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Research Papers

# A Monolithic Force-Balanced Oscillator

[+] Author and Article Information
Sybren L. Weeke

Department of Precision
and Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands;
Flexous B.V.,
Delft 2629 JD, The Netherlands
e-mail: sybren.weeke@flexous.com

Nima Tolou, Just L. Herder

Department of Precision
and Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands

Guy Semon

TAG Heuer,
La Chaux-de-Fonds 2300, Switzerland

1Corresponding author.

Manuscript received October 10, 2016; final manuscript received December 14, 2016; published online March 9, 2017. Assoc. Editor: James Schmiedeler.

J. Mechanisms Robotics 9(2), 021004 (Mar 09, 2017) (8 pages) Paper No: JMR-16-1299; doi: 10.1115/1.4035544 History: Received October 10, 2016; Revised December 14, 2016

## Abstract

Usage of compliant micromechanical oscillators has increased in recent years, due to their reliable performance despite the growing demand for miniaturization. However, ambient vibrations affect the momentum of such oscillators, causing inaccuracy, malfunction, or even failure. Therefore, this paper presents a compliant force-balanced mechanism based on rectilinear motion, enabling usage of prismatic oscillators in translational accelerating environments. The proposed mechanism is based on the opposite motion of two coplanar prismatic joints along noncollinear axes via a shape-optimized linkage system. Rigid-body replacement with shape optimized X-bob, Q-LITF, and LITF joints yielded a harmonic (R > 0.999), low frequency ($f=27 Hz$) single piece force-balanced micromechanical oscillator ($∅$ 35 mm). The experimental evaluation of large-scale prototypes showed a low ratio of the center of mass (CoM) shift compared to the stroke of the device ($≈$ 0.01) and proper decoupling of the mechanism from the base, as the oscillating frequency of the balanced devices during ambient disturbances was unaffected, whereas unbalanced devices had frequency deviations up to 1.6%. Moreover, the balanced device reduced the resultant inertial forces transmitted to the base by 95%.

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## Figures

Fig. 1

Nonisomorphic kinematic chains of a 1DOF mechanism were developed into acceptable and optimal specialized kinematic chains for a planar force-balanced mechanism comprising (at least) one prismatic joint (P) attached to a base (GR) (a)–(c). These specialized kinematic chains were individually translated back into their corresponding mechanisms: a crank-slider, a double crank-slider and an opposite movement mechanism.

Fig. 2

Variables that were used for the shape optimization of the X-bob joint, LITF joint, and Q-LITF joint. Flexures areshown in red where rigid elements are black. (a) One quadrant X-bob, (b) LITF for joint A+C, (c) Q-LITF for joint O, and (d) Q-LITF for joint B+D.

Fig. 3

Image of a 1:1 scale silicon prototype of the integrated system (b), together with finite-element simulations of the deflected system in its extreme positions (a) and (c). Revolute joint labels are in correspondence to Fig. 1.

Fig. 4

Measurement setups for experimental evaluation of the resultant inertial forces (a) and dynamic decoupling (b). (a) A large-scale prototype was clamped on two force sensors mounted in an L-configuration for measurement of in-plane resultant inertial forces. (b) A shaker table mimics external disturbances while the amplitude and frequency of the large-scale prototype were measured with a laser sensor.

Fig. 5

On-axial displacement of the prismatic joints tracked with a high-speed camera during oscillation for a time period of 1.4 s. The green line in both figures outlines the difference of the two signals and thus represents the movement of the center-of-mass.

Fig. 6

Results of the experimental evaluation of in-plane inertial forces in time (a) and frequency (b) domain. (a) Measured forces of sensor 1 and sensor 2 for both balanced (black dotted) and unbalanced (blue and green) devices. (b) Measured forces of sensor 1 and sensor 2 for both a balanced (black) and unbalanced (blue dashed) devices, represented in the frequency domain.

Fig. 7

Results experimental evaluation dynamic decoupling of balanced and unbalanced devices for different types of disturbance. (a) Oscillation of both the balanced and unbalanced mechanism while in rest (dotted black) and while subjected to a disturbance (blue) of 8 Hz and 1 mm. (b) Oscillation of both the balanced and unbalanced mechanism while in rest (dotted black) and while subjected to a disturbance (blue) of 1 Hz and 6 mm.

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