Classical Screw Theory: A Fresh Look using the Dual Eigenproblem Approach

Sandipan Bandyopadhyay, Ashitava Ghosal

ABSTRACT: This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

KEYWORDS: Screw theory, Principal screws, Eigen-problem, and Dual number

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