Stiffness estimation of the flexure-based five-bar micro-manipulator

This paper presents the forward kinematics and stiffness estimation methodologies of a flexure-based five-bar micro-manipulator. The mechanical design of the micro-manipulator is firstly descried. Base on the configuration of the proposed flexure-based micro-manipulator, the whole system has been divided into a five-bar parallel mechanism and an amplification mechanism. Two mathematical expressions describing the path traced by the tips of two passive links connected to each other are obtained. The Cartesian coordinates of the end-effector attached to one of the passive links is obtained according to the geometric relationship. The amplification factor of the lever mechanism is also derived based on the analytical solution of the four-bar linkage. By simplifying the flexure hinge as an ideal revolution joint with a linear torsional spring, the stiffness of the compliant five-bar mechanism is derived in both actuation and Cartesian spaces. It is noted that the stiffness of the compliant five-bar mechanism is positional dependant, and reaches up to infinite value at the singular configuration.