Rotational Mobility Analysis of the 3-RFR Class of Spherical Parallel Robots

none4noSpherical parallel manipulators (SPMs) are used to orient a tool in the space with three degrees of freedom exploiting the strengths of a multi-limb architecture. On the other hand, the performance of parallel kinematics machines (PKMs) is often affected by the occurrence of different kinds of singular configurations. The paper aims at characterizing a class of SPMs for which all singularities come to coincide and a single expression is able to describe all the singular configurations of the machines. The study is focused on a class of SPMs with 3-RFR topology (Revolute-Planar-Revolute pairs for each of the three limbs) addressing the mobility and singularity analysis by means of polynomial decomposition and screw theory. The neatness of the equations that are worked out, expressed in a robust formulation based on rotation invariants, allows a straightforward planning of singularity free tasks and simplifies the synthesis of dexterous machines.openCorinaldi, David; Carbonari, Luca; Palpacelli, Matteo-Claudio; Callegari, MassimoCorinaldi, David; Carbonari, Luca; Palpacelli, Matteo-Claudio; Callegari, Massim

Task Optimization of Functionally Redundant Parallel Kinematic Machines

Ad oggi, l'impiego di robot industriali è sempre più diffuso per via della loro versatilità. Spesso tali macchine hanno una completa abilità nel posizionare e orientare in terminale in modo da coprire un campo di compiti da eseguire più variegato. Tuttavia esiste una vasta classe di compiti industriali che rendono ininfluente, al fine di realizzazione del task, l'orientamento del terminale in una direzione, per esempio le operazioni di fresatura, saldatura e sgrossatura. Chiaramente questo implica una situazione di ridondanza tra robot e compito da eseguire, che porta alla domanda: quale orientamento attorno tale asse conviene far adottare al terminale? La ridondanza costituisce un potenziale e l'esigenza di risultati sempre più stingenti ha guidato la ricerca verso la formulazione di tale domanda in un problema di ottimizzazione, trovando risposta nella sua successiva risoluzione. Nella definizione del problema ci si affida ad una funzione obiettivo spesso legata ad indici che quantificano le prestazioni del robot e che dipendono dalla sua postura assunta. L’argomento principale della tesi è la ridondanza funzionale che finora ha coinvolto i manipolatori seriali; nonostante l’estensione di queste teorie alla classe dei robot paralleli sia spesso dedotta, uno studio esaustivo non è ancora presente. Queste macchine parallele sono conosciute per avere alta rigidità, precisione e capacità di carico, caratteristiche che le rendono allettanti per le lavorazioni meccaniche. La tesi affronta la scrittura e la risoluzione numerica del problema di ottimizzazione per individuare la postura migliore di manipolatori paralleli in situazioni di ridondanza funzionale. Lo studio ha come oggetto una particolare classe di robot paralleli in grado di moti di pura rotazione del terminale per mettere in luce i vantaggi legati all'architettura che li accomuna; il problema si estende fino alla pianificazione ottima di traiettorie di puntamento con speciale enfasi sui compiti manifatturieri

Task Optimization of Functionally Redundant Parallel Kinematics Machines

Ad oggi, l'impiego di robot industriali è sempre più diffuso per via della loro versatilità. Spesso tali macchine hanno una completa abilità nel posizionare e orientare il terminale in modo da coprire un campo di compiti da eseguire più variegato. Tuttavia esiste una vasta classe di compiti industriali che rendono ininfluente, al fine della realizzazione del compito, l'orientamento del terminale in una direzione, come ad esempio le operazioni di fresatura, saldatura e sgrossatura. Chiaramente questo implica una situazione di ridondanza tra robot e compito da eseguire, che porta alla domanda: quale orientamento attorno tale direzione conviene far adottare al terminale? La ridondanza costituisce un potenziale e l'esigenza di risultati sempre più stingenti ha guidato la ricerca verso la formulazione di tale domanda in un problema di ottimizzazione, trovando risposta nella sua successiva risoluzione. Nella definizione del problema ci si affida ad una funzione obiettivo spesso legata ad indici che quantificano le prestazioni del robot e che dipendono dalla configurazione assunta. L'argomento principale della tesi è la ridondanza funzionale che finora ha coinvolto i manipolatori seriali; nonostante l'estensione di queste teorie alla classe dei robot paralleli sia spesso dedotta, uno studio esaustivo non è ancora presente. I robot paralleli sono conosciuti per avere alta rigidezza, precisione e capacità di carico, caratteristiche che le rendono allettanti per le lavorazioni meccaniche. La tesi affronta la scrittura e la risoluzione numerica del problema di ottimizzazione per individuare la configurazione migliore di manipolatori paralleli in situazioni di ridondanza funzionale. Lo studio ha come oggetto la classe di robot paralleli il cui terminale può puramente ruotare per mettere in luce i vantaggi legati alla loro architettura; il problema viene esteso fino alla pianificazione ottima di traiettorie di puntamento con speciale enfasi sui compiti manifatturieri.Nowadays, the use of industrial robots is increasingly popular because of their versatility. Frequently, these manipulators have a full ability to position and to orient the end-effector so as to cover a more varied range of tasks to be performed. However, there is a large class of industrial tasks in which the orientation of the terminal in one direction makes no influence to the achievement of the task, e.g. in milling, welding and deburring operations. Clearly this implies a redundancy situation between the manipulator and the task at hand, leading to the question: which orientation along this axis should the end-effector take during the task? Redundancy is a potential and the need for better performances has recently driven research into the formulation of the questions in an optimization problem and the subsequent resolution by means of algorithms. In the definition of the problem, we entrust to an objective function, often linked to indices that quantify the kinematic-static or dynamic performances of the robot and which depend on the posture assumed by the manipulator. The main subject of the thesis is functional redundancy which, so far, has involved serial manipulators; although the extension of the theories to the parallel kinematic machines (PKM) class is often deducted, a comprehensive study is missing. PKM are known to have strengths like higher rigidity, precision and load capacity than serial robots, features that make them more attractive for machining purposes. This thesis addresses the formulation and the resolution of the optimization problem to and the best posture of PKM in functional redundancy situations. The focus is on a particular class of parallel robots, able to the pure rotation of their mobile platform, and it allows to detect the advantages related to the particular architecture that they share. The topic is then extended to the optimal planning of pointing trajectories, with special emphasis on manufacturing tasks

