R. Di Gregorio - Academia.edu (original) (raw)

Papers by R. Di Gregorio

Advances in Mechanism and Machine Science, 2019

The use of complex numbers for systematically writing the constraint equations of planar mechanis... more The use of complex numbers for systematically writing the constraint equations of planar mechanisms is often limited to linkages (i.e., mechanisms containing only lower pairs). The possible presence of higher pairs in these mechanisms is usually managed through either equivalent linkages or apparent velocity/acceleration equations. Both these methods are simple to implement for a single mechanism configuration, but become cumbersome when continuous motion has to be analyzed. Other approaches use ad hoc auxiliary equations. Here, a general notation that brings to select particular auxiliary equations is proposed. The proposed notation, over being numerically efficient, is easy to present in graduate and/or undergraduate courses for extending the complex number method to higher pairs.

Mechanism and Machine Theory, Dec 1, 2019

In the literature, velocity coefficients (VCs) and acceleration coefficients (ACs) were substanti... more In the literature, velocity coefficients (VCs) and acceleration coefficients (ACs) were substantially proposed for single-degree-of-freedom (single-DOF) planar mechanisms. Their effectiveness in solving the kinematic analysis of these mechanisms is due to the fact that they only depend on the mechanism configuration. Such property also holds when they are defined for spatial single-DOF scleronomic and holonomic mechanisms, but was not exploited; moreover, some extensions of the VC and AC concepts to multi-DOF planar (or spatial scleronomic and holonomic) mechanisms are possible, but have not proved their practical usefulness. Here, first, the velocity-coefficient vectors (VCVs) together with their Jacobians (acceleration-coefficient Jacobians (ACJs) are proposed as an extension of the concepts of VC and AC to multi-DOF scleronomic and holonomic mechanisms. Then, a general algorithm, based on VCVs and ACJs and on a notation, previously presented by the author, which uses the complex-number method, is proposed for solving the kinematic-analysis problems of multi-DOF planar mechanisms and to find their links' dead-center positions. The effectiveness of the proposed algorithm is also illustrated by applying it to a case study. The proposed algorithm is efficient enough for constituting the kinematic block of any dynamic model of these mechanisms, and simple enough for being presented in graduate courses.

Machines, Aug 26, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Journal of Mechanisms and Robotics, Feb 25, 2019

Mechanism and Machine Theory, Sep 1, 2019

Robotica

The concept of distance between two rigid-body poses is important in path planning, positioning p... more The concept of distance between two rigid-body poses is important in path planning, positioning precision, mechanism synthesis, and in many other applications. In the definition of such a distance, two approaches mainly prevail, which lead to a number of formulas devised to match the needs of motion tasks. Despite the different approaches and formulas, some important theoretical results, which drive toward distance-metrics definitions useful for design and application purposes, have been stated. This paper summarizes the two different approaches together with a critical review of the literature on the distance metrics they generated, and, then, it illustrates a technique, previously proposed by the author, for combining different metrics to obtain novel distance-metric definitions that are tailored to specific applications.

Volume 5B: 42nd Mechanisms and Robotics Conference, 2018

The extended Jacobian is a solution technique of redundant robot’s instantaneous kinematics. It i... more The extended Jacobian is a solution technique of redundant robot’s instantaneous kinematics. It is based on the definition of secondary tasks through constraint functions that are added to the mapping between joint rates and end-effector’s twist. Several approaches showed its potential, its applications and limitations. In general, the constraint functions are a linear combination of basic functions with constant coefficients. This paper proposes the use of adaptive coefficients in such equations by using the conditioning index of the extended Jacobian as a quality measure. A good conditioning of the extended Jacobian keeps the robot far from singularities and contributes to the solution of the inverse kinematics. In this paper, initially the extended Jacobian and the proposed algorithm are discussed, then two tests in different circumstances are presented to validate the proposal.

