism (articulated body inertia) for flexible multibody systems. Present recursive formalisms for flexible multibody systems require the inversion of the mass matrix with the dimension equal to the number of flexible degrees of freedom of particular bodies. This is completely removed. The paper describes the derivation of equations of motion expressed in the local coordinate system attached to the body, then the discretization of these equations of motion based on component mode synthesis and FEM shape functions and, finally, two versions of the new recursive formalism.

Contact Mechanics in Multibody Systems

Abstract: Contact forces are modeled as applied and constraint forces, the latter resulting from unilateral constraints. This modeling of a contact is called structure-variant. A description is presented which comprises all of the possibilities of constrained and unconstrained motion due to contact in one single set of equations. The corresponding contact forces can be activated and deactivated easily. The procedure yields an advantage in finding a compatible set of constraints and applied forces after a contact event, resulting in a discontinuity. It is necessary to formulate the constraint equations on a position, velocity, acceleration and velocity increment level. The first two choices are needed for time-integration. The third option is required to calculate the discontinuities in the accelerations, in case of a transition from sliding to stiction and vice versa. The constraint equations on velocity increment level are used to calculate the discontinuities in the velocities caused by an impact. The structure-variant modeling of contact is implemented in the multibody program SIMPACK using the procedures which are already available. Its applicability is illustrated by a simulation of a docking manoeuvre of spacecrafts and the analysis of the gripping with a robot hand. For both of the examples a comparison is made between the structure-variant modeling and an elastic contact approach applied frequently.

Nonlinear Dynamic Model of a System of Flexible Bodies Using Augmented Bodies

Abstract: The aim of this paper is to present kinematical and dynamical models of a system of flexible bodies in a compact form suitable for modeling, identification or control. Use of a Taylor series expansion of the body deformation in the kinematical model presents a way to refine the deformation description by increasing the expansion order. Including the definition of augmented bodies in the model permits us to write the equations of motion in a more compact form. It also gives a formulation of the dynamical model of the system that is linear in terms of the mass parameters. Then it a priori gathers the mass parameters in groups that have independent influences to the dynamical model. These properties are particularly appreciated when the purpose of modeling is to identify the multibody system.

Feedback Control of Planar Linkages Using a Linearizing Filter: Theory and Experiments

Abstract: The motion control of mechanical systems with flexible links is investigated. Issues addressed are the modeling and simulations, the design of a feedback control scheme and its implementation on an actual system. The modeling method used is a combination of a spline-based spatial discretization technique and the natural orthogonal complement of the kinematic constraints that eliminates the constraint forces and moments from the mathematical model. The control algorithm consists of two parts, namely, the uncoupling of nonlinear equations of motion and the filtering of consequent nonworking constraint forces. This control scheme is implemented on a prototype four-bar flexible mechanism. Results show that the proposed control scheme provides successful trajectory tracking while suppressing the vibration triggered by a doublet-type of disturbance.