文档介绍：Mechanism and Machine Theory 44 (2009) 1360–1370
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Mechanism and Machine Theory
journal homepage: ate/mechmt
An algebraic formulation of static isotropy and design of statically isotropic
6–6 Stewart platform manipulators
Sandipan Bandyopadhyay a,*, Ashitava Ghosal b
a Department of Engineering Design, Indian Institute of Technology-Madras, Chennai 600 036, India
b Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
article info abstract
Article history: In this paper, we present an algebraic method to study and design spatial parallel manip-
Received 6 December 2007 ulators that demonstrate isotropy in the force and moment distributions. We use the force
Received in revised form 2 October 2008 and moment transformation matrices separately, and derive conditions for their isotropy
Accepted 9 November 2008
individually as well as bination. The isotropy conditions are derived in closed-form
Available online 22 January 2009
in terms of the invariants of the quadratic forms associated with these matrices. The for-
mulation is applied to a class of Stewart platform manipulator, and a multi-parameter fam-
ily of isotropic manipulators is identified analytically. We show that it is impossible to
obtain a spatially isotropic configuration within this family. We pute the isotropic
configurations of an existing manipulator and demonstrate a procedure for designing the
manipulator for isotropy at a given configuration.
Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction
Isotropy is one of mon measures of performance of a manipulator. In the case of six-degrees-of-freedom (DOF)
spatial manipulators, the term isotropy is generally used in the context of kinematics. However, in practice, the concept
of twist-wrench duality is used to analyse the 6 Â 6 wrench transformation matrix H, to obtain conditions such that this ma-
trix has identical singular values (see