Study on the Effect of Elastic Deformations on Rigid Body Motions of a 3-PRR Flexible Parallel Manipulator

This paper presents the effect of elastic motions on rigid body motions of a 3-PRR parallel manipulator with three flexible intermediate links. The intermediate links are modeled as Euler-Bernoulli beams with pinned-pinned boundary conditions based on the assumed mode method (AMM). Using Lagrange multipliers, the fully coupled equations of motions of the flexible parallel manipulator are developed by incorporating the rigid body motions with elastic motions as a non-separated quantity. The mutual dependence of elastic deformations and rigid body motions are investigated by the analysis of the derived equations of motions. Open-loop simulation without joint motion controls and closed-loop simulation with joint motion controls are performed to illustrate the effect of elastic motions on rigid body motions. These analyses and results provide a valuable insight to the design and control of the parallel manipulator with flexible intermediate links.