2014 IEEE/ASME 10th International Conference on Mechatronic and Embedded Systems and Applications (MESA), 2014

The paper presents the concept of an underactuated spherical wrist with parallel kinematics archi... more The paper presents the concept of an underactuated spherical wrist with parallel kinematics architecture and the use of non-holonomic constraints: two linear actuators are sufficient to drive the 3 d.o.f.'s of the spherical motion since the instantaneous kinematics is limited to span a space of dimension 2 by the presence of a (non-holonomic) roller-sphere contact. The use of 4 position sensors allows to obtain just one solution for the direct orientation problem, with very simple mathematical passages. After having developed the direct and inverse orientation and velocity kinematics, the potential performances of the concept are investigated with reference to a virtual prototype and are compared with the corresponding performances of the original S-3SPU concept it is derived from.

$Research paper thumbnail of A new decoupled 6-DOF parallel mechanism for long bone fracture reduction$

Systems science, 2001

A new decoupled 6-dof parallel mechanism for long bone fracture reduction is presented

International Journal of Robotics and Automation, 2006

A wide family of parallel manipulators (PMs) is the one that groups all the PMs with three legs w... more A wide family of parallel manipulators (PMs) is the one that groups all the PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. One out of these topologies is the SP-PS-RS topology. This paper presents an algorithm that determines all the assembly modes of the structures with topology SP-PS-RS in analytical form. The presented algorithm can be applied without changes to solve, in analytical form, the forward position analysis of any parallel manipulator (SP-PS-RS architecture) which generates a SP-PS-RS structure when the actuators are locked. In particular, the closure equations of a generic SP-PS-RS structure are written. The eliminant of this system of equations is determined and the solution procedure is presented. Finally, the proposed procedure is applied to a real case. This work demonstrates that the solutions of the forward position analysis of any parallel manipulator which generates a SP-PS-RS structure when the actuators are locked are at most twelve.

Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B, 2004

ABSTRACT A wide family of parallel manipulators (PMs) is the one that groups all the PMs with thr... more ABSTRACT A wide family of parallel manipulators (PMs) is the one that groups all the PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. One out of these topologies is the SR-2PS topology (one SR leg and two PS legs). This paper presents an algorithm that determines all the assembly modes of the structures with topology SR-2PS in analytical form. The presented algorithm can be applied without changes to solve, in analytical form, the direct position analysis of any parallel manipulator which generates a SR-2PS structure when the actuators are locked. In particular, the closure equations of a generic structure with topology SR-2PS are written. The eliminant of this system of equations is determined and the solution procedure is presented. Finally, the proposed procedure is applied to a real case. This work demonstrates that the solutions of the direct position analysis of any parallel manipulator which generates a SR-2PS structure when the actuators are locked are at most eight.

Journal of Mechanisms and Robotics, 2015

Mechanisms' instantaneous kinematics is modeled by linear and homogeneous mappings whose coef... more Mechanisms' instantaneous kinematics is modeled by linear and homogeneous mappings whose coefficient matrices are also meaningful to understand their static behavior through the virtual work principle. The analysis of these models is a mandatory step during design. The superposition principle can be used for building and studying linear and homogeneous models. Here, multi-degree-of-freedom (multi-DOF) spherical mechanisms are considered. Their instantaneous-kinematics model is written by exploiting instantaneous-pole-axes' (IPA) properties and the superposition principle. Then, this general model is analyzed and an exhaustive analytic and geometric technique to identify all their singular configurations is deduced. Eventually, the effectiveness of the deduced technique is shown with two relevant case studies.

Volume 5: 27th Biennial Mechanisms and Robotics Conference, 2002

Orientating a rigid body without changing its position is required in many technical applications... more Orientating a rigid body without changing its position is required in many technical applications. This manipulation task is accomplished by manipulators (spherical manipulators) that are just able to make the end effector move according to controlled spherical motions. Spherical manipulators can be either serial or parallel. Parallel architectures are usually more stiff and precise than the serial ones, whereas their structures are more complex than the serial ones. This paper presents a new three-equal-legged spherical parallel manipulator, named 3-RRS wrist. The 3-RRS wrist is not overconstrained and exhibits a very simple architecture employing just three passive revolute pairs, three passive spherical pairs and three actuated revolute pairs adjacent to the frame. The kinematic analysis of the 3-RRS wrist is addressed and fully solved. Finally, its singularity conditions are written in explicit form and discussed. The results of this analysis lead to the conclusion that the new ...

