Mobility analysis is an important step in the conceptual design of flexure systems. It involves identifying directions with relatively compliant motion (freedoms) and directions with relatively restricted motion (constraints). This paper proposes a deterministic framework for mobility analysis of wire flexure systems based on characterizing a kinetostatic vector field known as “load flow” through the geometry. A hypothesis is proposed to identify constraints and freedoms based on the relationship between load flow and the flexure geometry. This hypothesis is mathematically restated to formulate a matrix-based reduction technique that determines flexure mobility computationally. Several examples with varying complexity are illustrated to validate the efficacy of this technique. This technique is particularly useful in analyzing complex hybrid interconnected flexure topologies, which may be nonintuitive or involved with traditional methods. This is illustrated through the computational mobility analysis of a bio-inspired fiber reinforced elastomer pressurized with fluids. The proposed framework combines both visual insight and analytical rigor, and will complement existing analysis and synthesis techniques.

References

References
1.
Smith
,
S. T.
,
2000
,
Flexures: Elements of Elastic Mechanisms
,
CRC Press
,
London
.
2.
Awtar
,
S.
,
Slocum
,
A. H.
, and
Sevincer
,
E.
,
2007
, “
Characteristics of Beam-Based Flexure Modules
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
625
639
.
3.
Hopkins
,
J. B.
,
2015
, “
A Visualization Approach for Analyzing and Synthesizing Serial Flexure Elements
,”
ASME J. Mech. Rob.
,
7
(
3
), p.
031011
.
4.
Maxwell
,
J. C.
, and
Niven
,
W.
,
1890
, “
General Considerations Concerning Scientific Apparatus
,”
The Scientific Papers of James Clerk Maxwell
,
W. D.
Niven
, ed.,
Dover
,
New York
.
5.
Blanding
,
D. K.
,
1999
,
Exact Constraint: Machine Design Using Kinematic Principles
,
ASME Press
,
New York
.
6.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2010
, “
Synthesis of Multi-Degree of Freedom, Parallel Flexure System Concepts Via Freedom and Constraint Topology (FACT) Part I: Principles
,”
Precis. Eng.
,
34
(
2
), pp.
259
270
.
7.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2010
, “
Synthesis of Multi-Degree of Freedom, Parallel Flexure System Concepts Via Freedom and Constraint Topology (FACT). Part II: Practice
,”
Precis. Eng.
,
34
(
2
), pp.
271
278
.
8.
Hopkins
,
J. B.
,
2007
, “
Design of Parallel Flexure Systems Via Freedom and Constraint Topologies (FACT)
,”
Master's thesis
,
Massachusetts Institute of Technology
,
Boston, MA
.http://dspace.mit.edu/handle/1721.1/39879
9.
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.
Hopkins
,
J. B.
,
2010
, “
Design of Flexure-Based Motion Stages for Mechatronic Systems Via Freedom, Actuation and Constraint Topologies (FACT)
,”
Ph.D. thesis
,
Massachusetts Institute of Technology
,
Boston, MA
.http://dspace.mit.edu/handle/1721.1/62511
11.
Vogel
,
S.
,
2003
,
Comparative Biomechanics
,
Princeton University Press
,
Princeton, NJ
.
12.
Yu
,
J.
,
Li
,
S.
,
Su
,
H.-J.
, and
Culpepper
,
M.
,
2011
, “
Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms
,”
ASME J. Mech. Rob.
,
3
(
3
), p.
031008
.
13.
Su
,
H.-J.
,
2011
, “
Mobility Analysis of Flexure Mechanisms Via Screw Algebra
,”
ASME J. Mech. Rob.
,
3
(
4
), p.
041010
.
14.
Su
,
H.-J.
,
Dorozhkin
,
D. V.
, and
Vance
,
J. M.
,
2009
, “
A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
4
), p.
041009
.
15.
Hao
,
G.
, and
Kong
,
X.
,
2013
, “
A Normalization-Based Approach to the Mobility Analysis of Spatial Compliant Multi-Beam Modules
,”
Mech. Mach. Theory
,
59
, pp.
1
19
.
16.
Zhang
,
Y.
,
Su
,
H.-J.
, and
Liao
,
Q.
,
2014
, “
Mobility Criteria of Compliant Mechanisms Based on Decomposition of Compliance Matrices
,”
Mech. Mach. Theory
,
79
, pp.
80
93
.
17.
Patterson
,
T.
, and
Lipkin
,
H.
,
1993
, “
A Classification of Robot Complance
,”
ASME J. Mech. Des.
,
115
(
3
), pp.
581
184
.
18.
Lipkin
,
H.
, and
Patterson
,
T.
,
1992
, “
Generalized Center of Compliance and Stiffness
,”
IEEE
International Conference on Robotics and Automation, Nice, France, May 12–14, Vol. 2, pp.
1251
1256
.
19.
Culpepper
,
M.
,
2011
, “
CoMeT
,”
iCampus
, Massachusetts Institute of Technology, Cambridge, MA.http://icampus.mit.edu/projects/comet/
20.
Juvinall
,
R. C.
, and
Marshek
,
K. M.
,
2006
,
Fundamentals of Machine Component Design
, Vol.
83
,
Wiley
,
New York
.
21.
Skakoon
,
J. G.
,
2008
,
The Elements of Mechanical Design
,
ASME
,
New York, NY
.
22.
Krishnan
,
G.
,
Kim
,
C.
, and
Kota
,
S.
,
2013
, “
A Kinetostatic Formulation for Load-Flow Visualization in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
5
(
2
), p.
021007
.
23.
Boresi
,
A. P.
,
Chong
,
K.
, and
Lee
,
J. D.
,
2010
,
Elasticity in Engineering Mechanics
,
Wiley
,
Hoboken, NJ
.
24.
Kelly
,
D.
, and
Tosh
,
M.
,
2000
, “
Interpreting Load Paths and Stress Trajectories in Elasticity
,”
Eng. Comput.
,
17
(
2
), pp.
117
135
.
25.
Harasaki
,
H.
, and
Arora
,
J. S.
,
2001
, “
New Concepts of Transferred and Potential Transferred Forces in Structures
,”
Comput. Methods Appl. Mech. Eng.
,
191
(
3
), pp.
385
406
.
26.
Hibbeler
,
R. C.
, and
Kiang
,
T.
,
2015
,
Structural Analysis
,
Prentice Hall
,
Upper Saddle River, NJ
.
27.
Hopkins
,
J.
,
2013
, “
Designing Hybrid Flexure Systems and Elements Using Freedom and Constraint Topologies
,”
Mech. Sci.
,
4
(
2
), pp.
319
331
.
28.
Krishnan
,
G.
,
Bishop-Moser
,
J.
,
Kim
,
C.
, and
Kota
,
S.
,
2015
, “
Kinematics of a Generalized Class of Pneumatic Artificial Muscles
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041014
.
You do not currently have access to this content.