Abstract

The nonlinear analysis and design of contact-aided compliant mechanisms (CCMs) are challenging. This paper presents a nonlinear method for analyzing the deformation of general beams that contact rigid surfaces in CCMs. The large deflection of the general beam is modeled by using the chained pseudo-rigid-body model. A geometry constraint from the contact surface is developed to constrain the beam’s deformed configuration. The contact analysis problem is formulated based on the principle of minimum potential energy and solved using an optimization algorithm. Besides, a novel technique based on the principle of work and energy is proposed to calculate the reaction force/moment of displacement-loaded cases. Several analysis examples of the compliant mechanisms with straight or curved beams are used to verify the proposed method. The results show that the proposed method and technique can evaluate the deformation of beam-based CCMs and the reaction force/moment with acceptable accuracy, respectively.

References

1.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
John Wiley & Sons, Inc.
,
New York
.
2.
Mankame
,
N. D.
, and
Ananthasuresh
,
G.
,
2004
, “
Topology Optimization for Synthesis of Contact-Aided Compliant Mechanisms Using Regularized Contact Modeling
,”
Comput. Struct.
,
82
(
15–16
), pp.
1267
1290
. 10.1016/j.compstruc.2004.02.024
3.
Mankame
,
N. D.
, and
Ananthasuresh
,
G.
,
2002
, “
Contact Aided Compliant Mechanisms: Concept and Preliminaries
,”
ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Montreal, Canada
,
Sep. 29–Oct. 2
,
Paper No. DETC2002/MECH–34211
.
4.
Mankame
,
N. D.
, and
Ananthasuresh
,
G.
,
2004
, “
A Novel Compliant Mechanism for Converting Reciprocating Translation Into Enclosing Curved Paths
,”
ASME J. Mech. Des.
,
126
(
4
), pp.
667
672
. 10.1115/1.1759360
5.
Cannon
,
J. R.
, and
Howell
,
L. L.
,
2005
, “
A Compliant Contact-Aided Revolute Joint
,”
Mech. Mach. Theory
,
40
(
11
), pp.
1273
1293
. 10.1016/j.mechmachtheory.2005.01.011
6.
Halverson
,
P. A.
,
Howell
,
L. L.
, and
Bowden
,
A. E.
,
2008
, “
A Flexure-Based Bi-Axial Contact-Aided Compliant Mechanism for Spinal Arthroplasty
,”
ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Brooklyn, USA
,
Aug. 3–6
,
Paper No. DETC2008–50121
.
7.
Montierth
,
J. R.
,
Todd
,
R. H.
, and
Howell
,
L. L.
,
2011
, “
Analysis of Elliptical Rolling Contact Joints in Compression
,”
ASME J. Mech. Des.
,
133
(
3
), p.
031001
. 10.1115/1.4003499
8.
Nelson
,
T. G.
,
Lang
,
R. J.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2016
, “
Curved-Folding-Inspired Deployable Compliant Rolling-Contact Element (d-core)
,”
Mech. Mach. Theory
,
96
, pp.
225
238
. 10.1016/j.mechmachtheory.2015.05.017
9.
Moon
,
Y.-M.
,
2007
, “
Bio-Mimetic Design of Finger Mechanism with Contact Aided Compliant Mechanism
,”
Mech. Mach. Theory
,
42
(
5
), pp.
600
611
. 10.1016/j.mechmachtheory.2006.04.014
10.
Mehta
,
V.
,
Frecker
,
M.
, and
Lesieutre
,
G. A.
,
2009
, “
Stress Relief in Contact-Aided Compliant Cellular Mechanisms
,”
ASME J. Mech. Des.
,
131
(
9
), p.
091009
. 10.1115/1.3165778
11.
Tummala
,
Y.
,
Wissa
,
A.
,
Frecker
,
M.
, and
Hubbard
,
J. E.
,
2014
, “
Design and Optimization of a Contact-Aided Compliant Mechanism for Passive Bending
,”
ASME J. Mech. Rob.
,
6
(
3
), p.
031013
. 10.1115/1.4027702
12.
