Rosario Sinatra

Kinematics, dynamics and control of a hybrid robot Wheeleg

Abstract In this paper, we propose a mathematical model for the kinematics of a hybrid robot, called Wheeleg. The wheeled-legged robot has two pneumatically actuated front legs, each with three degrees of freedom, and two rear wheels independently actuated. Based on the proposed model, the dynamics equations of the manipulator are developed using the natural orthogonal complement method. Equations are implemented in an algorithm used to study the kinematics and the dynamics of the mobile robot. Simulations are provided to demonstrate the method developed. Successively, a brief description is given of the control architecture designed and implemented. In conclusion, some experimental tests of the motion on the horizontal plane are reported.

Kinematics and dynamics of a six-degree-of-freedom parallel manipulator with revolute legs

This paper presents the kinematics and dynamics of a six-degree-of-freedom platform-type parallel manipulator with six revolute legs, i.e. each leg consists of two links that are connected by a revolute joint. Moreover, each leg is connected, in turn, to the base and moving platforms by means of universal and spherical joints, respectively. We first introduce a kinematic model for the manipulator under study. Then, this model is used to derive the kinematics relations of the manipulator at the displacement, velocity and acceleration levels. Based on the proposed model, we develop the dynamics equations of the manipulator using the method of the natural orthogonal complement. The implementation of the model is illustrated by computer simulation and numerical results are presented for a sample trajectory in the Cartesian space.

Tripod Dynamics and Its Inertia Effect

In this paper the tripod dynamics and its inertia effect is studied. The tripod design is becoming popular for the development of parallel kinematic machines (PKMs). The combination of a tripod with a gantry system forms a hybrid machine that offers the advantages from both serial and parallel structures. The tripod dynamics under study includes the mass of the moving platform as well as those of the legs. The natural orthogonal complement method is applied to derive the dynamic equations. The inertia effect of the moving platform and the legs is investigated in terms of two parameters, namely, the ratio of the total leg mass to the mass of the moving platform, and the velocity of the moving platform. The dynamic equations are separated by three terms, inertia, coupling, and gravity. Quantitative studies are carried out by simulation to examine how the two parameters affect the three respective terms. Based on the simulation results, the dynamic equations can be simplified by retaining the dominant terms while neglecting less significant ones. The simplified dynamic equations provide an efficient model for design and control of tripods.

An Algorithm to Study the Elastodynamics of Parallel Kinematic Machines With Lower Kinematic Pairs

In this paper, an algorithm to help designers to integrate the elastodynamics analysis along with the inverse positioning and orienting problems of a parallel kinematic machine (PKM) into a single package is conceived. The proposed algorithm applies concepts from the matrix structural analysis (MSA) and finite element analysis (FEA) to determine the generalized stiffness matrix and the linearized elastodynamics equations of a PKM with only lower kinematic pairs. A PKM is modeled as a system of flexible links and rigid bodies connected by means of joints. Three cases are analyzed to consider the combinations between flexible and rigid bodies in order to find the local stiffness matrices. The latter are combined to obtain the limb matrices and, then, the global stiffness matrix of the whole robotic system. The same nodes coming from the links discretization are considered to include joint masses/inertias into the model. Finally, a case study is proposed to show some feasible applications and to compare results to commercial software for validation.

Kinetostatic and Inertial Conditioning of the McGill Schönflies-Motion Generator

This paper focuses on the optimization of the McGill Schönflies Motion Generator. Recent trends on optimum design of parallel robots led us to investigate the advantages and disadvantages derived from an optimization based on performance indices. Particularly, we optimize here two different indices: the kinematic conditioning and the inertial conditioning, pertaining to the condition number of the Jacobian matrix and to that of the generalized inertia matrix of the robot, respectively. The problem of finding the characteristic length for the robot is first investigated by means of a constrained optimization problem; then plots of the kinetostatic and the inertial conditioning indices are provided for a particular trajectory to be tracked by the moving platform of the SMG. Deep connections appear between the two indices, reflecting a correlation between kinematics and dynamics.

