Forward kinematics and solution methodologies for a flexure-based micro-manipulator
This paper presents the forward kinematics of a five-bar compliant micro-manipulator, where lever mechanisms are used to enlarge the working range in Cartesian space. Based on the configuration of the proposed flexure-based micro-manipulator, the entire system has been divided into a five-bar mechanism and two four-bar amplification mechanisms. The amplification factor of the lever mechanism is derived based on the analytical solution of the four-bar linkage. For the five-bar mechanism, the closed-form forward kinematics is obtained according to the established geometric relationship. The velocity of the end-effector is also obtained by differentiating the forward position kinematic equation. Based on the simplified methodologies such as linearising the trigonometric functions and constant Jacobian matrix, numerical simulations have been carried out to investigate the performance of the five-bar compliant manipulator. The comparisons between the exact solution and the simplified methodologies are carried out. It is noted that the linearising trigonometric simplification has a higher accuracy and is more suitable for the kinematic calculation of the micro-manipulator, but the constant Jacobian matrix method can efficiently calculate the forward kinematics of the micro-manipulator with the acceptable accuracy.
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