Optimal Motion Planning for Fast Pointing Tasks with Spherical Parallel Manipulators

Spherical Parallel Manipulators can be effectively used for the execution of pointing tasks provided that their functional redundancy is well exploited. The present paper shows how the dynamic behavior of parallel wrists can be enhanced by optimizing their posture through suitable performance indices; the indices used in the paper are based on the manipulator inertia matrix reduced to the mobile platform, which can be readily worked out from the total kinetic energy of the wrist. First, the redundancy is solved by finding, for each pointing direction, the posture leading to the best dynamic manipulation capacity. First, the redundancy is solved by finding, for each pointing direction, the posture leading to the best dynamic manipulation capacity. and a path is planned on the surface of a sphere by means of B´ezier curves; in this case, the performance function of the optimization problem drives the platform through the spherical attitudes that grant the maximum angular accelerations along a useful direction. The theoretical results are verified in simulation for the 3-CPU manipulator by means of inverse dynamic analyses performed in a multi-body software environment; however, the developed methodology is of general use and the paper is aimed at showing how it can be applied to a whole class of spherical parallel robots

Sensitivity Analysis and Model Validation of a 2-DoF Mini Spherical Robot

This paper is focused on the development and validation of an error kinematic model of a mini spherical robot, aimed at its kinematic calibration. The robot is actually a spatial five-bar linkage, provided with two rotational degrees of freedom. A non-overconstrained kinematics is assumed for the robot in order to provide a simple mathematical model and allow a sensitivity analysis of all the involved geometric parameters. A simplified version of the model is proposed. It differs only for the degree of approximation. A comparison between full and reduced models is presented by means of numerical simulations, analyzing their behavior in a significant region of the robot workspace. In order to validate both of them a robot calibration is carried out on a physical prototype of the robot using a vision system, namely a fixed camera in a eye-to-hand configuration. An iterative algorithm aimed at the experimental identification of the geometric data of the robot is used. Some experimental results show the effectiveness of the study

Sensitivity analysis of a mini pointing device

The paper presents a preliminary study needed to carry out a kinematic calibration procedure for a mini pointing device. The latter inherits its kinematics from a conventional five-bar linkage. A sensitivity analysis of all the geometric parameters involved in the kinematic model of the device is performed within the device workspace. A model is proposed by assuming a non overconstrained kinematics for the machine. Such assumption allows to consider a coupled rotational and translational motion of its moving platform, that is usually designed to have a fixed center of rotation. Results show how the model can be simplified without a significant reduction of its position accuracy, at least in a significant region of the manipulator workspace

Synthesis of a Spatial 3-dof Deployable Mechanism to Grasp Stacked Non-Rigid Materials

The paper deals with the synthesis of a novel deployable mechanism with three decoupled degrees of freedom for the handling of large plies of non-rigid material stacked on a beam. The gripper structure is made up of a repeated deployable unit. This basic mechanism is an assembly of Sarrus and scissor linkage: the first to move the unit in three independent directions and the other to transmit the motion to adjacent elements. The particular shape of the beam requires a symmetrical transmission of motion solved by adding linkages of the same type. The final assembly keeps decoupled the three degrees of freedom, which actuated are able to make an anisotropic scaling of the whole on a skew but symmetrical surface. Moreover, the kinematics analysis highlights the scale transformation of the structure and simulations are performed to verify the reconfigurability

Automated disassembly of electronic components: Feasibility and technical implementation

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A Gripper For Handling Large Leather Plies Stacked On Beams

The paper presents the preliminary design of a novel gripper able to grasp large non-rigid materials that has been conceived to face the challenge of automatic handling tasks in the leather industry. The design has been driven by the requirements to limit production costs and the complexity of the grasping device. A statistical analysis of the different templates sizes has allowed to identify a fixed configuration of the gripping points able to properly pick all the sheets within a great confidence interval. According to the varying shape of the leather templates themselves, that is due to their stacking in plies on the beam, the trajectory of the gripping points has been studied and arranged. Due to the irregular shape of the large sheets that are handled, the edges of the non-rigid materials out of the gripping area might flutter during the transferring phase: a four-bar linkage has been specifically designed, so that the motion of its end-effector prevents unwanted leather creases