József Kövecses

Dynamics modeling and simulation of constrained robotic systems

Dynamic analysis is the basic element of mechanical design and control of mechanisms. This work intends to address dynamic methods relevant to constrained robots and mechanisms from a unified analytical point of view, which is based on differential variational principles. A constrained robotic system is a mechanical system, where we need to consider kinematic constraint conditions explicitly in dynamic modeling and analysis. Important classes of constrained robotic systems include, for example, parallel robots and closed-chain mechanisms where the loop closure conditions can be generally expressed by nonlinear holonomic constraint equations, and mobile robots where the system is subjected to linear nonholonomic constraints. Our primary focus is on systems with nonlinear holonomic constraint equations (e.g., parallel robots, robotic systems with closed kinematic chains). However, the approach and formulation discussed are also applicable for nonholonomic systems. In the framework presented, many approaches can be discussed, and new directions can be highlighted that can contribute to the better understanding of dynamic behavior. Two new approaches for the dynamic analysis and for the simulation of constrained robotic systems are introduced and discussed. The paper also points out some areas and methods where further exploration is necessary to shed light on problems and applications related to constrained robotic systems.

Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation

In this paper, we generalize the idea of the free-body diagram for analytical mechanics for representations of mechanical systems in configuration space. The configuration space is characterized locally by an Euclidean tangent space. A key element in this work relies on the relaxation of constraint conditions. A new set of steps is proposed to treat constrained systems. According to this, the analysis should be broken down to two levels: (1) the specification of a transformation via the relaxation of the constraints; this defines a subspace, the space of constrained motion; and (2) specification of conditions on the motion in the space of constrained motion. The formulation and analysis associated with the first step can be seen as the generalization of the idea of the free-body diagram. This formulation is worked out in detail in this paper. The complement of the space of constrained motion is the space of admissible motion. The parametrization of this second subspace is generally the task of the analyst. If the two subspaces are orthogonal then useful decoupling can be achieved in the dynamics formulation. Conditions are developed for this orthogonality. Based on this, the dynamic equations are developed for constrained and admissible motions. These are the dynamic equilibrium equations associated with the generalized free-body diagram. They are valid for a broad range of constrained systems, which can include, for example, bilaterally constrained systems, redundantly constrained systems, unilaterally constrained systems, and nonideal constraint realization.

Finite and impulsive motion of constrained mechanical systems via Jourdain's principle: discrete and hybrid parameter models

The main purpose of this paper is to present a unified analytical dynamics framework for the analysis of finite and impulsive motion of mechanical systems using Jourdains principle. Emphasis is given to the general case when a mechanical system is described by a hybrid (discrete-distributed) parameter model. A large group of finite and impulsive, generally non-holonomic, constraints are analysed in detail and a so-called extended Appellian classification is presented for these constrained motion problems. The fundamental dynamic equation of constrained systems is developed in terms of velocity variations (Jourdains principle). Based on this equation and the constraints, the methods of quasivelocities and Lagrangian multipliers are adopted and interpreted for the finite motion of hybrid parameter models of mechanical systems; and the methods of independent quasivelocity variations and Lagrangian multipliers are introduced for the analysis of impulsive motion of such models. To illustrate the proposed material, an example of a one-link flexible arm intercepting and capturing a moving target is considered.

Dynamics Modeling and Analysis of Thin-Walled Aerospace Structures for Fixture Design in Multiaxis Milling

Milling of thin-walled aerospace structures is a critical process due to the high flexibility of the workpiece. Current practices in the fixture design and the choice of cutting parameters rely solely on conservative guidelines and the designers experience. This is a result of the lack of computationally efficient dynamic models to represent the dynamic response of the workpiece during machining, and the interaction between the workpiece, fixture and the cutting forces. This paper presents a novel dynamic formulation of typical thin-walled pockets encountered in aerospace structures. It is based on an analytical description of a five-sided pocket using a plate model. An off-line calibration of the model parameters, using global and local optimization, is performed in order to match the dynamic response of the pocket structure. The developed simplified model is based on Rayleighs energy method. Various pocket shapes are examined under different loading conditions and compared to finite element (FE) predictions and experimental results. In both cases, the results obtained by the developed model are in excellent agreement. This proposed approach resulted in one to two orders of magnitude reduction in computational time when compared to FE models, with a prediction error less than 10%.

