Modeling, design, and control of 6-DoF flexure-based parallel mechanisms for vibratory manipulation

Small amplitude periodic motion of a 6-degree-of-freedom (DoF) rigid plate causes rigid parts on the surface to slide under the influence of friction as if immersed in a configuration-dependent velocity field. A plate whose motion is fully programmable is therefore a simple yet versatile manipulator. To develop such a manipulator, this paper addresses the design and control of a 6-DoF parallel mechanism intended for small-amplitude, high frequency vibration. We derive a linear model for the class of parallel mechanisms consisting of a rigid plate coupled to linear actuators through flexures. Using this model, we discuss manipulator design geared toward either universal parts feeding or single task automation. The design process is formulated as a constrained optimization over a design space that includes the geometry of the manipulator (actuator orientations and flexure attachment points) and the viscoelastic properties of the flexures. Finally, we present a frequency-based iterative learning controller for tracking periodic plate acceleration trajectories in image for all designs. Experimental data collected from our PPOD2 manipulator is used to validate the model and demonstrate the performance of the controller.