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RESEARCH PAPERS

Position Analysis of the RRP-3(SS) Multi-Loop Spatial Structure

[+] Author and Article Information
Carlo Innocenti

Department of Mechanical and Civil Engineering,  University of Modena and Reggio Emilia, via Vignolese, 905–41100 Modena, Italycarlo.innocenti@unimore.it

Philippe Wenger

 Institut de Recherche en Communications et Cybernetique de Nantes, 1, rue la Noe–BP 92101 44321 Nantes Cedex 3, Francephilippe.wenger@irccyn.ec-nantes.fr

J. Mech. Des 128(1), 272-278 (Jan 31, 2005) (7 pages) doi:10.1115/1.1992507 History: Received May 22, 2004; Revised January 31, 2005

The paper presents the position analysis of a spatial structure composed of two platforms mutually connected by one RRP and three SS serial kinematic chains, where R, P, and S stand for revolute, prismatic, and spherical kinematic pair, respectively. A set of three compatibility equations is laid down that, following algebraic elimination, results in a 28th-order univariate algebraic equation, which in turn provides the addressed problem with 28 solutions in the complex domain. Among the applications of the results presented in this paper is the solution to the forward kinematics of the Tricept, a well-known in-parallel-actuated spatial manipulator. Numerical examples show adoption of the proposed method in dealing with two case studies.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

A six-degree-of-freedom Tricept manipulator

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Figure 2

The UP-3(US) structure associated with a Tricept manipulator (type-I)

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Figure 3

The UP-3(SS) structure associated with a Tricept manipulator (type-I)

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Figure 4

The general-geometry RRP-3(SS) structure

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Figure 5

The RRP mechanism at the home configuration

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Figure 6

The UP-3(SS) structure associated with a Tricept manipulator (type-II)

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