Design of a zero stiffness six degrees of freedom compliant precision stage

Abstract

This paper presents the first zero stiffness six degrees of freedom (DoF) compliant precision stage. To deal with problems like backlash, friction and lubrication for performing ultra-precise positioning in a vacuum environment, a novel compliant structure is proposed. All six degrees of freedom are statically balanced (i.e. near zero stiffness) to balance the gravity force and cancel out the stiffness due to the compliant design of the structure. Cooperative action of post-buckling behavior of bi-stable beams and constant stiffness of v-shaped beams, arranged in three units in a triangular configuration, are proposed for out-of-the-horizontal-plane motions. The in-plane motions are achieved by three flexible rods loaded near their buckling load. An investigation on adjusting the design parameters to minimize the residual actuation force is also performed. A prototype was manufactured and finite element modeling was performed to evaluate the concept. Experimental evaluation showed that the design is successful: for the case study a gravity force of 34.4N was balanced with a residual stiffness of 1.75N/mm in a domain of 2mm for the out-of-plane translation, while the out-of-plane rotational stiffness was less than 18.5Nm/rad, caused by parasitic torsion of the bi-stable beams and v-shaped beams. The stiffness for in-plane translations and rotation was 0.4N/mm and 2Nm/rad, respectively. Near zero stiffness 6DoF positioning can thus be achieved. The novel mechanism or the principle may be extensively applied in several applications in precision engineering or in other relevant fields, such as vibration isolation.