IRI - Closed-form solution to the position analysis of Watt–Baranov trusses using the bilateration method

Publication

Closed-form solution to the position analysis of Watt–Baranov trusses using the bilateration method

Journal Article (2011)

Journal

Journal of Mechanisms and Robotics

Pages

1-10

Volume

Number

Doc link

http://dx.doi.org/10.1115/1.4004031

File

Download the digital copy of the doc pdf document

Authors

Projects associated

VALTEC: Sistema de muntatge de robots paral.lels

Abstract

The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial almost invariably involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. The use of kinematic loops to this end has seldom been questioned despite deriving the characteristic polynomial from them requires complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, the bilateration method has recently been used to obtain the characteristic polynomials of the three-loop Baranov trusses without relying on variable eliminations nor trigonometric substitutions and using no other tools than elementary algebra. This paper shows how this technique can be applied to members of a family of Baranov trusses resulting from the circular concatenation of the Watt mechanism irrespective of the resulting number of kinematic loops. To our knowledge, this is the first time that the characteristic polynomial of a Baranov truss with more that five loops has been obtained, and hence, its position analysis solved in closed form.

Author keywords

Baranov trusses, Assur kinematic chains, position analysis, bilateration, distance-based formulations

Scientific reference

N. Rojas and F. Thomas. Closed-form solution to the position analysis of Watt–Baranov trusses using the bilateration method. Journal of Mechanisms and Robotics, 3(3): 1-10, 2011.