Calogero
,
J.
,
Frecker
,
M.
,
Hasnain
,
Z.
, and
Hubbard
,
J. E.
, Jr.
,
2016
, “
A Dynamic Spar Numerical Model for Passive Shape Change
,”
Smart Mater. Struct.
,
25
(
10
), p.
104006
. 10.1088/0964-1726/25/10/104006
13.
Calogero
,
J.
,
Frecker
,
M.
,
Hasnain
,
Z.
, and
Hubbard
,
J. E.
,
2018
, “
Tuning of a Rigid-Body Dynamics Model of a Flapping Wing Structure With Compliant Joints
,”
ASME J. Mech. Rob.
,
10
(
1
), p.
011007
. 10.1115/1.4038441
14.
Song
,
Z.
,
Lan
,
S.
, and
Dai
,
J. S.
,
2019
, “
A New Mechanical Design Method of Compliant Actuators With Non-Linear Stiffness With Predefined Deflection-Torque Profiles
,”
Mech. Mach. Theory
,
133
, pp.
164
178
. 10.1016/j.mechmachtheory.2018.09.020
15.
Eastwood
,
K. W.
,
Francis
,
P.
,
Azimian
,
H.
,
Swarup
,
A.
,
Looi
,
T.
,
Drake
,
J. M.
, and
Naguib
,
H. E.
,
2018
, “
Design of a Contact-Aided Compliant Notched-Tube Joint for Surgical Manipulation in Confined Workspaces
,”
ASME J. Mech. Rob.
,
10
(
1
), p.
015001
. 10.1115/1.4038254
16.
Wriggers
,
P.
,
Rust
,
W.
, and
Reddy
,
B.
,
2016
, “
A Virtual Element Method for Contact
,”
Comput. Mech.
,
58
(
6
), pp.
1039
1050
. 10.1007/s00466-016-1331-x
17.
Wriggers
,
P.
, and
Zavarise
,
G.
,
1997
, “
On Contact Between Three-Dimensional Beams Undergoing Large Deflections
,”
Commun. Numer. Meth. Eng.
,
13
(
6
), pp.
429
438
. 10.1002/(SICI)1099-0887(199706)13:6<429::AID-CNM70>3.0.CO;2-X
18.
Litewka
,
P.
,
2010
,
Finite Element Analysis of Beam-to-Beam Contact
,
Springer-Verlag
,
Berlin Heidelberg
.
19.
Wriggers
,
P.
,
2002
,
Computational Contact Mechanics
,
John Wiley & Sons
,
Chichester
.
20.
Saxena
,
A.
,
2013
, “
A Contact-Aided Compliant Displacement-Delimited Gripper Manipulator
,”
ASME J. Mech. Rob.
,
5
(
4
), p.
041005
. 10.1115/1.4024728
21.
Kumar
,
P.
,
Sauer
,
R. A.
, and
Saxena
,
A.
,
2016
, “
Synthesis of C0 Path-Generating Contact-Aided Compliant Mechanisms Using the Material Mask Overlay Method
,”
ASME J. Mech. Des.
,
138
(
6
), p.
062301
. 10.1115/1.4033393
22.
Kumar
,
P.
,
Saxena
,
A.
, and
Sauer
,
R. A.
,
2019
, “
Computational Synthesis of Large Deformation Compliant Mechanisms Undergoing Self and Mutual Contact
,”
ASME J. Mech. Des.
,
141
(
1
), p.
012302
. 10.1115/1.4041054
23.
Howell
,
L. L.
, and
Midha
,
A.
,
1995
, “
Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
156
165
. 10.1115/1.2826101
24.
Venkiteswaran
,
V. K.
, and
Su
,
H.-J.
,
2016
, “
A Three-Spring Pseudorigid-Body Model for Soft Joints With Significant Elongation Effects
,”
ASME J. Mech. Rob.
,
8
(
6
), p.
061001
. 10.1115/1.4032862
25.
Yu
,
Y.-Q.
, and
Zhu
,
S.-K.
