In this paper, we apply screw theory to type synthesis of compliant parallel mechanisms (PMs) with translational degree-of-freedom (DOF). Compliant PMs are formed by a moving platform supported by three or more limbs each of which is a serial chain of flexure joints and rigid bodies. They achieve movement through the deformation of flexure joints and have been widely used in precision machinery. As an important task in the conceptual design stage, the goal of type synthesis is to determine the chain of each limb as well as their relationship when they are assembled in parallel for a prescribed motion pattern. In our approach, we study a category of commonly used flexure primitives and flexure elements whose freedom and constraint spaces are characterized by twists and wrenches in screw theory. Following the well-studied synthesis procedure for rigid body PMs, we propose a synthesis procedure for compliant PMs via screw theory. As an example, we demonstrate the procedure for synthesizing compliant PMs with three translational DOF. Tables of limbs, types, and geometric conditions for the assemblies of these limbs are presented. The paper provides a catalog of 3DOF translational compliant PM designs. At last, we developed finite element simulation to validate one of the synthesized designs.

References

1.
Huang
,
Z.
,
Kong
,
L. F.
, and
Fang
,
Y. F.
,
1997
,
Theory on Parallel Robotics and Control
,
Machinery Industry Press
,
Beijing, China
(in Chinese).
2.
Tsai
,
L.-W.
,
1999
,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators
, 1st ed.,
Wiley-Interscience
,
New York
.
3.
Merlet
,
J.
,
2006
,
Parallel Robots
, 2nd ed.,
Springer, Dordrecht
,
The Netherlands
.
4.
Ball
,
R. S.
,
1900
,
A Treatise on the Theory of Screws
,
Cambridge University Press
,
Cambridge, UK
(originally published in 1876 and revised by the author in 1900, now reprinted with an introduction by H. Lipkin and J. Duffy).
5.
Hunt
,
K. H.
,
1978
,
Kinematic Geometry of Mechanisms
,
Oxford University Press
,
New York
.
6.
Phillips
,
J.
,
1984
, “
Introducing Screw Theory
,”
Freedom in Machinery
, Vol.
1
,
Cambridge University Press
,
Cambridge, UK
.
7.
Phillips
,
J.
,
1990
, “
Screw Theory Exemplified
,”
Freedom in Machinery
, Vol.
2
,
Cambridge University Press
,
Cambridge, UK
.
8.
Yi
,
B.
,
Na
,
H.
,
Chung
,
G. B.
,
Kim
,
W. K.
, and
Suh
,
I. H.
,
2002
, “
Design and Experiment of a 3 DOF Parallel Micro-Mechanism Utilizing Flexure Hinges
,”
IEEE International Conference on Robotics and Automation
(
ICRA '02
), Washington, DC, May 11–15, pp.
1167
1172
.10.1109/ROBOT.2002.1014701
9.
Kang
,
B. H.
,
Wen
,
J. T.
,
Dagalakis
,
N. G.
, and
Gorman
,
J. J.
,
2005
, “
Analysis and Design of Parallel Mechanisms With Flexure Joints
,”
IEEE Trans. Rob.
,
21
(
6
), pp.
1179
1185
.10.1109/TRO.2005.855989
10.
Liang
,
Q.
,
Zhang
,
D.
,
Song
,
Q.
, and
Ge
,
Y.
,
2010
, “
Micromanipulator With Integrated Force Sensor Based on Compliant Parallel Mechanism
,”
IEEE International Conference on Robotics and Biomimetics
(
ROBIO
),
Tianjin
,
China
, Dec. 14–18, pp.
709
714
.10.1109/ROBIO.2010.5723413
11.
Chen
,
J.-S.
, and
Hsu
,
W.-Y.
,
2004
, “
Design and Analysis of a Tripod Machine Tool With an Integrated Cartesian Guiding and Metrology Mechanism
,”
Precis. Eng.
,
28
(
1
), pp.
46
57
.10.1016/S0141-6359(03)00073-4
12.
Chen
,
S.-C.
, and
Culpepper
,
M. L.
,
2006
, “
Design of a Six-Axis Micro-Scale Nanopositioner-Hexflex
,”
Precis. Eng.
,
30
(
3
), pp.
314
324
.10.1016/j.precisioneng.2005.11.002
13.
Wu
,
T.
,
Chen
,
J.
, and
Chang
,
S.
,
2008
, “
A Six-DOF Prismatic–Spherical–Spherical Parallel Compliant Nanopositioner
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
,
55
(
12
), pp.
2544
2551
.10.1109/TUFFC.2008.970
14.
Brouwer
,
D.
,
de Jong
,
B.
, and
Soemers
,
H.
,
2010
, “
Design and Modeling of a Six DOFs MEMS-Based Precision Manipulator
,”
Precis. Eng.
