Structural Dynamic Modeling, Dynamic Stiffness, and Active Vibration Control of Parallel Kinematic Mechanisms with Flexible Linkages

This thesis is concerned with modeling of structural dynamics, dynamic stiffness, and active control of unwanted vibrations in Parallel Kinematic Mechanisms (PKMs) as a result of flexibility of the PKM linkages. Using energy-based approaches, the structural dynamics of the PKMs with flexible links is derived. Subsequently, a new set of admissible shape functions is proposed for the flexible links that incorporate the dynamic effects of the adjacent structural components. The resulting mode frequencies obtained from the proposed shape functions are compared with the resonance frequencies of the entire PKM obtained via Finite Element (FE) analysis for a set of moving platform/payload masses. Next, an FE-based methodology is presented for the estimation of the configuration-dependent dynamic stiffness of the redundant 6-dof PKMs utilized as 5-axis CNC machine tools at the Tool Center Point (TCP). The proposed FE model is validated via experimental modal tests conducted on two PKM-based meso-Milling Machine Tool (mMT) prototypes built in the CIMLab.For active vibration control of the PKM linkages, a set of PZT transducers are designed, and bonded to the flexible linkage of the PKM to form a "smart link". An electromechanical model is developed that takes into account the effects of the added mass and stiffness of the PZT transducers to those of the PKM links. The electromechanical model is subsequently utilized in a controllability analysis where it is shown that the desired controllability of PKMs can be simply achieved by adjusting the mass of the moving platform. Finally, a new vibration controller based on a modified Integral Resonant Control (IRC) scheme is designed and synthesized with the "smart link" model. Knowing that the structural dynamics of the PKM link undergoes configuration-dependent variations within the workspace, the controller must be robust with respect to the plant uncertainties. To this end, the modified IRC approach is shown via a Quantitative Feedback Theory (QFT) methodology to have improved robustness against plant variations while maintaining its vibration attenuation capability. Using LabVIEW Real-Time module, the active vibration control system is experimentally implemented on the smart link of the PKM to verify the proposed vibration control methodology.Ph.D