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RESEARCH PAPERS

# A Compliant Transmission Mechanism With Intermittent Contacts for Cycle-Doubling

[+] Author and Article Information
Nilesh D. Mankame1

Vehicle Development Research Lab., General Motors Research & Development, Warren, MInilesh.mankame@gm.com

G. K. Ananthasuresh2

Department of Mechanical Engineering, Indian Institute of Science, Bangalore, Indiasuresh@mecheng.iisc.ernet.in

1

Formerly a doctoral student at University of Pennsylvania, Philadelphia.

2

Corresponding author; formerly an Associate Professor at University of Pennsylvania, Philadelphia.

J. Mech. Des 129(1), 114-121 (Sep 15, 2006) (8 pages) doi:10.1115/1.2403774 History: Received March 07, 2005; Revised September 15, 2006

## Abstract

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 mechanism 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 $170mm$ side) at an input frequency of $7.8Hz$; and meso (device footprint of a square of $3.78mm$ side) at an input frequency of $1kHz$.

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## Figures

Figure 1

Some force-displacement-frequency characteristics of an actuator. Compliant transmissions can transform one type to another.

Figure 2

Schematic of a compliant mechanism that transforms one cycle of reciprocating, rectilinear input (force, F) at the input port (IP) into two cycles of reciprocating, rectilinear output (displacement, d) at the output port (OP). The mechanism is anchored to the ground at the locations labeled E.

Figure 3

Comparison of the output displacements (δ) vs. normalized input force for the cycle-doubler with the modified gap using linear and nonlinear finite element analyses

Figure 4

Left: Modeling the influence of fillets at the beam interconnections with additional cross-segments. Right: the beam-model of the top symmetric half of the cycle-doubler. The line at the top shows the rigid surface.

Figure 5

Comparison of the experimental and simulation data of the modified design. The experimental setup and the mechanism details are in Fig. 6 and Table 1.

Figure 6

The experimental setup for testing the prototype. A microcontroller (BS2, Basic Stamp2, Parallax Inc.) is used to control the stepper motor (SM, EAD Motors LA23ECKJ-4) which actuates the input port (IP) of the mechanism at a frequency of approximately 0.1Hz. The cycle-doubler is mounted on and anchored to a clear Plexiglas frame (PF) at the locations labeled E in Fig. 2. The horizontal white strips in the figure correspond to the external contact surfaces (CS), which are lined with Teflon®. A rare earth magnet is glued to the output port (OP) of the cycle doubler. This allows the displacement of the output port to be monitored in a noncontact manner by a linear Hall-effect sensor (HS, Allegro Microdevices A1323) mounted on the Plexiglas frame near the output port. Salient parameters for the experiment are summarized in Table 1.

Figure 7

Frictionless and unloaded characteristics: salient displacements

Figure 8

Output displacements in the presence of output load and friction

Figure 9

Input, normal contact and frictional contact forces for the case of lLA

Figure 10

The deflected profiles (see Table 3 for explanation of the labels 0, a–d as well as values of the stress) of the compliant cycle-doubler

Figure 11

Dynamic simulation of the macroscale, polypropylene design: salient displacements

Figure 12

Dynamic simulation of the microscale, silicon design: salient displacements

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