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 GIOVANNI MOTTOLA Assegnista di ricercaDipartimento di Scienze e Metodi dell'Ingegneria

## Pubblicazioni

2023 - Nomograms in the History and Education of Machine Mechanics [Articolo su rivista]
Mottola, Giovanni; Cocconcelli, Marco
abstract

Computing formulae and solving equations are essential elements of scientific analysis. While today digital tools are almost always applied, analog computing is a rich part of the larger history of science and technology. Graphical methods are an integral element of computing history and still find some use today. This paper presents the history of nomograms, a historically-relevant tool for solving mathematical problems in various branches of science and engineering; in particular, we consider their role in mechanical engineering, especially for education, and discuss their mathematical properties. Each nomogram is a graphical description of a specific mathematical equation, designed such that the solution can be found through a simple geometric construction that can be performed with a straightedge. By design, using nomograms requires little skills and can be done even in adverse environments; a solution of sufficient accuracy for most purposes can then be found in a very short time. Another important advantage of nomograms is that they offer clear insight on the relationships between the variables, an insight which can be lost by looking at a complex equation. First introduced in the late 19th century, nomograms were used by engineers and scientists due to their speed with respect to manual calculations, before being superseded by computers. While now mostly obsolete in practice, nomograms can still prove useful in workshops and teaching classes: we thus also discuss their educational applications and present a few original examples.

2022 - Gravity Balancing of Parallel Robots by Constant-Force Generators [Capitolo/Saggio]
Mottola, G.; Cocconcelli, M.; Rubini, R.; Carricato, M.
abstract

This Chapter reviews the literature on gravity balancing for parallel robots by using so-called constant-force generators. Parallel robots are formed by several kinematic chains connecting, in parallel, a fixed base to a moving end-effector. A constant-force generator is a mechanism that is able to exert, at a given point, a force having constant magnitude and direction. Gravity balancing of serial robots is a well established technique; conversely, application in parallel robotics is controversial. Indeed, the addition of gravity-balancing mechanisms to a parallel robot may worsen its dynamic behavior, as shown in some referenced works. In this Chapter, we introduce a taxonomy of constant-force generators proposed so far in the literature, including mass and spring balancing methods, toghether with more niche concepts. We also summarize design considerations of practical concern.

2022 - Nomograms: An Old Tool with New Applications [Relazione in Atti di Convegno]
Mottola, G.; Cocconcelli, M.
abstract

In this paper, we consider the history of nomograms as a computational tool in mechanical engineering, together with their potential applications for teaching purposes, and summarize the mathematical methods used to derive them. Nomograms are graphical descriptions of a mathematical problem, such that the desired solution may be derived through a simple geometric construction, which usually requires nothing more than a straightedge. This way, a reasonably accurate solution to a complex problem can be quickly obtained even in adverse environmental conditions by low-skilled users; moreover, a nomogram can provide immediate insight on the relationship between the variables. Nomograms date back to the 1800s and have been used by engineers for decades, due to their convenience over manual computation, before computers became widespread. While nomograms have now been largely superseded as engineering tools, our analysis shows that they can still have some applications in workshops and for teaching purposes.

2019 - Dynamically feasible motions of a class of purely-translational cable-suspended parallel robots [Articolo su rivista]
Mottola, Giovanni; Gosselin, Clément; Carricato, Marco
abstract

We consider dynamic motions of a spatial robot suspended by six cables, arranged so as to form three parallelograms. Each parallelogram is composed by two parallel cables sharing the same length. Due to this arrangement, the end-effector can only translate. The cables in each parallelogram can be actuated by one motor: only three motors are then required, which reduces the robot complexity and cost. This robot may perform pick-and-place operations over large workspaces. We find tight conditions for feasibility of dynamic trajectories for the general architecture, and also special conditions such that the robot is dynamically equivalent to a 3-cable robot with a point-mass end-effector: then, the feasibility conditions previously developed for the dynamic trajectories of 3-cable point-mass robots can be profitably reused for the present case. To practically realize such dynamic trajectories, we also analyze the reachable, singularity-free and interference-free workspace, finding analytical expressions of their loci. Finally, we perform experiments where the robot follows dynamic trajectories outside its static workspace, thus finding confirmation that the orientation remains approximately constant.

2019 - Effect of Actuation Errors on a Purely-Translational Spatial Cable-Driven Parallel Robot [Relazione in Atti di Convegno]
Mottola, Giovanni; Gosselin, Clement; Carricato, Marco
abstract

In this paper, we analyze a spatial 3-DoF cable-driven robot with a finite-size end-effector. The robot has 6 cables that define 3 parallelograms, each composed by two cables: thus, the robot cannot rotate, but only perform translational motions. Also, since the two cables in a parallelogram are always kept at the same length, they can be actuated by the same motor, thereby meaning that the 3-DoF cable-suspended robot requires only 3 actuators. The kinematic and dynamic behaviour of such robots was studied in previous works. The property of purely-translational motion depends on a precise control of the extension of the cables. Therefore, in this paper we study how the platform pose changes as some errors of known maximum magnitude are introduced in the cable lengths. Finally, the results from both numerical simulations and tests are presented. The orientation of the platform is shown to be robust to cable extension errors.

2018 - Dynamically feasible periodic trajectories for generic spatial three-degree-of-freedom cable-suspended parallel robots [Articolo su rivista]
Mottola, Giovanni; Gosselin, Clément; Carricato, Marco
abstract

Cable-suspended robots may move beyond their static workspace by keeping all cables under tension, thanks to end-effector inertia forces. This may be used to extend the robot capabilities, by choosing suitable dynamical trajectories. In this paper, we consider three-dimensional (3D) elliptical trajectories of a point-mass end effector suspended by three cables from a base of generic geometry. Elliptical trajectories are the most general type of spatial sinusoidal motions. We find a range of admissible frequencies for which said trajectories are feasible; we also show that there is a special frequency, which allows the robot to have arbitrarily large oscillations. The feasibility of these trajectories is verified via algebraic conditions that can be quickly verified, thus being compatible with real-time applications. By generalizing previous studies, we also study the possibility to change the frequency of oscillation: this allows the velocity at which a given ellipse is tracked to be varied, thus providing more latitude in the trajectory definition. We finally study transition trajectories to move the robot from an initial state of rest (within the static workspace) to the elliptical trajectory (and vice versa) or to connect two identical ellipses having different centers.

2018 - Dynamically-feasible elliptical trajectories for fully constrained 3-DOF cable-suspended parallel robots [Capitolo/Saggio]
Mottola, Giovanni; Gosselin, Clément; Carricato, Marco
abstract

A cable suspended robot can be moved beyond its static workspace while keeping all cables in tension, by relying on end-effector inertia forces. This allows the robot capabilities to be extended by choosing suitable dynamical trajectories. In this paper, we study 3D elliptical motions, which are the most general case of spatial sinusoidal oscillations, for a robot with a point-mass end-effector and an arbitrary base architecture. We find algebraic conditions that define the range of admissible frequencies for feasible trajectories; furthermore, we show that, under certain conditions, a special frequency exists, which allows arbitrarily large oscillations to be reached. We also study transition trajectories that displace the robot from an initial state of rest (within the static workspace) to the elliptical trajectory, and vice versa.