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

AuthorsRojas, Nicolás ; Thomas, Federico
Position analysis
Assur kinematic chains
Baranov trusses
Issue Date2011
PublisherAmerican Society of Mechanical Engineers
CitationJournal of Mechanisms and Robotics 3 (2011)
AbstractThe 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. © 2011 American Society of Mechanical Engineers.
Publisher version (URL)http://dx.doi.org/10.1115/1.4004031
Identifiersdoi: 10.1115/1.4004031
issn: 1942-4302
e-issn: 1942-4310
Appears in Collections:(IRII) Artículos
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