This paper studies the workspace of a flexure-based, hexa-pod nanopositioner previously built by the National Institute of Standards and Technology (NIST) which can produce high-resolution motions in six degree of freedom by actuating linear actuators on planar tri-stage. Because there is a lack of work in workspace of such kind of compliant mechanisms, the controller is typically limited to a very small range of motion in order to avoid material failure. In this work, we seek to derive a kinematic model for predicting the workspace of such kind of flexure based platforms by assuming that their workspace is mainly constrained by the deformation of flexure joints. We first study the maximum deformation including bending and torsion angles of each flexure joint. We then derive the inverse kinematics and calculation of bending and torsion angles of this compliant platform. To obtain the workspace of the mechanism, we developed a computational algorithm that varies the displacement of the top platform to extreme positions till the deformation of any flexure exceeding a maximum value. To demonstrate this approach, we provided example studies including constant orientation workspace and constant position workspace. We compare results with a finite element model of the entire platform. The error is 4.74% for original analytical model and 8.26% for simplified analytical model. This model is beneficial in guiding design engineers in maximizing workspace of flexure based parallel compliant mechanisms. To the end-users of the positioner, it gives them a guidance on how to efficiently exploit the workspace of the nanopositioner.

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