José M. Rico-Martínez

The differential calculus of screws: Theory, geometrical interpretation, and applications

Abstract This article presents a novel and original formula for the higher-order time derivatives, and also for the partial derivatives of screws, which are successively computed in terms of Lie products, thus leading to the automation of the differentiation process. Through the process and, due to the pure geometric nature of the derivation approach, an enlightening physical interpretation of several screw derivatives is accomplished. Important applications for the proposed formula include higher-order kinematic analysis of open and closed kinematic chains and also the kinematic synthesis of serial and parallel manipulators. More specifically, the existence of a natural relationship is shown between the differential calculus of screws and the Lie subalgebras associated with the expected finite displacements of the end effector of an open kinematic chain. In this regard, a simple and comprehensible methodology is obtained, which considerably reduces the abstraction level frequently required when one resorts to more abstract concepts, such as Lie groups or Lie subalgebras; thus keeping the required mathematical background to the extent that is strictly necessary for kinematic purposes. Furthermore, by following the approach proposed in this article, the elements of Lie subalgebra arise in a natural way — due to the corresponding changes in screws through time — and they also have the typical shape of the so-called ordered Lie products that characterize those screws that are compatible with the feasible joint displacements of an arbitrary serial manipulator. Finally, several application examples — involving typical, serial manipulators — are presented in order to prove the feasibility and validity of the proposed method.

A novel five-degrees-of-freedom decoupled robot

In this work a new nonoverconstrained redundant decoupled robot, free of compound joints, formed from three parallel manipulators, with two moving platforms and provided with six active limbs connected to the fixed platform, called LinceJJP, is presented. Interesting applications such as multi-axis machine tools with parallel kinematic architectures, solar panels, radar antennas, and telescopes are available for this novel spatial mechanism.

Two Natural Dexterity Indices for Parallel Manipulators: Angularity and Axiality

This paper introduces two novel dexterity indices, namely, angularity and axiality, which are used to estimate the motion sensitivity of the mobile platform of a parallel manipulator undergoing a general motion involving translation and rotation. On the one hand, the angularity index can be used to measure the sensitivity of the mobile platform to change in rotation. On the other hand, the axiality index can be used to measure the sensitivity of the operation point (OP) of the mobile platform to change in translation. Since both indices were inspired by very fundamental concepts of classical kinematics (angular velocity vector and helicoidal velocity field), they offer a clear and simple physical insight, which is expected to be meaningful to the designer of parallel manipulators. Moreover, the proposed indices do not require obtaining a dimensionally homogeneous Jacobian matrix, nor do they depend on having similar types of actuators in each manipulators leg. The details of the methodology are illustrated by considering a classical parallel manipulator.

Angularity and axiality of a Schönflies parallel manipulator

Robotica / FirstView Article / April 2015, pp 1 25 DOI: 10.1017/S0263574715000090, Published online: 24 February 2015 Link to this article: http://journals.cambridge.org/abstract_S0263574715000090 How to cite this article: J. Jesús Cervantes-Sánchez, José M. Rico-Martínez and Víctor H. Pérez-Muñoz Angularity and axiality of a Schönies parallel manipulator. Robotica, Available on CJO 2015 doi:10.1017/S0263574715000090 Request Permissions : Click here

Synthesis of a novel planar linkage to visit up to eight poses

Abstract This article introduces a novel planar linkage which results from combining a Wanzer linkage with a four-bar linkage. It has one degree of freedom and is able to visit exactly up to eight poses. The proposed design approach yields linkages without branch and order defects, which can move continuously between all the desired poses without disassembly. Three illustrative examples show the applicability and the validity of the proposed synthesis process.

Kinematics of a hyper-redundant manipulator by means of screw theory

Abstract In this work the kinematics of a hyper-redundant manipulator built with an optional number of parallel manipulators with identical topologies assembled in series connection is carried out by using the theory of screws. First, closed-form solutions to solve the kinematics, up to the acceleration analysis, of the base module, an asymmetrical three-degree-of-freedom (dof) parallel manipulator with mixed motions, are derived using geometric procedures and the theory of screws; later, the symbolic results thus obtained are applied recursively to solve the kinema-tics of the proposed hyper-redundant manipulator. A 12-dof hyper-redundant manipulator is included as a case study.