,
2017
, “
5r Pseudo-Rigid-Body Model for Inflection Beams in Compliant Mechanisms
,”
Mech. Mach. Theory
,
116
, pp.
501
512
. 10.1016/j.mechmachtheory.2017.06.016
26.
Zhu
,
S.-K.
, and
Yu
,
Y.-Q.
,
2017
, “
Pseudo-Rigid-Body Model for the Flexural Beam With An Inflection Point in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
9
(
3
), p.
031005
. 10.1115/1.4035986
27.
Saggere
,
L.
, and
Kota
,
S.
,
2001
, “
Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation
,”
ASME J. Mech. Des.
,
123
(
4
), pp.
535
541
. 10.1115/1.1416149
28.
Pauly
,
J.
, and
Midha
,
A.
,
2006
, “
Pseudo-Rigid-Body Model Chain Algorithm, Part 1: Introduction and Concept Development
,”
ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Philadelphia, PA
,
Sep. 10–13
,
Paper No. DETC2006–99460
.
29.
Pauly
,
J.
, and
Midha
,
A.
,
2006
, “
Pseudo-Rigid-Body Model Chain Algorithm, Part 2: Equivalent Representations for Combined Load Boundary Conditions
,”
ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Philadelphia, PA
,
Sep. 10–13
,
Paper No. DETC2006–99463
.
30.
Awtar
,
S.
, and
Sen
,
S.
,
2010
, “
A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation
,”
ASME J. Mech. Des.
,
132
(
8
), p.
081008
. 10.1115/1.4002005
31.
Ma
,
F.
, and
Chen
,
G.
,
2016
, “
Modeling Large Planar Deflections of Flexible Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021018
. 10.1115/1.4031028
32.
Ma
,
F.
, and
Chen
,
G.
,
2017
, “
Bi-BCM: A Closed-Form Solution for Fixed-Guided Beams in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
9
(
1
), p.
014501
. 10.1115/1.4035084
33.
Chen
,
G.
,
Ma
,
F.
,
Hao
,
G.
, and
Zhu
,
W.
,
2019
, “
Modeling Large Deflections of Initially Curved Beams in Compliant Mechanisms Using Chained Beam Constraint Model
,”
ASME J. Mech. Rob.
,
11
(
1
), p.
011002
. 10.1115/1.4041585
34.
Zhang
,
A.
, and
Chen
,
G.
,
2013
, “
A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
5
(
2
), p.
021006
. 10.1115/1.4023558
35.
Venkiteswaran
,
V. K.
, and
Su
,
H.-J.
,
2016
, “
Pseudo-Rigid-Body Models for Circular Beams Under Combined Tip Loads
,”
Mech. Mach. Theory
,
106
, pp.
80
93
. 10.1016/j.mechmachtheory.2016.08.011
36.
Venkiteswaran
,
V. K.
, and
Su
,
H.-J.
,
2018
, “
A Versatile 3r Pseudo-Rigid-Body Model for Initially Curved and Straight Compliant Beams of Uniform Cross Section
,”
ASME J. Mech. Des.
,
140
(
9
), p.
092305
. 10.1115/1.4040628
37.
Chen
,
G.
,
Zhang
,
Z.
, and
Wang
,
H.
,
2018
, “
A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices
,”
ASME J. Mech. Rob.
,
10
(
3
), p.
031012
. 10.1115/1.4039223
38.
Chen
,
G.
,
Zhang
,
Z.
,
Kong
,
L.
, and
Wang
,
H.
,
2019
, “
Analysis and Validation of a Flexible Planar Two Degree-of-Freedom Parallel Manipulator with Structural Passive Compliance
,”
ASME J. Mech. Rob.
,
12
(
1
), p.
011011
. 10.1115/1.4045036
39.
Ynchausti
,
C.
,
Magleby
,
S. P.
,
Bowden
,
A. E.
, and
Howell
,
L. L.
,
2019
, “
Deployable Euler Spiral Connectors (descs)
,”
ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Anaheim, CA
,
Aug. 18–21
,
Paper No. IDETC2019–97546
.
You do not currently have access to this content.