Modal control of configuration dependent linkage vibration in closed-loop flexible-link mechanisms

Modal control algorithms have been widely used in civil structures and open-loop flexible mechanisms. This paper demonstrates the idea of applying modal control to closed-loop mechanisms using a parallel robot as an example, including the process of modal identification and active vibration control design. A lightweight planar parallel manipulator is designed to improve operational speed of "pick-and-place" processes and implement a "smart parallel manipulator" through the integration of a parallel mechanism architecture and active control of linkage vibration using Lead Zirconate Titanate (PZT) transducers. Boundary conditions and mode shapes of intermediate linkage are not conventional due to that linkages undergo constrained rigid body motion. Through numerical simulations using a substructuring dynamic model developed for the parallel manipulator, the boundary condition is determined close to a pinned-pinned boundary condition. This conclusion is confirmed using experimental modal analysis (EMA) using a random motion input. However, it is observed that linkage vibration exhibits configuration-dependency. Based on experimental observations, an assumption is taken to simplify the transfer function from the motor input to linkage vibration. Based on this simplification, a mode modal controller is designed and implemented. Experimental results in the time domain and frequency domain demonstrates dramatic vibration reduction.