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

journal contribution
posted on 2023-06-09, 00:28 authored by Nicola´s Rojas, Federico Thomas
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.

History

Publication status

  • Published

Journal

Journal of Mechanisms and Robotics

ISSN

1942-4302

Publisher

American Society of Mechanical Engineers (ASME)

Issue

3

Volume

3

Page range

031001

Department affiliated with

  • Engineering and Design Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2016-03-07

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