Abstract

Compliant shell mechanisms utilize thin-walled structures to achieve motion and force generation. Shell mechanisms, because of their thin-walled nature and spatial geometry, are building blocks for spatial mechanism applications. In spatial compliant mechanism design, the ratio of compliance is the representation of the kinetostatics involved. Using shell mechanisms in concept design, however, can prove difficult without a uniform characterization method. In this article, we make use of compliance ellipsoids to achieve characterization of the ratio of compliance for shell mechanisms. Ten promising shells are presented with the kinetostatic characteristics, combined with a uniform method of determining the kinetostatic characteristics for other unknown shells. Finally, we show how shells are indeed a valid alternative in the spatial mechanism design, compared to conventional flexure mechanisms.

References

1.
Seffen
,
K. A.
,
2012
, “
Compliant Shell Mechanisms
,”
Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
,
370
(
1965
), pp.
2010
2026
. 10.1098/rsta.2011.0347
2.
Howell
,
L.
,
2001
,
Compliant Mechanisms
,
Wiley & Sons
,
Hoboken, NJ
.
3.
Farshad
,
M.
,
1992
,
Design and Analysis of Shell Structures
,
Springer
,
New York
.
4.
Radaelli
,
G.
, and
Herder
,
J. L.
,
2017
, “
Gravity Balanced Compliant Shell Mechanisms
,”
Int. J. Solids Struct.
,
118–119
, pp.
78
88
. 10.1016/j.ijsolstr.2017.04.021
5.
Budiansky
,
B.
,
1974
,
Theory of Buckling and Post-Buckling Behavior of Elastic Structures
(
Vol. 14 of Advances in Applied Mechanics
),
Elsevier
, pp.
1
65
.
6.
Houwers
,
H. W. R.
,
2016
, “
Closed-Loop Two-Fold Tape Spring Transmissions
,” Master thesis,
Delft University of Technology
,
Delft, Netherlands
.
7.
Rommers
,
J.
,
Radaelli
,
G.
, and
Herder
,
J. L.
,
2017
, “
Pseudo-Rigid-Body Modeling of a Single Vertex Compliant-Facet Origami Mechanism
,”
ASME J. Mech. Rob.
,
9
(
3
), p.
031009
. 10.1115/1.4035881
8.
Pellegrino
,
S.
,
2005
, “
Bistable Shell Structures
,”
Collection of Technical Papers—AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
,
Austin, TX
,
Apr. 18-21
, vol.
3
, pp.
1658
1665
.
9.
Radaelli
,
G.
, and
Herder
,
J.
,
2014
, “
Isogeometric Shape Optimization for Compliant Mechanisms With Prescribed Load Paths
,”
Proceedings of the ASME Design Engineering Technical Conference
, Vol.
5A
,
Buffalo, NY
,
Aug. 17–20
.
10.
Alkisaei
,
H.
,
2016
, “
Statically Balanced Compliant Walls
,”
Master thesis
,
Delft University of Technology
,
Delft, Netherlands
.
11.
Ring
,
J.
, and
Kim
,
C.
,
2016
, “
A Passive Brace to Improve Activities of Daily Living Utilizing Compliant Parallel Mechanisms
,”
Proceedings of the ASME Design Engineering Technical Conference
, Vol.
5A
,
Charlotte, NC
,
Aug. 21–24
.
12.
Nijssen
,
J.
,
Radaelli
,
G.
,
Herder
,
J.
,
Kim
,
C.
, and
Ring
,
J.
,
2017
, “
Design and Analysis of a Shell Mechanism Based Two-Fold Force Controlled Scoliosis Brace
,”
Proceedings of the ASME Design Engineering Technical Conference
, Vol.
5A
,
Cleveland, OH
,
Aug. 6–9
.
13.
Kim
,
C. J.
,
2005
, “
A Conceptual Approach to the Computational Synthesis of Compliant Mechanisms
