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On closed-form solutions to the position analysis of Baranov trusses

journal contribution
posted on 2023-06-09, 00:28 authored by Nicolás Rojas, Federico Thomas
The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial usually involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. Although conceptually simple, the use of kinematic loops for deriving characteristic polynomials leads to complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, a method based on bilateration has recently been shown to permit obtaining the characteristic polynomials of the three-loop Baranov trusses without relying on variable eliminations or trigonometric substitutions. This paper shows how this technique can be applied to solve the position analysis of all cataloged Baranov trusses. The characteristic polynomials of them all have been derived and, as a result, the maximum number of their assembly modes has been obtained. A comprehensive literature survey is also included.

History

Publication status

  • Published

Journal

Mechanism and Machine Theory

ISSN

0094-114X

Publisher

Elsevier

Volume

50

Page range

179-196

Department affiliated with

  • Engineering and Design Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2016-03-07

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