,
34
(
2
), pp.
307
319
.10.1016/j.precisioneng.2009.08.001
15.
Kong
,
X.
, and
Gosselin
,
C. M.
,
2004
, “
Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Screw Theory
,”
ASME J. Mech. Des.
,
126
(
1
), pp.
83
92
.10.1115/1.1637662
16.
Kong
,
X.
, and
Gosselin
,
C. M.
,
2010
,
Type Synthesis of Parallel Mechanisms
,
Springer, Amsterdam
,
The Netherlands
.
17.
Hao
,
G.
, and
Kong
,
X.
,
2012
, “
Design and Modeling of a Large-Range Modular XYZ Compliant Parallel Manipulator Using Identical Spatial Modules
,”
ASME J. Mech. Rob.
,
4
(
2
), p.
021009
.10.1115/1.4006188
18.
Yue
,
Y.
,
Gao
,
F.
, and
Ge
,
H.
,
2011
, “
Prototype Design of a 6-DOF Compliant Parallel Micro-Manipulator
,”
ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Washington
,
DC
, Aug. 28–31, pp.
921
930
.
19.
Yu
,
J. J.
,
Li
,
S. Z.
,
Pei
,
X.
,
Su
,
H.-J.
,
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2010
, “
Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part I—General Methodology
,”
ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Montreal
,
QC
, Canada, Aug. 15–18, pp.
543
552
.
20.
Yu
,
J. J.
,
Li
,
S. Z.
,
Pei
,
X.
,
Bi
,
S.
, and
Zhou
,
G. H.
,
2011
, “
A Unified Approach to Type Synthesis of Both Rigid and Flexure Parallel Mechanisms
,”
Sci. China Technol. Sci.
,
54
(
5
), pp.
1206
1219
.10.1007/s11431-011-4324-1
21.
Hopkins
,
J.
,
2012
, “
Modeling and Generating New Flexure Constraint Elements
,”
12th International Conference of the European Society for Precision Engineering & Nanotechnology
,
Stockholm
,
Sweden
, June 4–8, Paper No. LLNL-PROC-527391.
22.
Hopkins
,
J.
,
2013
, “
Analyzing and Designing Serial Flexure Elements
,”
ASME
Paper No. DETC2013-12473. 10.1115/DETC2013-12473
23.
Su
,
H.-J.
, and
Yue
,
C.
,
2013
, “
Type Synthesis of Freedom and Constraint Elements for Design of Flexure Mechanisms
,”
J. Mech. Sci.
,
4
(
2
), pp.
263
277
.10.5194/ms-4-263-2013
24.
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
.10.1115/1.3211024
25.
Su
,
H.-J.
, and
Tari
,
H.
,
2010
, “
Realizing Orthogonal Motions With Wire Flexures Connected in Parallel
,”
ASME J. Mech. Des.
,
132
(
12
), p.
121002
.10.1115/1.4002837
26.
Su
,
H.-J.
, and
Tari
,
H.
,
2011
, “
On Line Screw Systems and Their Application to Flexure Synthesis
,”
ASME J. Mech. Rob.
,
3
(
1
), p.
011009
.10.1115/1.4003078
27.
Su
,
H.
,
2011
, “
Mobility Analysis of Flexure Mechanisms Via Screw Algebra
,”
ASME J. Mech. Rob.
,
3
(
4
), p.
041010
.10.1115/1.4004910
28.
Hopkins
,
J.
, and
Culpepper
,
M.
,
2006
, “
A Quantitative, Constraint-Based Design Method for Multi-Axis Flexure Stages for Precision Positioning and Equipment
,”
Annual Meeting of the American Society for Precision Engineering
,
Monterey
,
CA
, Oct. 15–20.
29.
Hopkins
,
J.
,
2007
, “
Design of Parallel Flexure Systems Via Freedom and Constraint Topologies (FACT)
,” Master’s thesis,
Massachusetts Institute of Technology
,
Cambridge, MA
.
30.
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
.10.1016/j.precisioneng.2009.06.007
31.
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
.10.1016/j.precisioneng.2009.06.008
32.
Pradeep
,
A.
,
Yoder
,
P. J.
, and
Mukundan
,
R.
,
1989
, “
On the Use of Dual-Matrix Exponentials in Robotic Kinematics
,”
Int. J. Rob. Res.
,
8
(
5
), pp.
57
66
.10.1177/027836498900800505
33.
Zhang
,
Y.
,
Su
,
H.-J.
, and
Liao
,
Q.
,
2014
, “
Mobility Criteria of Compliant Mechanisms Based on Decomposition of Compliance Matrices
,”
Mech. Mach. Theory
,
79
(9), pp.
80
93
.10.1016/j.mechmachtheory.2014.04.010
34.
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
35.
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
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