This paper presents a general framework for studying the mobility of flexure mechanisms with a serial, parallel or hybrid topology using the screw algebra. The current approach for mobility analysis of flexures is ad hoc and mostly done by intuition. In this methodology, we first build a library of commonly used flexure elements, flexure joints, and simple chains. We then apply the screw algebra to find their motion and constraint spaces in the form of twist and wrench matrices. To analyze a general flexure mechanism, we first apply a top-down approach to hierarchically subdivide it into multiple modules or building blocks down to the level of flexure structures that are already provided in the library. We then use a bottom-up routine to study the mobility of each module up to the level of the overall mechanism. Examples and case studies from simple flexure joints, chains to spatial compliant platforms are used to demonstrate the methodology. This systematic methodology is an important tool for guiding the qualitative design of flexure mechanisms.

References

References
1.
Smith
,
S. T.
, 2000,
Flexure: Element of Elastic Mechanisms
,
CRC Press LLC
,
London
.
2.
Howell
,
L. L.
, 2001,
Compliant Mechanisms
,
Wiley-Interscience
,
New York
.
3.
Smith
,
S.
, and
Chetwynd
,
D.
, 1992,
Foundations of Ultra-Precision Mechanism Design
,
Taylor & Francis Books Ltd
,
London, UK
.
4.
Blanding
,
D. L.
, 1999,
Exact Constraint: Machine Design Using Kinematic Processing
,
ASME Press
,
New York
.
5.
Hale
,
L. C.
, 1999, “
Principles and Techniques for Designing Precision Machines
,” Ph. D. thesis, MIT, Cambridge, MA.
6.
Awtar
,
S.
, and
Slocum
,
A. H.
, 2007, “
Constraint-Based Design of Parallel Kinematic xy Flexure Mechanisms
,”
ASME J. Mech. Des.
,
129
(
8
), pp.
816
830
.
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 I: Principles
,”
Precis. Eng.
,
34
(
2
), pp.
259
270
.
8.
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
.
9.
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
),
041009
.
10.
Ball
,
R. S.
, 1998,
The Theory of Screws
,
Cambridge University
,
Cambridge, England
. (Originally published in 1876 and revised by the author in 1900, now reprinted with an introduction by H. Lipkin and J. Duffy).
11.
Hunt
,
K. H.
, 1978,
Kinematic Geometry of Mechanisms
,
Oxford University
,
New York
.
12.
Su
,
H.-J.
, and
Tari
,
H.
, 2010, “
Realizing Orthogonal Motions With Wire Flexures Connected in Parallel
,”
ASME J. Mech. Des.
,
132
(
12
), p.
121002
.
13.
Lipkin
,
H.
, and
Duffy
,
J.
, 1985, “
The Elliptic Polarity of Screws
,”
ASME J. Mech., Transm., Autom. Des.
,
107
(
3
), pp.
377
386
.
14.
Dai
,
J. S.
, and
Jones
,
J. R.
, 2003, “
A Linear Algebraic Procedure in Obtaining Reciprocal Screw Systems
,”
J. Rob. Syst.
,
20
(
7
), pp.
401
412
.
15.
Su
,
H.-J.
, 2008, “
A Load Independent Pseudo-Rigid-Body 3R Model for Determining Large Deflection of Beams in Compliant Mechanisms
,”
Proceedings of ASME IDETC/CIE (43260)
, pp.
109
121
.
16.
Patil
,
C. B.
, 2008, “
Robust Design of Selectively Compliant Flexure-Based Precision Mechanisms
,” Ph.D. thesis, University of Texas, Austin.
17.
Su
,
H.-J.
,
Shi
,
H.
, and
Yu
,
J.
, 2011, “
Analytical Compliance Analysis and Synthesis of Flexure Mechanisms
,”
Proceedings of ASME IDETC/CIE
, Washington, DC, Aug. 29-31.
You do not currently have access to this content.