Publication

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

Journal Article (2011)

Journal

Mechanism and Machine Theory

Pages

112-126

Volume

46

Number

2

Doc link

http://dx.doi.org/10.1016/j.mechmachtheory.2010.10.004

File

Download the digital copy of the doc pdf document

Abstract

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.

Categories

robot kinematics.

Author keywords

Assur kinematic chains, position analysis, distance-based formulations, Cayley–Menger determinants, bilateration

Scientific reference

N. Rojas and F. Thomas. Distance-based position analysis of the three seven-link Assur kinematic chains. Mechanism and Machine Theory, 46(2): 112-126, 2011.