Dynamic Model And Active Vibration Control Of A 3-PRR Flexible Parallel Manipulator

The positioning manipulator with large workspace, high speed and high precision plays a critical role in advanced electronic manufacturing industry, which directly determined the manufacturing level. Hence, how to resolve the conflicts among large workspace, high speed and high precision, become a key issue of precise positioning manipulator. Considering the beneficial characteristics of parallel structure, linear ultrasonic motors, and flexible components, a 3-PRR flexible parallel manipulator actuated by linear ultrasonic motors for chip packaging and detecting is developed. However, when flexible linkages are adopted to meet the demands of high speed, unwanted vibration is introduced to the manipulator system unavoidably, which will decrease the accuracy of the end-effector, or even cause the system instability. Hence, to develop the rigid-flexible dynamic model of the flexible parallel manipulator and suppress the unwanted vibration of the flexible linkage is really a useful and challenging work. Furthermore, in order to achieve large stroke with nanometer resolution, a macro/micro dual drive parallel manipulator are developed. The positioning precision of the 3-PRR manipulator is compensated to nanometer level based on a 3 degree of freedom compliant manipulator designed by topology method. The main contents and achievements of this paper are presented as follows:1. A 3-PRR planar parallel manipulator with three rigid links actuated by linear ultrasonic motors is developed. The kinematic model and dynamic model of the 3-PRR rigid manipulator are obtained using the vector chain method and the virtual work principle, respectively. Based on a contour error controller and the visual feedback, the trajectory tracking experiments of the 3-PRR parallel manipulator are conducted. The experimental results show that the trajectory tracking errors of X and Y axes of the manipulator are less than 15μm when following a 3mm radius circle.2. A rigid-flexible dynamic model of a 3-PRR parallel manipulator with three flexible links is developed. To obtain the exact boundary conditions, the 3-PRR flexible parallel manipulator is cut into 3 symmetrical individual chains and a moving platform. Based on the extend Hamilton’s principle, assumed mode method, and the substructure approach, a rigid-flexible dynamic equations related to the rigid motions and elastic motions is formulated. The modal testing of the flexible link is implemented, and the results match the assumed mode shape well, which further validate the effectiveness of the dynamic model.3. MATLAB simulation show that, compared with the pure rigid dynamic model, the tracking error of the moving platform is of sustained oscillation due to the unwanted vibration introduced by the flexible links, leading a longer settling time of the manipulator. Hence, based on dynamic model and modal testing results, the Zero-Vibration-Derivative input shaping controller and singular perturbation controller are developed to suppress the unwanted vibration, respectively. Simulation and experimental results show that the joint motion control has the vibration suppression ability in flexible parallel manipulator, and the amplitude of the first vibration mode of the first flexible link are reduced by 34.5% using ZVD input shaper. The experimental results also valiadate that the residual vibration of the moving platform can be attenuated effectively when the vibration of the flexible links are suppressed.4. The dynamic model of a 3-PRR flexible parallel manipulator incorporated with PZT sensors and actuators are developed, and the procedures that how the PZT transducers add the active damping item into the dynamic equations are analyzed. The direct output feedback controller are adopted to control the unwanted vibration, and MATLAB simulations show that the the first mode vibration of the flexible links are suppressed by 97.1% using the direct output feedback controller, which is better than the 48.9% of the singular perturbation approach. To avoid the control spillover phenomenon, the efficient modal control approach is designed to suppress the multiple vibration modes of the flexible links. The modal filter and modal synthesizer are also developed to realize the multiple vibration modes control. The results show that the vibration amplitudes for the first two vibration modes at 92 Hz and 244 Hz are reduced by 57.78% and 44.96%, respectively..5. Dynamic stiffening and buckling behavior of a 3-PRR parallel manipulator considering the effect of axial forces are investigated. The functional relationship between the natural frequencies of the flexible links and the axial forces are obtained. Experimental results show that: when the speed of the moving platform is low such at f =1Hz and f =2 Hz, the effect due to the dynamic stiffening is acceptable. However, with the increasing velocity of the moving platform, the effect of the dynamic stiffening becomes a dominant factor and must be considered.6. A macro/micro dual drive manipulator is established. The positioning precision of the 3-PRR manipulator is compensated to nanometer level based on a 3 degree of freedom compliant manipulator designed by topology method. Experimental results show that the macro/micro dual drive manipulator can achieve large stroke(2mm, 2mm, 0 rad) positioning with high precision(±50nm,±1μrad)of 3 planar degree of freedom(x, y,j) in 60 ms.Through the above investigation, the planar 3-DOF macro/micro dual drive manipulator based on 3-PRR parallel manipulator actuated by LUSM and compliant manipulator designed by topology method can achieve large stroke, high precise and fast postioning task, which has promiseing application in chip packaging and detecting.