Nilesh D. Mankame
1
Vehicle Development Research Lab.,
General Motors Research & Development,
Warren, MI
e-mail: nilesh.mankame@gm.com
G. K. Ananthasuresh
2
Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore, India
e-mail: suresh@mecheng.iisc.ernet.in
A Compliant Transmission
Mechanism With Intermittent
Contacts for Cycle-Doubling
A novel compliant transmission mechanism that doubles the frequency of a cyclic input is
presented in this paper. The compliant cycle-doubler is a contact-aided compliant mecha-
nism that uses intermittent contact between itself and a rigid surface. The conceptual
design for the cycle-doubler was obtained using topology optimization in our earlier
work. In this paper, a detailed design procedure is presented for developing the topology
solution into a functional prototype. The conceptual design obtained from the topology
solution did not account for the effects of large displacements, friction, and
manufacturing-induced features such as fillet radii. Detailed nonlinear finite element
analyses and experimental results from quasi-static tests on a macro-scale prototype are
used in this paper to understand the influence of the above factors and to guide the design
of the functional prototype. Although the conceptual design is based on the assumption of
quasi-static operation, the modified design is shown to work well in a dynamic setting for
low operating frequencies via finite element simulations. The cycle-doubler design is a
monolithic elastic body that can be manufactured from a variety of materials and over a
range of length scales. This makes the design scalable and thus adaptable to a wide
range of operating frequencies. Explicit dynamic nonlinear finite element simulations are
used to verify the functionality of the design at two different length scales: macro (device
footprint of a square of 170 mm side) at an input frequency of 7.8 Hz; and meso (device
footprint of a square of 3.78 mm side) at an input frequency of 1 kHz.
DOI: 10.1115/1.2403774
1 Introduction
The focus of this paper is a compliant transmission that is ca-
pable of doubling the frequency of an actuator. In this section, we
begin with a brief description of compliant transmissions and then
explain the motivation for this work.
1.1 Compliant Transmissions. The selection of an actuator
for an application is primarily based on the range and resolution
of its attributes such as displacement i.e., stroke, force, and op-
erating frequency 1. Considerations of size, cost, efficiency, ease
of maintenance, and power supply also play important roles in the
choice of an actuator. When it is not possible to find an actuator
that meets the above requirements for an application, a transmis-
sion is used. Transmissions transform the work done by actuators
to match the requirements of various applications or of varying
loads and speeds within an application. Transmissions based on
rigid-body mechanisms such as linkages and gear trains have been
widely used in mechanical and electromechanical systems. How-
ever, these transmissions are not suitable for many applications
that require high repeatability or small sizes 2. Compliant
mechanisms CMs, which are single-piece elastic bodies that de-
form to transmit and transform force and motion, are useful in
those cases. In this case, an important advantage of CMs over
rigid-body mechanisms is that the CMs can be tightly integrated
with an actuator to yield a compact system. This is especially
important for microactuators.
Figure 1 schematically illustrates some of the attributes that
have been modified by compliant transmissions that are used for
microactuators. Compliant displacement-amplifiers such as the
ones reported in Refs. 2–4 change the force-displacement char-
acteristic represented by C
1
to C
2
for electrostatic and thermal
microactuators. Force-amplifiers do the reverse: they transform C
2
to C
1
. Pedersen and Seshia 5 presented a compliant force-
amplifier for a resonant-mode inertial microsensor. Pedersen et al.
6 showed that compliant transmissions can also modify the
shape of the force-displacement characteristic to C
3
from C
1
or
C
2
. In microactuators, there is a need for a fourth kind of compli-
ant transmission that changes the frequency of actuation, i.e.,
transforming C
1
to C
4
. The novel compliant device presented in
this paper was motivated by this need, as explained below.
1.2 Motivation. Among the existing microactuators, thermal
actuators which are based on constrained thermo-elastic expan-
sion, phase change, etc. form an important class with capabilities
of high forces and displacements. However, they are restricted to
low operation frequencies due to the time delays caused by cool-
ing and reheating of the actuators between successive cycles. Hu-
ber et al. 1 recommend that due to their high work-density work
output per unit mass, thermal actuators should be considered for
macro-scale applications that require compact actuators and low
frequencies of operation 10 Hz. Improved heat transfer rates
at the microscale, allow thermal actuators to be operated at higher
frequencies e.g., 1 kHz for bent-beam thermal microactuators
4, but these frequencies are still small as compared to other
actuation schemes such as electrostatic comb drives, which can
run at frequencies of O 10 MHz7. However, electrostatic mi-
croactuators cannot generate large forces over large distances. Un-
like thermal actuators, which can work in the voltage-current re-
gime of conventional microelectronics, electrostatic actuators
require much higher voltages. Thermal actuators can be used for
more applications if a transmission can be designed to transform
the high force, high stroke, but low frequency output of a thermal
1
Formerly a doctoral student at University of Pennsylvania, Philadelphia.
2
Corresponding author; formerly an Associate Professor at University of Pennsyl-
vania, Philadelphia.
Contributed by the Power Transmission and Gearing Committee of ASME for
publication in the JOURNAL OF MECHNICAL DESIGN. Manuscript received March 7,
2005; final manuscript received September 15, 2006. Review conducted by Prof.
David Dooner. Paper presented at the ASME 2004 Design Engineering Technical
Conferences and Computers and Information in Engineering Conference
DETC2004, September 28–October 2, 2004, Salt Lake City, Utah, USA.
114 / Vol. 129, JANUARY 2007 Copyright © 2007 by ASME Transactions of the ASME