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

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, t...

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Bibliographic Details
Authors: Rojas Libreros, Nicolás Enrique, Thomas, Federico|||0000-0001-9341-5528
Format: article
Publication Date:2012
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/17912
Online Access:https://hdl.handle.net/2117/17912
https://dx.doi.org/10.1016/j.mechmachtheory.2011.10.010
Access Level:Open access
Keyword:Kinematics
Position analysis
Baranov trusses
Bilateration
Characteristic polynomial
Cinemàtica
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica::Cinemàtica
Description
Summary: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 catalogued 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.