Coupling characteristics of rigid body motion and elastic deformation of a 3-PRR parallel manipulator with flexible links
The authors extend their earlier study [Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, 1805--1810 (1997)] on the effect of elastic deformations on the rigid body motions of a 3-PRR flexible parallel manipulator. The equations of motion are nonlinear partial differential equations, and for their dynamic modelling different discretizations for flexible links have earlier been investigated and compared [\textit{R. J. Theodore} and \textit{A. Ghosal}, Comparison of the assumed modes and the finite element models for flexible multi-link manipulators, Int. J. Robot Res. 14, 91--111 (1995)]. Here the dynamic modelling is carried out based on the assumed modes method. The coupled equations of motion are developed utilizing the one-pass method, i.e. the incorporation of rigid motions with elastic motions as non-separated quantities based on the use of Lagrange multipliers, and then the subsequent reduction in order of dynamic equations in a closed form, suitable for the design of a controller. The equations clearly reveal coupling of the elastic and rigid body motions. The authors perform pen-loop simulations without joint motion controls and closed-loop simulations with joint motion controls. The open-loop simulation results show that the elastic motion of the links has a significant effect on the rigid body motions of the manipulator system, whereas the results of the closed-loop simulation with joint motion controls show that the effect of elastic motions on the rigid body motions is negligible on the level of linear and angular displacements of the manipulator system. A numerical example for a 3-PRR parallel manipulator with three flexible intermediate links is presented.
scientific article; zbMATH DE number 5565157
scientific article