Meccanica, 2014

The direct position analysis of parallel manipulators (PMs) brings to determine a finite number o... more The direct position analysis of parallel manipulators (PMs) brings to determine a finite number of platform poses compatible with an assigned set of actuated-joint variables' values. Therefore, when, during functioning, the need to check the actual platform pose arises, the sensors usually located on the actuators are not sufficient and the additional pieces of information coming from ad-hoc-devised extra sensors are necessary. Here, for the first time, the actual implementation of extra sensors in underactuated parallel wrists (PWs) which contain a nonholonomic constraint is addressed. Differently from ''ordinary'' (i.e., non-underactuated) PWs, these PWs requires a continuous monitoring of the actual platform orientation to compensate the possible sliding in the nonholonomic constraint. Thus, in this case, the algorithms that interpret the pieces of information coming from the sensors must work in real time and must be integrated in the control software that manages the motion of the machine. All these special requirements are satisfied by the proposed algorithm. Moreover, the proposed hardware can also be implemented in some ordinary PWs with a cheap add-on kit.

Robotica, 2005

Tools that make it possible to measure the performances of manipulators are essential in many tec... more Tools that make it possible to measure the performances of manipulators are essential in many technical applications, for instance, when the optimal path to accomplish a task has to be chosen, or when different manipulator architectures have to be compared. This paper proposes some indices that fully describe the passive dynamic performances of manipulators with two degrees of freedom (dof). The pro- posed indices make it possible to compare the passive dynamic performances of different manipulator architectures, which can perform the same tasks, and can be used to build diagrams which highlight the effects of variations in the manipulator geometry on the manipulator dynamics. These features make them easy to be used in a design context. Finally, some applications of the proposed indices will be presented and discussed.

Meccanica, 1996

A procedure for the determination of the actual configuration of the 6–3 type Stewart Platform is... more A procedure for the determination of the actual configuration of the 6–3 type Stewart Platform is presented. The procedure makes use of one extra sensor in addition to the six that provide the mechanism leg lengths. The use of one extra sensor suitably located on the mechanism allows the direct position analysis to be solved in closed form and makes it possible to obtain a one-to-one correspondence between the sensor measurements and the configuration of the mechanism in almost the entire workspace. Particular configurations where the correspondence is not one-to-one are outlined and criteria to identify them given. Sensitivity to sensor measurement errors is investigated.

Journal of Mechanical Design, 1999

In this paper the direct and the inverse position analysis of a 3-dof fully-parallel mechanism, k... more In this paper the direct and the inverse position analysis of a 3-dof fully-parallel mechanism, known as 3-PSP mechanism, is addressed and solved in analytical form. The 3-PSP mechanism consists of two rigid bodies, one movable (platform) and the other fixed (base), connected to each other by means of three equal serial kinematic chains (legs) of type PSP, P and S standing for prismatic and spherical pair respectively. Both the direct and the inverse position analysis of this mechanism lead to nonlinear equations that are difficult to solve. In particular, the inverse position analysis comprises different subproblems which need specific solution techniques. Finally a numerical example is reported.

Journal of Mechanical Design, 2012

Design criteria and constructive schemes are presented for a nonholonomic spherical (nS) pair pro... more Design criteria and constructive schemes are presented for a nonholonomic spherical (nS) pair proposed previously, along with a reconfigurable version of the same pair, named nS pair. Type synthesis of the underactuated parallel wrists derived from the fully parallel wrist (FPW) topology is addressed by replacing passive spherical (S) pairs with nS or nS pairs. Ten novel topologies of underactuated spherical wrists with practically the same workspace as the original FPW are identified. Wrist architectures based on these novel underactuated-wrist topologies are proved to be globally controllable, and a general path planning algorithm is proposed for these wrists. Here, the substitution of holonomic constraints with nonholonomic ones reduces the number of actuators and, sometimes, the number of links, too.