,” Ph.D. thesis,
University of Michigan
,
Ann Arbor, MI
.
14.
Norman
,
A. D.
,
Seffen
,
K. A.
, and
Guest
,
S. D.
,
2008
, “
Multistable Corrugated Shells
,”
Proc. R. Soc. A: Math. Phys. Eng. Sci.
,
464
(
2095
), pp.
1653
1672
. 10.1098/rspa.2007.0216
15.
Koiter
,
W. T.
,
1966
, “
On the Nonlinear Theory of Thin Elastic Shells, I–III
,” Kon. Ndeerl. Akad. v. Wet. Amsterdam, 1–54.
16.
Calladine
,
C. R.
,
1983
,
Theory of Shell Structures
,
Cambridge University Press
,
Cambridge, UK
.
17.
Ciarlet
,
P.
,
2005
,
An Introduction to Differential Geometry With Applications to Elasticity
, 1st. ed.,
Springer
,
New York
.
18.
Wolfs
,
J.
,
2013
, “
Modelling of Multistable Shells, A Differential Geometry Based Approach
.”
19.
Struik
,
D.
,
2012
,
Lectures on Classical Differential Geometry
, 2nd ed.,
Courier Corporation
,
MA
.
20.
Schenk
,
M.
,
2011
, “
Folded Shell Structures
,” Ph.D. thesis, University of Cambridge, Cambridge.
21.
Krivoshapko
,
S.
, and
Ivanov
,
V.
,
2015
,
Encyclopedia of Analytical Surfaces
,
Springer
,
New York
.
22.
Howell
,
L. L.
,
Magleby
,
S. P.
, and
Olsen
,
B.
,
2013
,
Handbook of Compliant Mechanisms
, 1st ed.,
Wiley
,
Hoboken, NJ
.
23.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2011
, “
Synthesis of Precision Serial Flexure Systems Using Freedom and Constraint Topologies (FACT)
,”
Precis. Eng.
,
35
(
4
), pp.
638
649
. 10.1016/j.precisioneng.2011.04.006
24.
Hopkins
,
J. B.
,
2013
, “
Designing Hybrid Flexure Systems and Elements Using Freedom and Constraint Topologies
,”
Mech. Sci.
,
4
(
2
), pp.
319
331
. 10.5194/ms-4-319-2013
25.
Soemers
,
H.
,
2011
,
Design Principles for Precision Mechanisms
,
T-Point print, University of Twente
,
Enschede
.
26.
Leemans
,
J. R.
,
Kim
,
C. J.
,
van de Sande
,
W. W. P. J.
, and
Herder
,
J. L.
,
2019
, “
Unified Stiffness Characterization of Nonlinear Compliant Shell Mechanisms
,”
ASME J. Mech. Rob.
,
11
(
1
), p.
011011
. https://doi.org/10.1115/1.4041785
27.
Norman
,
A. D.
,
Seffen
,
K. A.
, and
Guest
,
S. D.
,
2009
, “
Morphing of Curved Corrugated Shells
,”
Int. J. Solids Struct.
,
46
(
7
), pp.
1624
1633
. 10.1016/j.ijsolstr.2008.12.009
28.
Krivoshapko
,
S.
,
2001
, “
Stress-Strain Analysis of Thin Elastic Evolvent Helicoidal Shells
,”
Shells in Architecture and Strength Analysis of Thin-Walled Civil Engineering and Machine Building Constructions of Complex Forms International Conference Proceedings
,
Moscow, Russia
,
June 4–8
, pp.
193
200
.
29.
Nijenbanning
,
G.
,
1998
, “
Scoliosis Redress. Design of a Force Controlled Orthosis
,” Ph.D. thesis,
University of Twente
,
Enschede, The Netherlands
.
30.
Rolton
,
D.
,
Nnadi
,
C.
, and
Fairbank
,
J.
,
2014
, “
Scoliosis: A Review
,”
Paediatr. Child Health
,
24
(
5
), pp.
197
203
. 10.1016/j.paed.2013.09.014
31.
Nijssen
,
J.
,
Radaelli
,
G.
,
Herder
,
J.
,
Ring
,
J.
, and
Kim
,
C.
,
2018
, “
Spatial Concept Synthesis of Compliant Mechanisms Utilizing Non-Linear Eigentwist Characterization
,”
Proceedings of the ASME Design Engineering Technical Conference
, Vol.
5A
,
Quebec City, Canada
,
Aug. 26–29
.
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