JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 21, NO. 3, JUNE 2012 605 High-Angular-Range Electrostatic Rotary Stepper Micromotors Fabricated With SOI Technology Marc Stranczl, Edin Sarajlic, Hiroyuki Fujita, Member, IEEE, Martin A. M. Gijs, and Christophe Yamahata Abstract—Flexible bearings are advantageous for microelectro- mechanical systems as they enable precise, accurate, repeatable, and reliable motion without frictional contact. Based on the principle of a rotary folded-beam suspension, we have designed, fabricated, modeled, and characterized an electrostatic rotary stepper micromotor in silicon. Using 3-D finite-element analysis simulations that were corroborated by extensive characterizations performed in quasi-static, transient, and dynamic regimes, we could establish a consistent electromechanical model of the mo- tor. In particular, dynamic nonlinearities such as superharmonic and subharmonic resonances are well described by the proposed model. Two prototypes of monolithic three-phase stepper motors have been fabricated with standard silicon-on-insulator (SOI) technology, using either a two-mask or a single-mask process. The two-mask SOI motor has a rotor diameter of 1.4 mm and has an angular range of 30 ◦ (±15 ◦ ) for a 65-V (130 V pp ) sinusoidal actu- ation. The single-mask SOI motor has a rotor diameter of 1.8 mm and incorporates a differential capacitive sensor for angular po- sition measurement. It reaches a maximum angular speed of 1 ◦ /ms and has an angular range of 30 ◦ for a 23-V (46 V pp ) sinusoidal actuation. The exceptional performance of the motor and the demonstration of successful capacitive sensing make it suitable for use as an active joint module in future microrobotic applications. [2011-0339] Index Terms—Active joint, differential capacitive sensor, elec- trostatic rotary stepper micromotor, flexural pivot, folded-beam suspension, microrobotics, modal analysis, silicon-on-insulator (SOI), variable-capacitance micromotor. I. I NTRODUCTION F LEXURE mechanisms are devices consisting of rigid bod- ies connected together by compliant elements known as flexure joints or flexible bearings. As flexure joints rely on Manuscript received November 16, 2011; revised January 25, 2012; accepted February 2, 2012. Date of publication March 23, 2012; date of current version May 28, 2012. This work was supported by the Swiss National Science Foundation through Ambizione under Grant PZ00P2_121827. Subject Editor J. A. Yeh. This paper has supplementary downloadable multimedia material available at http://ieeexplore.ieee.org, provided by the authors. This material consists of two MPEG videos, one demonstrating the operation of the two-mask rotary stepper motor (RSM_SOI_two-mask.mpg; size 10 MB) and one demonstrating the operation of the single-mask rotary stepper motor (RSM_SOI_single- mask.mpg; size 15.8 MB). M. Stranczl, M. A. M. Gijs, and C. Yamahata are with the Laboratory of Microsystems, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland (e-mail: marc.stranczl@a3.epfl.ch; martin.gijs@epfl.ch; christophe.yamahata@a3.epfl.ch). E. Sarajlic is with SmartTip B.V., 7522 NB Enschede, The Netherlands (e-mail: e.sarajlic@smarttip.nl). H. Fujita is with the Center for International Research on MicroMechatron- ics, Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan (e-mail: fujita@iis.u-tokyo.ac.jp). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2012.2189367 the elastic deformation of matter, flexure mechanisms can be fabricated monolithically to produce geometrically well defined motion upon application of a force. Compared to conventional mechanical bearings, flexure joints have several advantages due to their frictionless behavior: no need for lubrication, no wear (no dust is emitted), and no risk of jamming. Furthermore, the load–displacement characteristic of flexures does not present mechanical hysteresis because they do not have any mechanical clearance (no backlash). Thus, despite their limited stroke, flexure mechanisms have been commonly used for decades in precision engineering and in harsh environment applications since they provide precise, accurate, and repeatable displace- ments [1]–[3]. As a prelude to the design of flexure-based mechanisms, it is worthwhile to recall the two main types of joints encountered in robotic systems: the revolute or hinged joint (denoted by an R) and the prismatic or sliding joint (denoted by a P). Most other joints used for spatial linkages can be modeled and constructed as combinations of revolute and prismatic joints. As an example, consider the planar joint which allows a plane on one rigid body to slide and rotate in the plane of another rigid body. It has three degrees of freedom (DOFs) and can be constructed either as a planar RRR, RRP, RPR, PRR, RPP, PRP, or PPR serial chain [4]–[6]. It is therefore understandable that the design of compliant R/P joints with large displacement capabilities is of special interest for precision robotics [7], [8]. Hereafter, we will nevertheless limit the discussion to in-plane monolithic flexure mechanisms. The folded-beam flexure or double-parallelogram flexure— which produces purely rectilinear movement—has probably been the most frequently encountered prismatic flexure joint in silicon-based microelectromechanical systems (MEMS) since its introduction in a push–pull electrostatic microactuator [9]– [11]. Conversely, rotary flexure micromechanisms have been much less applied in MEMS devices. However, there is no shortage of possible applications: To mention just a few exam- ples, they can be used for skew angle compensation in hard- disk drives (HDDs) [12], [13], as rotary actuators in variable optical attenuators or other optical MEMS devices [14]–[19], or in microgrippers (in lever mechanisms for grasping) as an alternative to push–pull linear actuation [20], [21]. However, most flexure-based MEMS rotary devices developed so far have angular ranges limited to a few degrees [22]–[25]. To our knowledge, the “butterfly pivot” devised by Henein et al. (see Fig. 1) is the monolithic rotational guiding with the largest angular range (±15 ◦ ) that has been proposed to date both macroscopically [3], [8], [26] or integrated in a MEMS microactuator [13], [27], [28]. 1057-7157/$31.00 © 2012 IEEE