Abstract
This paper presents the implementation of the floating frame of reference formulation to model the flexible multibody dynamics of a nonsymmetric planar 3PRR parallel manipulator. All of the links, including the moving platform, of the manipulator under study are assumed flexible whereas the joints are assumed rigid. Using the Euler-Bernoulli beam, the flexibility of the links is modeled by using the Rayleigh-Ritz and finite element approximations. In both approximations, fixed-free boundary conditions are applied to the elastic coordinates of the links. These boundary conditions enable the evaluation of the elastic displacement at a link tip coincident with the end-effector of the manipulator which is of interest in the high precision robotics application. Both the approximations were compared by applying two different types of loads to the manipulator. It is shown that the elastic displacements obtained by using both the approximations have an agreement with a slight difference in the magnitude. In addition, the sensitivity analysis shows that the rigidity of the manipulator is much affected by the in-plane depth of the manipulator links’ cross section.
Highlights
The finite element formulation of the floating frame of reference formulation is different from the common finite element modeling as the former separates the elastic coordinates from the rigid coordinates
A more realistic model of a flexible parallel manipulator was presented in this paper by assuming that all the links, including the moving platform, are flexible
The non-symmetry of the manipulator represents a more general topology of planar parallel manipulators. The simulation using both the Rayleigh-Ritz and finite element approximations, as expected, showed that the manipulator undergoes a larger displacement when the link flexibility is taken into account
Summary
The finite element model of a flexible multibody dynamics can be categorized broadly into two approaches—the incremental finite element modeling [3,4] and the floating frame of reference formulation (FFRF) [5,6,7,8] In the former approach, the shape function can only describe a small (infinitesimal) rotation and a convected coordinate system is used in order to deal with the finite rigid body motion. This is crucial for a high precision application such as machining It aims at comparing the elastic displacements of the manipulator at hand obtained by Rayleigh-Ritz and finite element methods based on FFRF.
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