A novel method for measuring the coupled linear and angular motions of XYΘ-type flexure-based manipulators

For XYΘ-type flexure-based manipulators with nanometer accuracy, the coupled linear/angular motions of the end effector cause unwanted misalignments to the measurement system, leading to measurement error or even measurement failure. This paper proposes an indirect measuring method for such manipulators, where the 3-PRR topology is adopted to kinematically transfer the coupled motions of the end effector to the linear motions of three prismatic joints. Unlike the other XYΘ manipulators, three linear position sensors are used to measure the linear motions of the prismatic joints, not the coupled motions of the end effector. Accordingly, the position and orientation of the end effector can be obtained via the forward kinematics. This indirect method aims to eliminate the influence of the coupled motions of the end effector on the measurement system, and to guarantee the accuracies and effectiveness of the sensors´ outputs. An XYΘ flexure-based manipulator is developed following this method. The design and kinematics modeling is presented, and the effectiveness of this method is computationally verified. The future work will focus on the experimental verification of this method.