Inverse dynamics of hexapods using the natural orthogonal complement method

The hexapods under study are parallel mechanisms made of fixed-length legs, as opposed to conventional hexapods with extensible legs. The former are becoming popular in developing machine tools for high-speed machining applications. In this paper, the inverse dynamics of hexapods with fixed-length legs is analyzed using the natural orthogonal complement method. This analysis includes the mass of the moving platform as well as those of the legs. The leg masses become important for high-speed applications. In this development, the Newton-Euler formulation is used to model the dynamics of each individual body, including the moving platform and the legs. This is followed by assembling the individual dynamics equations to form the global dynamics equations. Based on the complete kinematics model developed in the paper, an explicit expression is derived for the natural orthogonal complement that effectively eliminates the constraint forces in the global dynamics equations. This leads to the inverse dynamics equations of the hexapods that can be used to compute required actuator forces for given motions. Simulations are provided to demonstrate the developed method.

Effect of dynamic balancing on four-bar linkage vibrations

Investigated in this paper is the effect of dynamic balancing on four-bar linkage vibrations. To conduct this research, cubic spline functions are applied to model link deflections. After deriving the unconstrained link dynamic equations, the natural orthogonal complement is used to assemble the constrained dynamical equations of a dynamically balanced four-bar linkage. Then simulations are performed, the results indicating that the dominant factor on the vibrations of a dynamically balanced four-bar linkage may be the moment of inertia of the counterweight attached to the input link, because the larger the said moment of inertia, the more severe the vibrations undergone by the dynamically balanced four-bar linkage.

Evaluation of the effect of preload force on resonance frequencies for a traveling wave ultrasonic motor

In this paper, a novel method of numerical computation of the natural frequencies, depending on the most important running parameters for an ultrasonic motor, is described. The analyzed configuration by the Space Division of Alenia Spazio, Rome, within an Italian Space Agency (ASI) development program, is the flexural traveling wave one. The dynamic equations for the stator and the rotors of the ultrasonic motor are assumed into a differential system, whose equations are coupled by terms that represent interface generalized forces. In order to calculate natural frequencies of the motor-coupled terms of the equations are worked out with respect to the variables of the degrees of freedom. Hence, the mass, damping, and stiffness matrix for the whole system are obtained, then resonance frequencies, depending on the most important running parameters such as axial preload of the motor, are calculated. The results are compared with numerical ones, obtained by a finite element modeling (FEM) model, showing a good agreement.

The dynamics of parallel Schönflies motion generators: The case of a two-limb system

Abstract The formulation of the mathematical model governing the dynamics of parallel Schönflies motion generators (SMGs) is the subject of this paper. These are robotic systems intended to produce motions that entail displacements of the Schönflies subgroup of rigid-body displacements. Such motions are representative of those produced by the serial robots termed SCARA, which involve three independent translations and one rotation about an axis of fixed direction. The main features of SMGs are illustrated with the aid of the McGill Schönflies motion generator. This robot is composed of two limbs, each being a four-joint RΠΠR - R representing a revolute, Π a Π joint, or a parallelogram linkage - kinematic chain, with only two joints actuated. One important feature of the McGill SMG is its mass distribution, as its moving parts account for about 10 per cent of the mass of its drive units, which are (a) fixed to the robot frame and (b) the only steel parts of the whole robot. Moreover, its joints account for roughly 10 per cent of the total mass of its moving parts, fabricated from aluminium, which justifies neglecting the joint inertia in the mathematical model. This feature calls for a formulation of the model in question in terms of the motor displacements, rather than the joint displacements, as the generalized coordinates of the model. Furthermore, in order to derive the model, the robot is decomposed into two subsystems, the drive and the linkage, the drive being decomposed, in turn, into two subsubsystems, the epicyclic gear train and the right-angled gearbox. The robot kinematics is first derived and then the dynamics model is formulated by means of the natural orthogonal complement. In the framework of this methodology, the inertia and what are called the Coriolis matrices of the mathematical model are additive, in the sense that they can be computed as the sum of the contributions of the different subsystems and subsubsystems of a given mechanical system. The contributions of the subsystems and subsubsystems, in turn, can be computed as the sum of the contributions of the individual moving parts of these. Some general results applicable to all SMGs are derived, which leads to the simplification of the mathematical model of such systems.

Modelling and simulation of multibody mobile robot for volcanic environment explorations

This paper presents a dynamics analysis of a mobile robot, named M6, developed for volcanic environment exploration. The architecture of this kind of robot has six wheels which are coupled to the chassis by means of revolute joints. The robot is built by the DEES of Catania University. A multibody model of the system was constructed in a calculation code. Particular attention was given to the choice of tyre model to simulate the real tyre-road contact. A comparison of the simulation and experimental results confirmed the good agreement between the model and the real system.