Closed-Form Modeling and Analysis of an XY Flexure-Based Nano-Manipulator
Qin et al. Chin. J. Mech. Eng.
Closed-Form Modeling and Analysis of an XY Flexure-Based Nano-Manipulator
Yan‑Ding Qin 0
Xin Zhao 0
Bijan Shirinzadeh 2
Yan‑Ling Tian 1
DaW‑ei Zhang 1
0 Institute of Robotics and Automatic Information System (Tianjin Key Laboratory of Intelligent Robotics), Nankai University , Tianjin 300350 , China
1 School of Mechanical Engineering, Tianjin University , Tianjin 300072 , China
2 Robotics and Mechatronics Research Laboratory, Department of Mechanical and Aerospace Engineering, Monash University , Clayton, VIC 3800 , Australia
Flexure‑ based mechanisms are widely utilized in nano manipulations. The closed‑ form statics and dynamics modeling is difficult due to the complex topologies, the inevitable compliance of levers, the Hertzian contact interface, etc. This paper presents the closed‑ form modeling of an XY nano‑ manipulator consisting of statically indeterminate symmetric (SIS) structures using leaf and circular flexure hinges. Theoretical analysis reveals that the lever's compliance, the contact stiffness, and the load mass have significant influence on the static and dynamic performances of the system. Experiments are conducted to verify the effectiveness of the established models. If no piezoelectric actuator (PEA) is installed, the influence of the contact stiffness can be eliminated. Experimental results show that the estimation error on the output stiffness and first natural frequency can reach 2% and 1.7%, respectively. If PEAs are installed, the contact stiffness shows up in the models. As no effective method is currently available to measure or estimate the contact stiffness, it is impossible to precisely estimate the performance of the overall system. In this case, the established closed‑ form models can be utilized to calculate the bounds of the performance. The established closed‑ form models are widely applicable in the design and optimization of planar flexure‑ based mechanisms.
Flexure‑ based mechanism; Statically indeterminate structure; Dynamics; Lever mechanism; Piezoelectric actuator
1 Introduction
The integrations of piezoelectric actuators (PEAs) and
flexure-based mechanisms have been widely utilized in
nano-positioning and manipulations [1–5]. On the one
hand, the shape of a PEA changes if charge or voltage
is exerted, and thus generating sub-nanometer
resolution actuation. However, PEAs suffer from the inherent
hysteresis and creep nonlinearities [6–8]. Many
feedforward and feedback methodologies have been proposed to
compensate for the hysteresis and creep nonlinearities of
PEAs [9, 10]. On the other hand, flexure-based
mechanisms are capable of transmitting high-precision motions
via the elastic deformations of the flexure hinges, making
it ideal in building the transmission chains for PEAs [11,
12]. Widely utilized flexure hinge profiles include circular
[13–16] and leaf [17, 18].
A single flexure hinge can be treated as a revolute
joint during micro- and nano-scale motions. In
literature, many analytical and empirical models have been
established for the compliance/stiffness of a single
flexure hinge [19–21]. In order to improve the performance,
multiple flexure hinges are generally combined in various
configurations, such as the parallelograms [22–24] and
the statically indeterminate symmetric (SIS) structures
[25]. In these structures, it is common to treat the flexure
hinges as flexible, and all the other components as rigid.
Considering the widely-utilized lever mechanism as an
example, the lever is frequently assumed to be rigid [26,
27] so as to facilitate the design and modeling processes.
However, this assumption may increase the estimation
error of the analytical model, especially when the lever is
long or the compliance of the lever is not negligible.
A PEA is brittle and very weak when subjected to large
lateral forces or torques. As a result, a PEA is not allowed
to be firmly fixed to the mechanism during the
installation. Many commercial PEAs use ball tips to eliminate
the bending torques. In this case, a Hertzian contact
interface forms between the tip and the mechanism. One
significant drawback of Hertzian contact is its low
contact stiffness that consumes large portion of the PEA’s
displacement. The contact stiffness is highly dependent
on the material properties and the contact status.
Currently, there is no effective and reliable model to estimate
the contact stiffness. Thus, the contact stiffness is
frequently identified from the measured data [2].
As a flexure-based mechanism is generally light and
compact, its performance is likely to be affected by the
load mass, including the sensors, end-effectors, fixtures,
and other accessories installed on the mechanism. The
load mass increases the effective mass and moment of
inertia of the system, leading to a slow response. Thus,
the influence of the load mass should be taken into
consideration in the design and modeling of flexure-based
mechanisms.
This paper presents the cl (...truncated)