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 kinematics of the proposed hyper-redundant manipulator. A 12-dof hyper-redundant manipulator is included as a case study.are among the most important benefits of such an exceptional degree of manipulability. Examples of the excellent performance of HRMs can be found in nature itself, giving rise to several complex mechanisms with adopted names such as snake [2], serpentine [3], tentacle [4], or elephant's trunk [5]. On the other hand, HRMs are considered as not anthropomorphic, and because of the lack of an effective methodology of kinematic analysis, both finite and infinitesimal, in addition to programming problems, HRMs remained only as laboratory curiosities a few years ago.Since the pioneering contribution of Anderson and Horn [6], traditionally HRMs are obtained by assembling in series connection several parallel manipulators with identical limbs, called symmetrical parallel manipulators, see for instance references [7] to [13]. Certainly, the merits of SPMs such as simplified mechanical assembly and minimum cost (because of identical mechanical components and repetitive manufacturing operations) are factors to be considered in the design process of an HRM. However, another type of mechanical architecture known as asymmetrical parallel manipulators are emerging requesting an opportunity to play a central role in the development of HRMs. The easy generation of closed-form solutions, which is prohibitive for most SPMs, for solving the finite kinematics is the main attraction of APMs. JMBD188

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