Mobility analysis of a 3-PUU flexure-based manipulator based on screw theory and compliance matrix method

Abstract

This paper presents the mobility analysis of a 3-PUU flexure-based compliant parallel XYZ pure translational positioning stage. A 3-PUU positioning stage is constructed with a symmetric structure by employing three parallel PUU legs, a moving platform, and a fixed platform. Screw theory and compliance matrix method are utilized to analyze the three pure translational degrees of freedom (DOF) mechanism. The procedure is based on the screw theory deducted analytic equations that incorporate both the instaneous mobility at the initial position and the mobility during the whole working space. The kinematical and the dynamical modeling of this system are built by resorting to compliance characteristics analysis based on compliance matrix method. The analytical results also clarify effectively that the 3-PUU parallel positioning stage is with a pure translational mobility. Independent finite element simulation confirms that the motion of the stage is a pure translational positioning stage.