Scaling Analysis of Large Stroke Piezoelectric Cellular Actuators Thomas W. Secord and H. Harry Asada ∗ ∗ Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: {secord,asada}@mit.edu). Abstract: This paper presents a scaling analysis for a novel method of amplifying the motion of piezoelectric stack actuators. The amplification method involves nesting, or layering, of individual flexure mechanisms atop piezoelectric stacks to create a large stroke actuator subunit. A single subunit is referred to as an actuator cell. First, we develop an augmented kinematic model and a deterministic design process to arrive at closed form equations of cell performance. We then describe performance metrics that are used to evaluate the cell design as the size of the piezoelectric stacks is varied. For each performance metric, we provide numerical scaling contours that are determined using only mild design assumptions and realistic manufacturing constraints. With respect to maximum work density and cell packing efficiency, we find that there exists an relatively narrow optimal scale region for the cell designs. Keywords: Piezoelectric actuator, scaling analysis, compliant mechanisms, flexures. 1. INTRODUCTION Piezoelectric stack actuators have a long history of high force (kN), high bandwidth (kHz), and high precision (µm) applications. In typical robotics applications, however, the actuation requirements involve much larger displacements at lower bandwidth. Furthermore, for bio-robotics appli- cations involving environmental interaction, inherent com- pliance is a key characteristic. Thus, our goal in this work is to quantitatively describe the scaling properties of an artificial muscle actuator system that meets the demands of several bio-robotics applications. Our actuator design utilizes nested flexure mechanisms to amplify the motion of piezoelectric stacks. Each flexure operates on a principle similar to that described in Dogan et al. (1994) and provides a displacement increase gain and force reduction gain of approximately 10. A two layer nesting, or cascading, scheme allows an overall mechanical amplification gain of 100 to be achieved. The combination of the piezoelectric stack and the nested flexures is referred to as an actuator cell. Similar to biological muscle, these cells may then be placed in series, antagonistic, or parallel configurations to achieve a wide range of force and dis- placement characteristics. Although the design has many promising features, the optimum scale or size for a cell has not yet been determined. This paper draws upon our previous work in Ueda et al. (2007) and Secord et al. (2008) where we describe the basic operating principle and static model for the actuator. We build upon these previous investigations by addressing a crucial design question: how does the flexure-based actuator design performance scale with the size of the piezoelectric actuator? To address the scaling question, the paper is organized into two main sections. Section 2 describes necessary background information on piezoelectric stack actuators and the basic concept of our design. Section 3 then describes a simplified model of the flexure based system that is then used for numerical scaling analysis. In this section, we evaluate the effects of changing piezoelectric stack size on several performance metrics. 2. PIEZOELECTRIC STACKS AND KINEMATIC AMPLIFICATION 2.1 Piezoelectric Stack Actuators Piezoelectric materials generate strain in response to applied electric fields and generate charge in response to applied stress. Piezoelectric stack actuators are most commonly constructed from several thin layers of lead- zirconate-titanate (PZT). When designed to operate at low voltages (≈ 100 V), the stack actuators are monolithic structures having embedded electrodes that form many parallel capacitive elements. The construction of a typical stack is shown in Fig. 1 (a). For the purposes of this paper, we will focus our attention on rectangular cross section stacks although circular and annular geometries cross sections also common. The geometric parameters of a rectangular PZT stack are its length (L pzt ), height (h pzt ), width (w pzt ), and film thickness (t f ilm ). The number of films in the stack is then Lpzt t f ilm . In response to an applied voltage of V pzt , an electric field of strength Vpzt t f ilm is generated in each layer of the stack. If the ends of the stack actuator are unconstrained and the maximum voltage V max pzt is applied, then the free displacement (Δx free pzt ) of the stack is generated: Δx free pzt = N f ilm d 33 V max pzt , (1) 5th IFAC Symposium on Mechatronic Systems Marriott Boston Cambridge Cambridge, MA, USA, Sept 13-15, 2010 978-3-902661-76-0/10/$20.00 © 2010 IFAC 131 10.3182/20100913-3-US-2015.00061