文档介绍：Mechanism and Machine Theory 44 (2009) 1256–1269
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Mechanism and Machine Theory
journal homepage: ate/mechmt
An eigenproblem approach to classical screw theory
Sandipan Bandyopadhyay a,*, Ashitava Ghosal b
a Department of Engineering Design, Indian Institute Technology – Madras, Chennai 600 036, India
b Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
article info abstract
Article history: This paper presents a novel algebraic formulation of the central problem of screw theory,
Received 6 December 2007 namely the determination of the principal screws of a given system. Using the algebra of
Received in revised form 25 July 2008 dual numbers, it shows that the principal screws can be determined via the solution of a
Accepted 26 July 2008
generalised eigenproblem of two real, symmetric matrices. This approach allows the study
Available online 16 October 2008
of the principal screws of the general two-, three-systems associated with a manipulator of
arbitrary geometry in terms of closed-form expressions of its architecture and configura-
tion parameters. We also present novel methods for the determination of the principal
screws for four-, five-systems which do not require the putation of the recipro-
cal systems. Principal screws of the systems of different orders are identified from one uni-
form criterion, namely that the pitches of the principal screws are the extreme values of
the pitch.
The classical results of screw theory, namely the equations for the cylindroid and the
pitch-hyperboloid associated with the two- and three-systems, respectively have been
derived within the proposed framework. Algebraic conditions have been derived for some
of the special screw systems. The formulation is also illustrated with several examples
including two spatial manipulators of serial and parallel architecture, respectively.
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