Research Papers: Design of Mechanisms and Robotic Systems

Linear Variable-Stiffness Mechanisms Based on Preloaded Curved Beams

[+] Author and Article Information
Yi-Syuan Wu

Department of Mechanical Engineering,
National Cheng Kung University,
No. 1, University Road,
Tainan City 701, Taiwan
e-mail: q331110@gmail.com

Chao-Chieh Lan

Department of Mechanical Engineering,
National Cheng Kung University,
No. 1, University Road,
Tainan City 701, Taiwan
e-mail: cclan@mail.ncku.edu.tw

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 20, 2014; final manuscript received September 11, 2014; published online October 20, 2014. Assoc. Editor: Shorya Awtar.

J. Mech. Des 136(12), 122302 (Oct 20, 2014) (10 pages) Paper No: MD-14-1181; doi: 10.1115/1.4028705 History: Received March 20, 2014; Revised September 11, 2014

A machine with an internal variable-stiffness mechanism can adapt its output force to the working environment. In the literature, linear variable-stiffness mechanisms (LVSMs) are rarer than those producing rotary motion. This paper presents the design of a class of novel LVSMs. The idea is to parallel connect two lateral curved beams with an axial spring. Through preload adjustment of the curved beams, the output force-to-displacement curves can exhibit different stiffness. The merit of the proposed LVSMs is that very large-stiffness variation can be achieved in a compact space. The stiffness can even be tuned to zero by assigning the appropriate stiffness to the axial spring. LVSMs with pinned curved beams and fixed curved beams are investigated. To achieve the largest stiffness variation with sufficient linearity, the effects of various parameters on the force curves are discussed. Techniques to scale an LVSM and change the equilibrium position are introduced to increase the usefulness of the proposed design. Finally, the LVSMs are experimentally verified through prototypes.

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Fig. 4

Pinned beams with a semicircular shape

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Fig. 5

Actual F-ye curve versus fitted line

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Fig. 3

Different ranges of stiffness variation: (a) the smallest stiffness is positive, (b) the smallest stiffness is zero, and (c) the smallest stiffness is negative

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Fig. 2

(a) F-ye curves of the curved beams (b) F-ye curves of the axial spring only

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Fig. 1

(a) Schematic of the proposed LVSM (b) F-ye curves of using different values of Δs

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Fig. 12

(a) Triangular beam and (b) rectangular beam

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Fig. 6

Original and deformed shapes of the semicircular beam

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Fig. 7

F-ye curves of the semicircular beams (lines are the GMSM results and circles are the corresponding FEA results)

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Fig. 8

F-ye curves of the LVSM (ka = 7.1737 N/mm)

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Fig. 9

σm-ye curves of the semicircular beam (lines are the GMSM results and circles are the corresponding FEA results)

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Fig. 10

FEA of the semicircular beam (a) ye = 5.5, Δs = 3 mm and (b) ye = −5.5, Δs = −3 mm

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Fig. 11

Stiffness-to-preload curves

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Fig. 13

Different trial shapes, (a) one-arc, (b) two-arc, and (c) three-arc

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Fig. 14

(a) Schematic of the fixed beam design and (b) parameterization of a segment of the beam

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Fig. 19

Schematics of changing the equilibrium position and static force

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Fig. 25

Experimental F-ye curves of the LVSM using the pinned beams (marks are simulation results, calibrated EI = 0.2336 Nm2)

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Fig. 27

Experimental F-ye curves of the LVSM using the fixed beams (five layers)

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Fig. 15

Optimal shape of the fixed beam

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Fig. 16

F-ye curves of the fixed beams

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Fig. 17

σm-ye curves of the fixed beams

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Fig. 18

FEA of the fixed beam (a) ye = 5.5, Δs = 3 mm (b) ye = −5.5, Δs = −3 mm

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Fig. 20

(a) CAD model of the LVSM and (b) the inclined links

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Fig. 21

(a) Schematic of the axial spring design, (b) one half of a cell, and (c) prototype

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Fig. 22

Experiment setup (pinned beams)

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Fig. 23

Experiment setup (fixed beams)

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Fig. 24

Experimental F-ye curves of the LVSM using the pinned beams (marks are simulation results)

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Fig. 26

Experimental F-ye curves when the equilibrium position is changed to ye = −5.5 mm (pinned beams)




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