Modelling and analysis of a three-revolute parallel micro-positioning mechanism

This article presents the modelling and analysis methodologies of a three-degree-of-freedom (DOF) flexure-based mechanism. The mechanical design and working principle of a three revolute parallel mechanism is briefly provided. The kinematics of the proposed mechanism is established by simplifying flexure hinges into the revolute joints. The relationship of velocity between the Cartesian space and joint space is established. For small displacements of piezoelectric actuators, this velocity mapping can be simplified as the displacement relationship for the flexure-based mechanism. Two simplified methodologies, linearizing triangular functions and constant Jacobian, are utilized to conduct computational analysis for the flexure-based mechanism. The reachable workspace and theoretical resolution are also investigated. A novel empirical displacement mapping model is proposed based on finite-element analysis. Experiments are carried out to verify the established models of the three-DOF flexure-based mechanism. The maximum reachable workspace can reach up to approximately±68 and±76 µm in x and y directions, and the translational and rotational resolutions of the flexure-based mechanism are approximately 3 nm and 0.4 µrad, respectively.