Effect of axial forces on lateral stiffness of a flexible 3-PRR parallel manipulator moving with high-speed

This paper investigates the effect of longitudinal forces on lateral stiffness of a moving 3-PRR parallel manipulator with three flexible intermediate links based on the assumed mode method. First, a dynamic model of the manipulator system is developed by adopting the assumed mode method. In this dynamic model, the effect of longitudinal forces on lateral stiffness is included, and flexible intermediate links are modeled as Euler-Bernoulli beams with proper pinned-pinned boundary conditions which are validated by experimental modal tests. Then, natural frequencies of bending vibration of intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. The effect of longitudinal forces on lateral stiffness of intermediate links and configuration-dependant frequency properties are revealed by the frequency functions. Numerical simulations and analysis of configuration-dependent frequency properties are performed, and further validate the theoretical derivation. These analyses and results provide a valuable insight to the design and control of the parallel manipulator with flexible intermediate links.