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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October 2018
Research-Article
The Moore–Penrose Dual Generalized Inverse Matrix With Application to Kinematic Synthesis of Spatial Linkages
E. Pennestrì,
E. Pennestrì
Department of Enterprise Engineering,
University of Rome Tor Vergata,
Via del Politecnico, 1,
Roma 00133, Italy
University of Rome Tor Vergata,
Via del Politecnico, 1,
Roma 00133, Italy
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P. P. Valentini,
P. P. Valentini
Department of Enterprise Engineering,
University of Rome Tor Vergata,
Roma 00133, Italy
University of Rome Tor Vergata,
Via del Politecnico, 1
,Roma 00133, Italy
Search for other works by this author on:
D. de Falco
D. de Falco
Department of Industrial and
Information Engineering,
University of Campania,
Aversa 81031, Italy
Information Engineering,
University of Campania,
Via Roma, 29
,Aversa 81031, Italy
Search for other works by this author on:
E. Pennestrì
Department of Enterprise Engineering,
University of Rome Tor Vergata,
Via del Politecnico, 1,
Roma 00133, Italy
University of Rome Tor Vergata,
Via del Politecnico, 1,
Roma 00133, Italy
P. P. Valentini
Department of Enterprise Engineering,
University of Rome Tor Vergata,
Roma 00133, Italy
University of Rome Tor Vergata,
Via del Politecnico, 1
,Roma 00133, Italy
D. de Falco
Department of Industrial and
Information Engineering,
University of Campania,
Aversa 81031, Italy
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. Oct 2018, 140(10): 102303 (7 pages)
Published Online: July 31, 2018
Article history
Received:
March 19, 2018
Revised:
July 10, 2018
Citation
Pennestrì, E., Valentini, P. P., and de Falco, D. (July 31, 2018). "The Moore–Penrose Dual Generalized Inverse Matrix With Application to Kinematic Synthesis of Spatial Linkages." ASME. J. Mech. Des. October 2018; 140(10): 102303. https://doi.org/10.1115/1.4040882
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