Research Papers: Design of Mechanisms and Robotic Systems

The Moore–Penrose Dual Generalized Inverse Matrix With Application to Kinematic Synthesis of Spatial Linkages

[+] Author and Article Information
E. Pennestrì

Department of Enterprise Engineering,
University of Rome Tor Vergata,
Via del Politecnico, 1,
Roma 00133, Italy

P. P. Valentini

Department of Enterprise Engineering,
University of Rome Tor Vergata,
Via del Politecnico, 1,
Roma 00133, Italy

D. de Falco

Department of Industrial and
Information Engineering,
University of Campania,
Via Roma, 29,
Aversa 81031, Italy

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 19, 2018; final manuscript received July 10, 2018; published online July 31, 2018. Assoc. Editor: Massimo Callegari.

J. Mech. Des 140(10), 102303 (Jul 31, 2018) (7 pages) Paper No: MD-18-1229; doi: 10.1115/1.4040882 History: Received March 19, 2018; Revised July 10, 2018

The paper initially reports about the properties of an expression of dual generalized inverse matrix currently available in the literature. It is demonstrated that such a matrix does not fulfill all the Penrose conditions. Hence, novel and computationally efficient algorithms/formulas for the computation of the Moore–Penrose dual generalized inverse (MPDGI) are herein proposed. The paper also contains a new algorithm for the singular value decomposition (SVD) of a dual matrix. The availability of these formulas allows the simultaneous solution of overdetermined systems of dual linear equations without requiring the traditional separation in primal and dual parts. This should prove useful for the solution of many kinematic problems. The algorithms/formulas herein deduced have been also tested on the kinematic synthesis of the constant transmission ratio RCCC spatial linkage.

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Grahic Jump Location
Fig. 1

The RCCC linkage: nomenclature

Grahic Jump Location
Fig. 2

Dual Denavit–Hartenberg parameters



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