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RESEARCH PAPERS

Design of Compliant Mechanisms for Minimizing Input Power in Dynamic Applications

[+] Author and Article Information
Tanakorn Tantanawat

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109tanakorn@umich.edu

Sridhar Kota

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109kota@umich.edu

J. Mech. Des 129(10), 1064-1075 (Oct 25, 2006) (12 pages) doi:10.1115/1.2756086 History: Received July 13, 2006; Revised October 25, 2006

In this paper, we investigate power flow in compliant mechanisms that are employed in dynamic applications. More specifically, we identify various elements of the energy storage and transfer between the input, external load, and strain energy stored within the compliant transmission. The goal is to design compliant mechanisms for dynamic applications by exploiting the inherent energy storage capability of compliant mechanisms in the most effective manner. We present a detailed case study on a flapping mechanism, in which we compare the peak input power requirement in a rigid-body mechanism with attached springs versus a distributed compliant mechanism. Through this case study, we present two approaches: (1) generative-load exploitation and (2) reactance cancellation, to describe the role of stored elastic energy in reducing the peak input power requirement. We propose a compliant flapping mechanism and its evaluation using nonlinear transient analysis. The input power needed to drive the proposed compliant flapping mechanism is found to be 50% less than a rigid-link four-bar flapping mechanism without a spring, and 15% less than the one with a spring. This reduction of peak input power is primarily due to the exploitation of elasticity in compliant members. The results show that a compliant mechanism can be a better alternative to a rigid-body mechanism with attached springs.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Four-bar flapping mechanism adapted from Madangopal (2)

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Figure 2

Variation of inertial torque over a cycle of flapping motion

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Figure 3

Variation of lift over a cycle of flapping motion

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Figure 4

Input powers of the mechanism with and without a spring. Adding a spring reduces peak input power by 42%.

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Figure 5

Various power components of the mechanism with a spring, including kinetic energy rate (KER), potential energy rate (PER), input power (Pin), and output power (Pout)

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Figure 6

For Case I (constant output force only), adding a spring reduces peak input power by 84%

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Figure 7

For Case I (constant output force only) without a spring, the motor has to supply and absorb the full amount of energy to balance the energy extracted and injected by the output force

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Figure 8

For Case I (constant output force only) with a spring, the presence of a spring helps the motor supply and absorb energy extracted and injected by the output force, thus reducing the effort needed by the motor to balance the system

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Figure 9

For Case II (inertial force only), adding a spring reduces peak input power by 83%

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Figure 10

For Case II (inertial force only) without a spring, the motor has to supply and absorb the full amount of energy stored and released by links’ masses

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Figure 11

For Case II (inertial force only), the spring added to the system helps absorb and supply energy as the links decelerate and accelerate, thus reducing the power requirement from the motor

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Figure 12

For Case III (damping output force only), adding a spring increases peak input power by 78%

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Figure 13

For Case III (damping output force only) without a spring, the motor has to supply energy equal to the amount extracted by the output force

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Figure 14

For Case III (damping output force only) with a spring, besides supplying energy to the output force, the motor also has to supply energy to be stored in the spring

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Figure 15

For Case III (damping output force only), adding a spring of any stiffness, in this case with a free length of 50mm, results in undesired increase in peak input power

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Figure 16

For Case III (damping output force only), adding a spring of any free length, in this case with a stiffness of 38N∕m, results in undesired increase in peak input power. At best it keeps the peak input power as low as that resulting from not adding a spring into the system.

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Figure 17

Concept of using elasticity to reduce peak input power requirement in dynamic systems

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Figure 18

A 2DOF system used to validate the concept of generative-load exploitation and reactance cancelation in compliant mechanisms

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Figure 19

A general plot of ∣G1∣ and ∣G2∣ as functions of k3 when k1 is zero

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Figure 20

Front view of the compliant flapping mechanism showing the initial design before optimization

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Figure 21

Top view of the compliant flapping mechanism showing a wing section with nonuniform mass and stiffness distribution

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Figure 22

An example of input displacement with gradually increasing amplitude to facilitate the convergence of nonlinear transient analysis

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Figure 23

Design variables include (a) ten variables of x and y locations for five keypoints, (b) 25 variables of beam heights for nine beam segments, and two variables for amplitude and average values of input displacement (see Fig. 2)

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Figure 24

Optimal design of a compliant flapping mechanism obtained from the use of NOMADm and SQP algorithms

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Figure 25

The mechanism produces a flapping angle of 44.8deg, generating a sufficient lift for the vehicle at 4Hz

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Figure 26

Wing rotation over a flapping cycle at steady state (after seven cycles)

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Figure 27

Variation of different power components over a flapping cycle at steady state

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