Generalization of the Energetic Coefficient of Restitution for Contacts in Multibody Systems

This paper introduces a new interpretation of the energetic coefficient of restitution, especially applicable to contact involving multibody systems. This interpretation generalizes the concept of the energetic coefficient of restitution and allows for consideration of simultaneous multiple-point contact scenarios. Such a generalization is obtained by an analysis of energy absorption and restitution during impact, using a decomposition technique, which exactly decouples the kinetic energy associated with the normal and tangential directions of the contact pairs. The main advantages of the new definition and its potential applications are highlighted.

Development of a New Model for the Varying Dynamics of Flexible Pocket-Structures During Machining

Many of the aerospace components are characterized by having pocket-shaped thin-walled structures. During milling, the varying dynamics of the workpiece due to the change of thickness affects the final part quality. Available dynamic models rely on computationally prohibitive techniques that limit their use in the aerospace industry. In this paper, a new dynamic model was developed to predict the vibrations of thin-walled pocket structures during milling while taking into account the continuous change of thickness. The model is based on representing the change of thickness of a pocket-structure with a two-directional multispan plate. For the model formulation, the Rayleigh–Ritz method is used together with multispan beam models for the trial functions in both the x- and y-directions. An extensive finite element (FE) validation of the developed model was performed for different aspect ratios of rectangular and nonrectangular pockets and various change of thickness schemes. It was shown that the proposed model can accurately capture the dynamic effect of the change of thickness with prediction errors of less than 5% and at least 20 times reduction in the computation time. Experimental validation of the models was performed through the machining of thin-walled components. The predictions of the developed models were found to be in excellent agreement with the measured dynamic responses.

Parameter Analysis and Normalization for the Dynamics and Design of Multibody Systems

In this paper, we introduce a novel concept for parametric studies in multibody dynamics. This includes a technique to perform a natural normalization of the dynamics in terms of inertial parameters. This normalization technique rises out from the underlying physical structure of the system and the trajectory investigated. This structure is mathematically expressed in the form of eigenvalue problems. It leads to the introduction of the concept of dimensionless inertial parameters. This, in turn, makes it possible to introduce an analysis approach for studying design and control problems where parameter estimation and sensitivity are of importance.

Dynamic Modeling and Analysis of a Robot Manipulator Intercepting and Capturing a Moving Object, with the Consideration of Structural Flexibility

In this paper we investigate the dynamics of robotic interception and capture of a moving object. This problem, i.e., the interception and capture of a moving object by a robot, is called dynamic mass capture. The effects of structural flexibility of the robot is taken into consideration. In terms of time, the analysis is divided into three phases: before capture (finite motion), at the vicinity of interception and capture (impulsive motion), and after capture (finite motion). Special attention is paid to the modeling of the second phase when the robot captures the target and it becomes part of the end effector, thus, the systems degrees of freedom suddenly change. To decribe this event, a novel approach is proposed. This is based on the use of a class of impulsive constraints, the so-called inert constraints. Jourdains principle is employed to derive the dynamic equations for both finite and impulsive motions. Simulation results are presented for two examples: a single flexible link and a two-link manipulator capturing moving objects. In the example of the single link, the results are compared with the observations of an experiment, and good agreement is found between experimental and simulation results.

A Penalty Formulation for Dynamics Analysis of Redundant Mechanical Systems

Redundancy in the constraining of mechanical systems achieves more stability and larger load capacity for the system, while in actuation it provides better robustness against singularities and higher maneuverability. Few techniques have been developed with the aim to handle redundancy and singularities in dynamics analysis, and further research is still needed in this area. In this paper, we illustrate the concept of actuating and passive constraints. Then, we expand on the existing penalty techniques by incorporating the concept of actuating and passive constraints to present a penalty formulation that is capable of efficiently handling singularities and redundancy in constraining and actuation and can carry out either forward or inverse dynamics analysis of mechanical systems. As such, the proposed approach is referred to as the actuating-passive constraints penalty approach.

A piezoresistive tactile sensor for tissue characterization during catheter-based cardiac surgery

Currently, most of mitral valve annuloplasty surgeries are performed by using open heart surgery. However, if such operation would be performed by using minimally invasive surgery via catheter‐based techniques (CBT), it offers various advantages for both surgeons and patients.