Dynamic modeling and vibration control of high speed planar parallel manipulator

Presents dynamic formulations of a planar parallel manipulator including structural flexibility of several linkages. The equations of motion are formulated using the Lagrangian equations of the first type. To avoid complexity in calculating passive coordinates of the parallel manipulator, we introduce Lagrangian multipliers, which combine with constraint equations representing the geometry of multiple closed loop chains. Then, an approach for active damping using a PZT actuator is described to attenuate structural vibration of the linkage. Attached on the linkage, the PZT actuator produces a bending moment according to a linear velocity feedback control scheme. Overall dynamic behavior of the manipulator, induced from structural flexibility of the linkage, is well illustrated through simulations. This analysis is used to develop the prototype parallel manipulator