In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new and efficient method is introduced to obtain a closed-form finite dimensional dynamic model for planar Flexible-link Flexible-joint Manipulators (FFs). To derive the dynamic model, this new method separates (disassembles) a FF into two subsystems. The first subsystem is the counterpart of the FF but without joints’ flexibilities and rotors’ mass moment of inertias; this subsystem is referred to as a Flexible-link Rigid-joint manipulator (FR). The second subsystem has the joints’ flexibilities and rotors’ mass moment of inertias, which are excluded from the FR; this subsystem is called Flexible-Inertia entities (FI). While the method proposed here employs the Lagrange’s equations, it neither requires the derivation of the lengthy Lagrangian function nor its complex derivative calculations. This new method only requires the Lagrangain function evaluation and its derivative calculations for a Single Flexible link manipulator on a Moving base (SFM). By using the dynamic model of a SFM and the Lagrange multipliers, the dynamic model of the FR is first obtained in terms of the dependent generalized coordinates. This dynamic model is then projected into the tangent space of the constraint manifold by the use of the natural orthogonal complement of the Jacobian constraint matrix. Therefore, the dynamic model of the FR is obtained in terms of the independent generalized coordinates and without the Lagrange multipliers. Finally, the joints’ flexibilities and rotors’ mass moment of inertias, which are included in the FI, are added to the dynamic model of the FR and a closed-form dynamic model for the FF is derived. To verify this new method, the results of simulation examples, which are obtained from the proposed method, are compared with those of a full-nonlinear finite element analysis, where the comparisons indicate sound agreement
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e-mail: reza.fotouhi@usask.ca
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February 2012
Technical Briefs
A New Method for Dynamic Modeling of Flexible-Link Flexible-Joint Manipulators
M. Vakil,
M. Vakil
Mechanical Engineering Department,
University of Saskatchewan
, Saskatoon, Saskatchewan, Canada
S7N 5A9
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R. Fotouhi,
R. Fotouhi
Mechanical Engineering Department,
e-mail: reza.fotouhi@usask.ca
University of Saskatchewan
, Saskatoon, Saskatchewan, Canada
S7N 5A9
Search for other works by this author on:
P. N. Nikiforuk
P. N. Nikiforuk
Mechanical Engineering Department,
University of Saskatchewan
, Saskatoon, Saskatchewan, Canada
S7N 5A9
Search for other works by this author on:
M. Vakil
Mechanical Engineering Department,
University of Saskatchewan
, Saskatoon, Saskatchewan, Canada
S7N 5A9
R. Fotouhi
Mechanical Engineering Department,
University of Saskatchewan
, Saskatoon, Saskatchewan, Canada
S7N 5A9e-mail: reza.fotouhi@usask.ca
P. N. Nikiforuk
Mechanical Engineering Department,
University of Saskatchewan
, Saskatoon, Saskatchewan, Canada
S7N 5A9J. Vib. Acoust. Feb 2012, 134(1): 014503 (11 pages)
Published Online: December 28, 2011
Article history
Received:
July 12, 2010
Revised:
March 25, 2011
Online:
December 28, 2011
Published:
December 28, 2011
Citation
Vakil, M., Fotouhi, R., and Nikiforuk, P. N. (December 28, 2011). "A New Method for Dynamic Modeling of Flexible-Link Flexible-Joint Manipulators." ASME. J. Vib. Acoust. February 2012; 134(1): 014503. https://doi.org/10.1115/1.4004677
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