Analytic Form Solution of the Direct Position Analysis of a Wide Family of Three-Legged Parallel Manipulators

[+] Author and Article Information
Raffaele Di Gregorio

Department of Engineering,  University of Ferrara, Via Saragat 1, 44100 Ferrara, Italyrdigregorio@ing.unife.it

J. Mech. Des 128(1), 264-271 (Jan 17, 2005) (8 pages) doi:10.1115/1.1913703 History: Received May 20, 2004; Revised January 17, 2005

A wide family of parallel manipulators (PMs) is the one that groups all 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. Two out of these topologies are the SR-2PS topology (one SR leg and two PS legs) and the SP-2RS topology (one SP leg and two RS legs). This paper presents two algorithms. The first one determines all the assembly modes of the SR-2PS structures. The second one determines all the assembly modes of the SP-2RS structures. The presented algorithms can be applied without changes to solve, in analytical form, the direct position analysis (DPA) of all the parallel manipulators that generate a SR-2PS structure or a SP-2RS structure when the actuators are locked. In particular, the closure equations of two generic structures, one of type SR-2PS and the other of type SP-2RS, are written. The eliminants of the two systems of equations are determined and the solution procedures are presented. Finally, the proposed procedures are applied to real cases. This work demonstrates that (i) the DPA solutions of any PM that becomes a SR-2PS structure are at most eight, and (ii) the DPA solutions of any PM that becomes a SP-2RS structure are at most sixteen.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 7

The leg of type SP

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Figure 8

Notation of Sec. 3

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Figure 1

SR-2PS structure

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Figure 2

The ith leg of type PS (i=1,2)

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Figure 3

The leg of type SR

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Figure 4

Notation of Sec. 2

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Figure 5

SP-2RS structure

Grahic Jump Location
Figure 6

The ith leg of type RS (i=1,2)



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