József Kövecses

A Comparative Study of Approaches to Dynamics Modeling of Contact Transitions in Multibody Systems

This paper presents detailed discussions and a potential grouping of various approaches to the dynamic analysis of the transition phase in multibody contacts. The methods considered are able to address the general case of multiple-point contact. The main grouping principle relies on the fundamental unilateral nature of the contact between two bodies in a multibody system. Based on this, three main classes of modeling techniques are considered.Copyright

Servo-constraint based computed torque control of underactuated mechanical systems

This paper aims to generalize the computed torque control method for underactuated systems which are modeled by a non-minimum set of generalized coordinates subjected to geometric constraints. The control task of the underactuated robot is defined in the form of servo constraint equations that have the same number as the number of independent control inputs. A PD controller is synthesized based on projecting the equations of motion into the nullspace of the distribution matrix of the actuator forces/torques. The results are demonstrated by numerical simulation and experiments conducted on a two degrees-of-freedom device.Copyright

Sensitivity Analysis of Mobile Robots for Unstructured Environments

Simulating mobile robots in unstructured environments requires knowledge of the wheel/terrain interaction phenomena. Even assuming that the terramechanics models available accurately represent the physics of the interaction, estimation of soil parameters can be a source of error. In applications where high robot reliability is mandatory, it is important to realize the influence of possible sources of error on the system behavior. The effect of small variations of parameters on system performance can be studied under sensitivity analysis. In this work, sensitivity analysis is conducted to investigate the effect of perturbations in the soil parameters on the behavior of a single rigid wheel and a vehicle on soft terrain. For the first system the two widely used terramechanics models, Bekker’s and Wong and Reace’s are studied, sensitivity analysis being conducted using direct differentiation. The second system is modeled using Bekker model, sensitivity being obtained using finite differences.Copyright

The Mathematical Model of a Procedure for Percutaneous Annuloplasty

Existing mathematical models of the mitral valve allow the simulation of ring open-heart annuloplasty procedures intended to reduce the lumen of the valve. Using these models, only a posteriori effects can be predicted. With the advent of novel percutaneous annuloplasty approaches, there is a need to describe a priori effects; in particular, this paper focuses on a technique which consists of sequentially installing interconnected anchors around the mitral annulus, whose lumen is reduced by the tightening of the tethered wire. We develop here a static mathematical model of the mitral annulus that takes into account the mechanical response of its tissue and the surrounding muscular tissue. A number of roughly coplanar points corresponding to anchor positions, at about equal distantes, are identified on the annulus. Each of these points is then attached to a linearly elastic spring of a given stiffness, The spring-end is connected to a fixed pinned support, the other end supporting the wire, that forms a loop. With this model we estimate the anchor-points position vectors after lumen reduction and the wire tension that is needed to reduce the perimeter of the polygon defined by the anchor points to a given value, which, for each patient, is related to the desired lumen. This formulation leads to the minimization of the potential energy of the mechanical system over the position vectors of the anchor points after tightening, which are the design variables. These are found by solving the first-order normality conditions of the equality-constrained optimization problem. Preliminary experimental data obtained on cadaveric swine hearts validate the model: it can be used to predict, for a given perimeter size reduction, the wire tension as well as the anchor position after repair.Copyright

EFFECTS OF MASS DISTRIBUTION AND CONFIGURATION ON THE ENERGETIC LOSSES AT IMPACTS OF BIPEDAL WALKING SYSTEMS

Understanding the dynamics of human walking is a complex task due to the interaction of the musculoskeletal and the central nervous systems. Nevertheless, the use of simple models can provide useful insight into the mechanical aspects of bipedal locomotion. Such models exploit the observations that human walking significantly relies on passive dynamics and inverted pendulum-like behaviour. The mechanical analysis of walking involves the study of the finite motion single support phase and the impulsive motion of the impacts that occur at heel strike. Such impacts are dominant events because they represent a sudden topology transition and moreover, they are the main cause of energy consumption during the gait cycle. The aim of this work is to gain insight into the dynamics and energetics of heel strike. We use a concept that decouples the dynamics of the biped to the spaces of admissible and constrained motions at the topology transition. This approach is then applied to a straight-legged biped with upper body. Detailed analysis and discussions are presented to quantify the effects of the mass distribution and the impact configuration on the energetics of walking.Copyright

Dynamics of Multibody Haptic Systems

An essential requirement in haptics is accuracy and transparency of the haptic interface. Haptic devices are usually lightweight robotic systems with which a human operator interacts. In the current literature, dynamic analyses of haptic devices are limited to single degree-of-freedom (DoF) point mass models. In this paper, experimental and simulation studies are conducted to investigate the effects of mechanical design parameters on the performance of such devices. For this purpose two commonly used haptic devices were considered: a two-DoF PANTOGRAPH and a three-DoF PHANToM. The results show that dynamic coupling between the rendered (controlled) and free directions of motion can influence the desired performance. An alternative formulation is outlined in which dynamic behavior of a haptic interface is modeled as a multibody system. The dynamic equations are separated to two sets of equations associated with the rendered and admissible motions. Effects of time delay and discretization stemming from digital realization of the virtual environment can be analyzed using the rendered dynamic equations, while the equations associated with the admissible motions can serve as a basis for performance measure. This formulation can be efficiently used for the complex nonlinear dynamics and stability analyses of haptic interfaces and can provide essential details on the performance of these devices. Stability analysis of a two-DoF five-bar linkage is presented as an example using the proposed formulation.Copyright

Stability Analysis for Haptic Rendering of Virtual Kelvin Viscoelastic Objects

In this paper we investigate the stability properties of a single degree of freedom (DoF) haptic display while a virtual viscoelastic object is touched where the viscoelastic object is modeled using the standard linear solid model (also called the Kelvin model). We will demonstrate that this model leads to a discrete-time PID control-like representation of the virtual environment. A detailed dynamic analysis and simulations are presented in this paper with a particular attention to determine stability charts in the space of the parameters given by the virtual viscoelastic model.Copyright

A Penalty Formulation for Dynamics Analysis of Redundant Mechanical Systems

Redundancy in 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 maneuvrability. Few techniques have been developed to handle redundancy and singularities in dynamics analysis, yet difficulties and mathematical problems continue to manifest. This paper expands on the existing penalty techniques and incorporates the concept of actuating/passive constraints to present an elegant 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, or the APCPA.© 2009 ASME

DYNAMICS OF NON-IDEAL TOPOLOGY TRANSITIONS IN MULTIBODY MECHANICAL SYSTEMS

Mechanical systems with time-varying topology appear frequently in various applications. In this paper, topology changes that can be modeled by means of bilateral impulsive constraints are analyzed. We present a concept to project kinematic and kinetic quantities to two mutually orthogonal subspaces of the tangent space of the mechanical system. This can be used to obtain decoupled formulations of the kinetic energy and the dynamic equations at topology transition. It will be shown that the configuration of the multibody system at topology change significantly influences the projection of non-ideal forces to both subspaces. Experimental analysis, using a dual-pantograph robotic prototype interacting with a stiff environment, is presented to illustrate the material.

Parameter Normalization in Multibody Dynamics

In this paper, we introduce a novel concept for parametric studies in multibody dynamics. This is based on a technique that makes it possible 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, which 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 the decomposition of the array of parameters possible for studying design and control problems where parameter estimation and sensitivity is of importance.Copyright