Marco Giovagnoni

A Numerical and Experimental Analysis of a Chain of Flexible Bodies

A flexible multi-body dynamics approach is described. It uses an equivalent rigid link system from which are measured small displacements. The equations of motion are obtained by direct application of the principle of virtual work. Some terms in the virtual and real components have been neglected by virtue of the small displacement assumption. The use of sensitivity coefficients allows one to obtain a formulation which can be easily interfaced with any kinematic solution algorithm. It also enables one to check the correctness of the chosen equivalent rigid link system. The theory is then employed to reproduce numerically the experimental recordings obtained from a flexible linkage. Agreement between experimental and numerical data is good

Frequency dependence of Poisson's ratio using the method of reduced variables

Abstract Measurements of the complex Poissons ratio versus frequency are presented for a common PVC material. Measurements are obtained at several temperatures and then gathered in master-curves for absolute values and phases, by applying the reduced variables method. The curves are flat and this requires special care in applying this method. Reasonable coefficients for the WLF equation have been obtained by applying the causality check before shifting to build up the master curves. Plots of the absolute value at different temperatures overlap well; phase-plots show slopes which do not agree with the general behavior of the master-curve, while mean values of the same plots agree with each other and with the slope of the absolute value. Mismatching of the slopes for the phases is probably due to the plate-effect of the specimen. The causality check, used in determining shifts, compensates for this phenomenon.

Application of causality check and of the reduced variables method for experimental determination of Young's modulus of a viscoelastic material

An accurate determination of the complex dynamic Youngs modulus of a viscoelastic material, in a broad frequency range, is presented in this paper. Curves of Youngs modulus of the tested material (a mixture of polypropylene and calcium carbonate), at different temperatures, are experimentally obtained by means of a laser sensor. The experimental curves are then gathered into a unique master curve, by applying the reduced variables method and a causality check on the curves. The master curve represents Youngs modulus of the viscoelastic material over a much broader frequency range, with respect to the range of a single experimental curve.

Design of a Screw Jack Mechanism to Avoid Self-excited Vibrations

This paper deals with vibratory phenomena that are encountered in screw jack mechanisms, down-motion especially. One can find many practical instances where such mechanisms are subject to vibratory conditions. Besides producing loud noise, vibrations can easily damage the mechanism. Although the screw jack mechanism has been widely employed, its behavior is still not fully understood. In order to explain the vibration phenomenon, we propose a simple two D.o.F. dynamic model. Using this kind of model, it is shown that vibrations can be avoided by reducing the axial stiffness of the screw.

Transient analysis of a flexible crank

Abstract A finite element approach is presented for the dynamic analysis of flexible planar linkages with l d.o.f. An equilibrium equation involving all the mechanisms members is obtained by means of sensitivity coefficients. Numerical results are compared with experimental recordings for the transient response of a flexible crank. Agreement between computed and experimental responses is satisfactory even if some mismatching arises from internal damping.

A method for modeling three-dimensional flexible mechanisms based on an equivalent rigid-link system

Accurate modeling of flexible mechanisms is an open research topic, and different models have been presented since the 1970s. In this work, a novel approach for modeling of three-dimensional flexible mechanisms is presented, based on an equivalent rigid-link system, with respect to which elastic deformations are defined and computed. Concepts of three-dimensional kinematics are used in order to define an effective relationship between the rigid body and the elastic motion. The model is based on a compact kinematic formulation and, for a specific mechanism, there is no need for customizing the formulation. By using the principle of virtual work, a coupled dynamic formulation is found. A crucial advantage of this method is that it is not necessary to explicitly formulate the compatibility equations expressing the link connections, since they are included in the matrices of the system dynamics. The model was applied to a specific three-dimensional flexible mechanism. The results, compared with the Adams-Flex™ software, show a good agreement, thus proving the effectiveness of the methodology.

Experimental Validation of a Dynamic Model for Lightweight Robots

Nowadays, one of the main topics in robotics research is dynamic performance improvement by means of a lightening of the overall system structure. The effective motion and control of these lightweight robotic systems occurs with the use of suitable motion planning and control process. In order to do so, model-based approaches can be adopted by exploiting accurate dynamic models that take into account the inertial and elastic terms that are usually neglected in a heavy rigid link configuration. In this paper, an effective method for modelling spatial lightweight industrial robots based on an Equivalent Rigid Link System approach is considered from an experimental validation perspective. A dynamic simulator implementing the formulation is used and an experimental test-bench is set-up. Experimental tests are carried out with a benchmark L-shape mechanism.

Design and Implementation of a Simulator for 3D Flexible-Link Serial Robots

In this paper, an effective method in dynamic modeling of spatial flexible-link robots under large displacements and small deformations is discussed and a generic Matlab™ software simulator based on it is presented and validated. The adopted method is based on an Equivalent Rigid Link System (ERLS) that enables to decouple the kinematic equations of the ERLS from the compatibility equations of the displacements at the joints allowing an easy and recursive procedure to build the robot dynamic matrices.The simulator is suitable for dynamic modelling of generic 3D serial flexible-link robots. The Matlab™ software simulator is validated with respect to the Adams-Flex™ commercial software, which implements Floating Frame of Reference (FFR) formulation, one of the most used methods for dynamic modeling of multibody flexible-link mechanisms with large displacements and small deformations.Copyright

A fractional derivative model for single-link mechanism vibration

A model for a flexible pinned-free link is defined, which is based on a set of linear uncoupled equations and which is even valid for large rotations. A stress-strain relationship based on fractional derivatives is used to define the material properties. Experimental findings and numerical results are compared.SommarioViene definito un modello matematico lineare per lo studio della dinamica di un meccanismo a membro unico deformabile. Tale modello é costituito da equazioni disaccoppiate che rappresentano sia il moto del corpo rigido di riferimento sia i contributi modali alla vibrazione. La relazione tensione deformazione del materiale considerato é definita a mezzo di derivoidi. I risultati ottenuti numericamente sono confrontati con registrazioni sperimentali.

Modeling the vibration of spatial flexible mechanisms through an equivalent rigid-link system/component mode synthesis approach

In this paper, a novel formulation for modeling the vibration of spatial flexible mechanisms and robots is introduced. The formulation is based on the concepts of equivalent rigid-link system (ERLS) that allows kinematic equations of motion for the ERLS decoupled from the compatibility equations of the displacement at the joint to be written. With respect to the available literature, in which the ERLS concept has been proposed together with a finite element method (FEM) approach (ERLS-FEM), the formulation is extended in this paper through a modal approach and, in particular, a component mode synthesis technique which allows a reduced-order system of dynamic equations to be maintained even when a fine discretization is needed. The model is validated numerically by comparing it with the results obtained from the Adams-Flex™ software, which implements the well-known floating frame of reference approach for a benchmark L-shaped mechanism. A good agreement between the two models is shown.