Dynamics and isotropic control of parallel mechanisms for vibration isolation

Parallel mechanisms have been employed as architectures of high-precision vibration isolation systems. However, their performances in all degrees of freedom (DOFs) are nonidentical. The conventional solution to this problem is isotropic mechanism design, which is laborious and can hardly be achieved. This article proposes a novel concept; namely, isotropic control, to solve this problem. Dynamic equations of parallel mechanisms with base excitation are established and analyzed. An isotropic control framework is then synthesized in modal space. We derive an explicit relationship between modal control force and actuation force in joint space, enabling implementation of the isotropic controller. The multi-DOF system is transformed into multiidentical single-DOF systems. Under the framework of isotropic control, parallel mechanisms obtain an identical frequency response for all modes. An identical corner frequency, active damping, and rate of low-frequency transmissibility are achieved for all modes using a combining proportional, integral, and double integral compensator as a subcontroller. A 6-UPS parallel mechanism is presented as an example to demonstrate effectiveness of the new approach.