Bruno Fausto Zappa

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.

A contribution to the dynamics of free-flying space manipulators

This paper deals with the analysis of the motion of free flying space manipulators. One of the problems of this class of robots is that any movement of the joints produces a rotation of its base. This should be avoided. Approximate solutions to this problem have been proposed using the concept of the disturbance map. The paper presents an exact solution showing how a proper design of the robot introduces some dynamic singularities which allow us to plan sequences of movements that do not affect the orientation of the robot base.

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.