0
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.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 4

Pinned beams with a semicircular shape

Grahic Jump Location
Fig. 5

Actual F-ye curve versus fitted line

Grahic Jump Location
Fig. 6

Original and deformed shapes of the semicircular beam

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
Fig. 11

Stiffness-to-preload curves

Grahic Jump Location
Fig. 12

(a) Triangular beam and (b) rectangular beam

Grahic Jump Location
Fig. 13

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

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
Fig. 15

Optimal shape of the fixed beam

Grahic Jump Location
Fig. 16

F-ye curves of the fixed beams

Grahic Jump Location
Fig. 17

σm-ye curves of the fixed beams

Grahic Jump Location
Fig. 18

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

Grahic Jump Location
Fig. 19

Schematics of changing the equilibrium position and static force

Grahic Jump Location
Fig. 20

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

Grahic Jump Location
Fig. 21

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

Grahic Jump Location
Fig. 22

Experiment setup (pinned beams)

Grahic Jump Location
Fig. 23

Experiment setup (fixed beams)

Grahic Jump Location
Fig. 24

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

Grahic Jump Location
Fig. 25

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

Grahic Jump Location
Fig. 26

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

Grahic Jump Location
Fig. 27

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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In