Dynamic Modeling and Active Vibration Control of a Planar 3-PRR Parallel Manipulator with Three Flexible Links
Keywords: parallel manipulator
flexible manipulator
smart structure
active vibration control
assumed mode method
experimental modal analysis
modal filter
dynamic stiffening and buckling

Given the advantages of parallel manipulators and lightweight manipulators, a 3-PRR planar parallel manipulator with three lightweight intermediate links has been developed to provide an alternative high-speed pick-and-place positioning mechanism to serial architecture manipulators in electronic manufacturing, such as X-Y tables or gantry robots. Lightweight members are more likely to exhibit structural defection and vibrate due to the inertial forces from high speed motion, and external forces from actuators. Structural flexibility effects are much more pronounced at high operational speeds and accelerations. Therefore, this thesis presents the dynamics and vibration control of a 3-PRR parallel manipulator with three flexible links. Firstly, a procedure for the generation of dynamic equations for a 3-PRR parallel manipulator with three flexible intermediate links is presented based on the assumed mode method. The dynamic equations of the parallel manipulator with three flexible intermediate links are developed using pinned-pinned boundary conditions. Experimental modal tests are performed using an impact hammer and an accelerometer to identify the mode shapes, frequencies, and damping ratios of flexible intermediate links. The mode shapes and frequencies, obtained from experimental modal tests, match very well the assumed mode shapes and frequencies obtained based on pinned-pinned boundary conditions, and therefore the dynamic model developed is validated. Secondly, this thesis presents the investigation on dynamic stiffening and buckling of the flexible links of a 3-PRR parallel manipulator by including the effect of longitudinal forces on the modal characteristics. Natural frequencies of bending vibration of the intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. Dynamic stiffening and buckling of intermediate links is investigated and configuration-dependant frequencies are analyzed. Furthermore, 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. The mutual dependence of elastic deformations and rigid body motions are investigated from the analysis of the derived equations of motion. Open-loop simulation without joint motion controls and closed-loop simulation with joint motion controls are performed to illustrate the effect of elastic motion on rigid body motions and the coupling effect amongst flexible links. These analyses and results provide valuable insight into the design and control of the parallel manipulator with flexible intermediate links. Thirdly, an active vibration control strategy is developed for a moving 3-PRR parallel manipulator with flexible links, each of which is equipped with multiple PZT control pairs. The active vibration controllers are designed using the modal strain rate feedback (MSRF). The amplification behavior of high modes is addressed, and the control gain selection strategy for high modes is developed through modifying the IMSC method. The filters are developed for the on-line estimation of modal coordinates and modal velocity. The second compensator is used to cut off the amplified noises and unmodeled dynamics due to the differentiation operation in the developed controller. The modal coupling behavior of intermediate links is examined with the modal analysis of vibrations measured by the PZT sensors. The error estimation of the moving platform is examined using the measurement of PZT sensors. Finally, an active vibration control experimental system is built to implement the active vibration control of a moving 3-PRR parallel manipulator with three flexible links. The smart structures are built through mounting three PZT control pairs to each intermediate flexible link. The active vibration control system is set up using National Instruments LabVIEW Real-Time Module. Active vibration control experiments are conducted for the manipulator moving with high-speed, and experimental results demonstrate that the vibration of each link is significantly reduced.