Dynamics modelling and control of the 3-RCC translational platform

The article presents the inverse dynamics model of a novel translating parallel machine and proposes the structure of a force controller for the execution of tasks characterised by interaction with the environment. The task space model of machine’s dynamics is obtained in an efficient and compact form by means of the principle of virtual work. A virtual prototyping environment has been set up to test by computer simulation the potential of such kinematic architecture: the resulting dynamics is rather poor, mainly due to the high moving masses, but it is shown that hybrid position/force control schemes should be able to provide good performances, including the case of rather difficult operations, such as the peg-in-hole assembly.     

Numerical solution of certain classes of transport equations in any dimension by Shannon sampling

A method is developed for computing solutions to some class of linear and nonlinear transport equations (hyperbolic partial differential equations with smooth solutions), in any dimension, which exploits Shannon sampling, widely used in information theory and signal processing. The method can be considered a spectral or a wavelet method, strictly related to the existence of characteristics, but allows, in addition, for some precise error estimates in the reconstruction of continuous profiles from discrete data. Non-dissipativity and (in some case) parallelizability are other features of this approach. Monotonicity-preserving cubic splines are used to handle nonuniform sampling. Several numerical examples, in dimension one or two, pertaining to single linear and nonlinear (integro-differential) equations, as well as to certain systems, are given.     

Prototype design of a translating parallel robot

The paper describes the mechanical design of a parallel manipulator for motions of pure translation, whose kinematic analysis has shown very good performances such as a large workspace and small overall dimensions of the mobile platform; in particular, the “Cartesian” structure of the machine allowed to obtain constant accuracy and kinematic properties throughout the workspace. The structural design has minimized the mass of the moving links and, by the combined use of FEM and multibody codes, allowed to take into consideration the high stresses coming from inertial forces and to evaluate a-priori the resulting dynamic properties. A physical prototype has just been built in order to validate the developed models and assess the actual robot performances in real operating conditions. The present research has been partially co-funded by the Italian Ministry of Research and University and by the Polytechnic University of Marche under PRIN03 project “Design and prototyping of application-oriented mini-PKM”.     

Interplay between shape and roughness in early-stage microcapillary imbibition

Flows in microcapillaries and associated imbibition phenomena play a major role across a wide spectrum of practical applications, from oil recovery to inkjet printing and from absorption in porous materials and water transport in trees to biofluidic phenomena in biomedical devices. Early investigations of spontaneous imbibition in capillaries led to the observation of a universal scaling behavior, known as the Lucas-Washburn (LW) law. The LW allows abstraction of many real-life effects, such as the inertia of the fluid, irregularities in the wall geometry, and the finite density of the vacuum phase (gas or vapor) within the channel. Such simplifying assumptions set a constraint on the design of modern microfluidic devices, operating at ever-decreasing space and time scales, where the aforementioned simplifications go under serious question. Here, through a combined use of leading-edge experimental and simulation techniques, we unravel a novel interplay between global shape and nanoscopic roughness. This interplay significantly affects the early-stage energy budget, controlling front propagation in corrugated microchannels. We find that such a budget is governed by a two-scale phenomenon: The global geometry sets the conditions for small-scale structures to develop and propagate ahead of the main front. These small-scale structures probe the fine-scale details of the wall geometry (nanocorrugations), and the additional friction they experience slows the entire front. We speculate that such a two-scale mechanism may provide a fairly general scenario to account for extra dissipative phenomena occurring in capillary flows with nanocorrugated walls.     

Configuration-dependent modal analysis of a Cartesian parallel kinematics manipulator: numerical modeling and experimental validation

In the design optimization of a robot the configuration-dependent modal analysis can be a powerful tool to be exploited when high stiffness and high dynamic performances are concurrently required. In this paper the elastodynamics of a lower-mobility Parallel Kinematic Machine for pure translational motions is analyzed. The vibrational modes and the natural frequencies of the robot are evaluated as functions of the end effector position inside the workspace. A finite element model including kinematic joints is used to perform a series of modal analyses in a grid of points inside the workspace. A polynomial regression gives continuous volume maps of the natural frequencies distributions. The numerical model is validated by comparison with experiments: a modal analysis is conducted on a set of inertance Frequency Response Functions acquired on several points of the machine components as a result of an excitation given by an instrumented hammer. A Natural Frequency Difference analysis validates the model under certain conditions and highlights some critical issues to be focused on in future works.