Paolo Righettini

A homogeneous matrix approach to 3D kinematics and dynamics — I. Theory

Abstract In this paper we present a new approach to the kinematic and dynamic analysis of rigid body systems in the form of a consistent method employing 4 × 4 matrices. This method can be considered a powerful extension of the well known method of homogeneous transformations proposed by Denavit and Hartenberg. New matrices are introduced to describe the velocity and the acceleration, the momentum, the inertia of bodies and the actions (forces and torques) applied to them. Each matrix contains both the angular and the linear terms and so the “usual” kinematic and dynamic relations can be rewritten, halving the number of equations. The resulting notation and expressions are simple, and very suitable for computer applications. A useful tensor interpretation of this method is also explained, and some connections of this notation with the screw theory and dual-quantities are quoted.

A homogeneous matrix approach to 3D kinematics and dynamics—II. Applications to chains of rigid bodies and serial manipulators

In this paper we present applications of the new approach to the kinematic and dynamic analysis of systems of rigid bodies presented in Part I. An extension of the method to the Lagrangian formulation of the dynamics of chains of rigid bodies is also presented. The kinematic and dynamic analysis is preformed for a generic serial manipulator either in open and closed loop. Two numerical examples concerning an open loop and a closed loop are presented too. Two software packages based on our approach are also briefly introduced.

Vibration control input-laws in point to point motion: Theory and experiments

This paper deals with the common problem of reducing the residual vibration in the point-to-point motion of an elastic system. Preshaped input laws based on acceleration varying only by steps of equal duration has been presented by the authors. In this article a deep investigation on the properties of these laws of motion together with a collection of experimental results is exposed.

Nonlinear modeling and experimental validation of uni-Axial servo-hydraulic shaking table

An effective way for the testing of a large number of systems is using single and multi-Axis shaking tables. Among the possible applications, the civil engineering field stands out for the testing of structures, or part of them, both on a reduced and on a full scale. However, design a high performance controller for a servo-hydraulic shaking table is a difficult problem due to its non-linarites and large friction forces. The goal of this pa- per is to develop and experimentally validate a robust numerical model that simulates the acceleration behavior of a uni-Axial servo-hydraulic shaking table system with considering three friction models, the LuGre model, the modified LuGre model and the new modified LuGre model. First, a full system model of servo- hydraulic system is developed based on fluid mechanical expressions and then the friction force of hydraulic cylinder is modeled and validated on the real shaking table. Data of the experiment are gathered from input command valve, and the output acceleration and position of the table. All models are simulated by using MATLAB and SIMULINK computer program. The parameters of the system and the friction models are estimated by using least square method (LSM). Finally, the comparisons of simulated reults with experimental ones show that the model of the system with considering third model of the friction can predict accurately the shaking tables behaviors.

Design and development of a Cartesian plotter as a way to teach Mechatronics to Mechanical Engineering students

The need for interdisciplinary skills in mechanics, electronics, control theory and computer science was recognized as becoming more and more important for mechanical designers. At this aim, it is since the academic year 2002/2003 that a course on Mechatronic Systems is delivered at Bergamo University as an option in the BS curriculum for mechanical engineering students. The course is mainly based on project oriented learning activities; actually a practical project is developed each year. This paper mainly deals with the description of the mechatronics education activity at Bergamo University, with reference to the 2005/2006 academic year course project: a Cartesian plotter driven by stepper motors

TEACHING TYRE TESTING AND MODELLING TO UNDERGRADUATE MECHANICAL ENGINEERING STUDENTS

Tyre characterization is an important step for full vehicle dynamic simulation: main tyre companies have their own testing machines based on rotating drums or flat beds, while special vehicles are used for tyre testing on real tracks with various road conditions (wet, dry, smooth, harsh…). The use of these experimental data, during a vehicle dynamics simulation performed with a multibody code, is allowed by means of several tools, such as data interpolation, physical or empirical tyre models. Many tyre models, with different degrees of complexity, have been proposed in literature: among them we can cite, because of their widespread use, Pacejka formulas. These well-known formulas present various degrees of load interaction capabilities that, generally, can be switched on/off in Multibody codes used for vehicle simulations. Usually, these programs come with a set of example files, based on these formulas, that describe tyres with various sizes (for cars ranging from city to sport) and that can be used at academic level to perform full vehicle simulations. To foresee the behaviour of such models is not easy and the simple calculation of formula outputs with plenty of graphs is not completely satisfactory; it is more intuitive discover the tyre characteristics using a testing procedure similar to the experimental setups. To this aim a virtual model of a testing machine with serial architecture has been built using MSC Adams. Users of this virtual testing environment, in our case undergraduate Mechanical Engineering students of a course on Vehicle Dynamics at Bergamo University, can obtain quite easily tyre characteristics, varying both test rig settings (camber, slip angle, vertical load and driving torque) as well as acting on tyre models parameters (for example scale factors of Pacejka formulas). Students can also appreciate the differences in tyre behaviour that arise when various load case combinations are activated. Students, that already have some background in Multibody Dynamics, appreciated this approach and after a very short training on the lab they were able to proceed by themselves with a better understanding of tyre characteristics.

Design and experimental tests of a mechatronic device for both active vibration and motion control

This paper deals with the mechatronic design of an active device for both the control of vibration and the trims regulation. In particular, the design concerns a 3 dof actuated device which controls vibrations and trim of a platform. A detailed model of the system has been developed, also identifying some unknown parameters by means of specific experimental tests. The detailed model of the system allowed to set-up an effective control system able also to compensate friction. After the design phase, several experimental tests have been performed, in order to evaluate the performances of the control strategy chosen.