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

Singularity-free Path-planning of Dexterous Pointing Tasks for a Class of Spherical Parallel Mechanisms

The subject of the paper is the optimization of the pose of redundant spherical parallel manipulators (SPMs) performing pointing tasks, i.e., orienting a line in space; a few hints for the synthesis of dextrous machines are also provided. The strengths of parallel mechanisms are often limited by their singular configurations; to overcome this problem, a class of SPMs with 3-RFR topology (Revolute-Planar-Revolute pairs for each of the three limbs) is investigated, with a comprehensive analysis to identify their singular configurations. The geometric parameters of the architectures are chosen in such a way that all kinds of singularity surfaces come to coincide and a single 3 × 3 Jacobian matrix is able to describe all the singular configurations of the machines. Then, singularities are avoided by exploiting the functional redundancy of the manipulator with respect to the task: an optimization algorithm allows the user to find, for each pointing direction, the robot posture that yields the highest dexterity. Finally, an optimal path is traced on the surface of the sphere of motion by finding the Bézier curve that minimizes a task performance index. The kinematic analysis and optimization are worked out by using a robust formulation based on rotation invariants that allows for a straightforward generalization of the results obtained

Reconfigurability of a class of parallel kinematics machines with lower mobility

The complexity of the kinematic models related to parallel kinematics machines (PKMs) with full mobility has directed recent studies toward the search for lower mobility PKMs. The latter generally have simpler analytic models at the expense of a reduced mobility. More recent works have shown that some kinematic architectures can have a degree of reconfigurability, namely they can change the mobility of their moving platform with local interventions on their mechanical structure [1],[2]. The reconfigurability is often obtained by means of lockable joints, which can be activated or deactivated in order to change leg kinematics. In particular the authors have found that a 3-CPU manipulator, which has three legs with a cylindrical-prismatic-universal sequence of joints, can change its mobility from pure translation to pure rotation if all the universal joints are reconfigurable [3]. In fact, the universal joints can be thought of as lockable spherical joints, which are obtained as a serial chain of three revolute joints where one axis can be locked. Two different configurations of the universal joints can be realized [4]: the first provides the robot with a translating behavior of its moving platform, whereas the second with a rotating one. The present paper extends such study to other kinematics architectures, inheriting the concept of lockable spherical joints. Mathematical tools, like screw theory and group theory, have allowed to identify new topologies of reconfigurable 3-DoF PKMs. All machines can be either translating or rotating PKMs alternately, according to the configuration of the spherical lockable joints. The reconfigurable joints can be activated manually or automatically by means of solenoids or simple brakes

Experimental analysis of a fractional-order control applied to a second order linear system

This paper presents the application of a PDD1/2 fractional order controller to a purely inertial second order system, with the aim of deepening the study of the half-derivative contribution on control performances, in particular on settling time and settling energy of a step response. An approximation of the half-derivative term is proposed for a discrete time version of the controller. The choice is justified by the results obtained by an analysis of order and sampling time influence on accuracy and computation time of a discrete-time fractional derivative. Afterwards, simulation results, all obtained in dimensionless form, are extended to the physical case by means of experimental tests on a rotary axis. In the end it is shown that the half-derivative approximation still allows to improve the system dynamics if compared with a conventional PD controller

Tiny Earth: A big idea for stem education and antibiotic discovery

The world faces two seemingly unrelated challenges—a shortfall in the STEM workforce and increasing antibiotic resistance among bacterial pathogens. We address these two challenges with Tiny Earth, an undergraduate research course that excites students about science and creates a pipeline for antibiotic discovery

Tiny Earth: A Big Idea for STEM Education and Antibiotic Discovery.

The world faces two seemingly unrelated challenges-a shortfall in the STEM workforce and increasing antibiotic resistance among bacterial pathogens. We address these two challenges with Tiny Earth, an undergraduate research course that excites students about science and creates a pipeline for antibiotic discovery