Distance-based position analysis of the three seven-link Assur kinematic chains

The position analysis of planar linkages has been dominated by resultant elimination and tangent-half-angle substitution techniques applied to sets of kinematic loop equations. This analysis is thus reduced to finding the roots of a polynomial in one variable, the characteristic polynomial of the li...

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Detalles Bibliográficos
Autores: Rojas, Nicolás, Thomas, Federico
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2011
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/96800
Acceso en línea:http://hdl.handle.net/10261/96800
Access Level:acceso abierto
Palabra clave:Bilateration
Position analysis
Distance-based formulations
Cayley-Menger determinants
Assur kinematic chains
Descripción
Sumario:The position analysis of planar linkages has been dominated by resultant elimination and tangent-half-angle substitution techniques applied to sets of kinematic loop equations. This analysis is thus reduced to finding the roots of a polynomial in one variable, the characteristic polynomial of the linkage. In this paper, by using a new distance-based technique, it is shown that this standard approach becomes unnecessarily involved when applied to the position analysis of the three seven-link Assur kinematic chains. Indeed, it is shown that the characteristic polynomials of these linkages can be straightforwardly derived without relying on variable eliminations nor trigonometric substitutions, and using no others tools than elementary algebra. © 2010 Elsevier Ltd. All rights reserved.