A three-revolute prismatic spherical (3-RPS) parallel kinematic machine (PKM) module is proposed as an alternative solution for high-speed machining (HSM) tool. Considering the PKM as a typical compliant parallel device, whose three limb assemblages have bending, extending, and torsional deflections, this paper applies screw theory to establish an analytical compliance model for the device. The developed compliance model is then combined with the energy method to deduce a comprehensive dynamic model of the 3-RPS module. The solution for the characteristic equations of the dynamic model leads to the modal properties of the PKM module. Based on the eigenvalue decomposition of the characteristic equations, a modal analysis is conducted. The natural frequencies and corresponding mode shapes at typical and nontypical configurations are analyzed and compared with finite element analysis (FEA) results. With an algorithm of workspace partitions combining with eigenvalue decompositions, the distributions of natural frequencies throughout the workspace are predicted to reveal a strong dependency of dynamic characteristics on mechanism's configurations. At the last stage, the effects of some design parameters on system dynamic characteristics are investigated with the purpose of providing useful information for the conceptual design and performance improvement for the PKM.

References

References
1.
Wahl
,
J.
,
2000
, “
Articulated Tool Head
,” WIPO Patent No. WO 00/25976.
2.
Hennes
,
N.
, and
Staimer
,
D.
,
2004
, “
Application of PKM in Aerospace Manufacturing - High Performance Machining Centers ECOSPEED, ECOSPEED-F and ECOLINER
,”
Proceedings of the 4th Chemnitz Parallel Kinematics Seminar
, pp.
557
577
.
3.
Fernandez
,
A. J. S.
,
Jimenez
,
V. C.
, and
Olazabal
,
M. G.
,
2002
, “
Kinematical System for a Movable Platform of a Machine
,” European Patent No. EP1245349A1.
4.
Ray
,
P.
,
2005
, “
Design of New High Speed Machining Machines
,”
Prod. Eng.
, pp.
379
396
.10.1007/1-4020-2933-0
5.
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
6.
Caccavale
,
F.
,
Siciliano
,
B.
, and
Villani
,
L.
,
2003
, “
The Tricept Robot: Dynamics and Impedance Control
,”
IEEE/ASME Trans. Mechatron.
,
8
(
2
), pp.
263
268
.10.1109/TMECH.2003.812839
7.
Terrier
,
M.
,
Gimenez
,
M.
, and
Hascoet
,
J. Y.
,
2005
, “
VERNE - A Five-Axis Parallel Kinematics Milling Machine
,”
Proc. Inst. Mech. Eng., Part B
,
219
(
3
), pp.
327
336
.10.1243/095440505X30177
8.
Olazagoitia
,
J. L.
, and
Wyatt
,
S.
,
2007
, “
New PKM Tricept T9000 and Its Application to Flexible Manufacturing at Aerospace Industry
,”
SAE
Technical Paper No. 2007-01-3820, 07ATC-94. 10.4271/2007-01-3820
9.
Li
,
Y. G.
,
Liu
,
H. T.
,
Zhao
,
X. M.
,
Huang
,
T.
, and
Chetwynd
,
D. G.
,
2010
, “
Design of a 3-DOF PKM Module for Large Structural Component Machining
,”
Mech. Mach. Theory
,
45
(
6
), pp.
941
954
.10.1016/j.mechmachtheory.2010.01.008
10.
Wiens
,
G. J.
,
Shamblin
,
S. A.
, and
Oh
,
Y. H.
,
2002
, “
Characterization of PKM Dynamics in Terms of System Identification
,”
J. Multi-Body Dyn.
,
216
(
1
), pp.
59
72
.10.1243/146441902760029393
11.
Wu
,
P. D.
,
Xiong
,
H. G.
, and
Kong
,
J. Y.
,
2012
, “
Dynamic Analysis of 6-SPS Parallel Mechanism
,”
Int. J. Mech. Mater. Des.
,
8
(
2
), pp.
121
128
.10.1007/s10999-012-9181-y
12.
Ji
,
Z. M., J.
,
1993
, “
Study of the Effect of Leg Inertia in Stewart Platforms
,”
Proceedings of the IEEE Conference on Robotics and Automation
, pp.
121
126
.
13.
Xi
,
F.
,
Sinatra
,
R.
, and
Han
,
W.
,
2001
, “
Effect of Leg Inertia on Dynamics of Sliding-Leg Hexapods
,”
ASME J. Dyn. Syst. Meas. Contr.
,
123
(
2
), pp.
265
271
.10.1115/1.1369600
14.
Lee
,
J. D.
, and
Geng
,
Z.
,
1993
, “
A Dynamic Model of a Flexible Steward Platform
,”
Comput. Struct.
,
48
(
3
), pp.
367
374
.10.1016/0045-7949(93)90313-3
15.
Fattah
,
A.
,
Angeles
,
J.
, and
Misra
,
A. K.
,
1995
, “
Dynamics of a 3-DOF Spatial Parallel Manipulator With Flexible Links
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Vol.
1
, pp.
627
632
.
16.
Wang
,
X. Y.
, and
Mills
,
J. K.
,
2006
, “
Dynamic Modeling of a Flexible-Link Planar Parallel Platform Using a Substructuring Approach
,”
Mech. Mach. Theory
,
41
(
6
), pp.
671
687
.10.1016/j.mechmachtheory.2005.09.009
17.
Zhang
,
X. P.
,
Mills
,
J. K.
, and
Cleghorn
,
W. L.
,
2007
, “
Dynamic Modeling and Experimental Validation of a 3-PRR Parallel Manipulator With Flexible Intermediate Links
,”
J. Intell. Rob. Syst.
,
50
(
4
), pp.
323
340
.10.1007/s10846-007-9167-4
18.
Kang
,
B.
, and
Mills
,
J. K.
,
2002
, “
Dynamic Modeling of Structurally Flexible Planar Parallel Manipulator
,”
Robotics
,
20
(
3
), pp.
329
339
.10.1017/S0263574701004039
19.
Piras
,
G.
,
Cleghorn
,
W. L.
, and
Mills
,
J. K.
,
2005
, “
Dynamic Finite-Element Analysis of a Planar High-Speed, High-Precision Parallel Manipulator With Flexible Links
,”
Mech. Mach. Theory
,
40
(
7
), pp.
849
862
.10.1016/j.mechmachtheory.2004.12.007
20.
Wiens
,
G. J.
, and
Hardage
,
D. S.
,
2006
, “
Structural Dynamics and System Identification of Parallel Kinematic Machines
,”
Proceedings of the IDETC/CIE
, Philadelphia, PA, September 10–13, 2006,
ASME
Paper No. DETC2006-99671, pp.
749
758
. 10.1115/DETC2006-99671
21.
Shiau
,
T. N.
,
Tsai
,
Y. J.
, and
Tsai
,
M. S.
,
2008
, “
Nonlinear Dynamic Analysis of a Parallel Mechanism With Consideration of Joint Effects
,”
Mech. Mach. Theory
,
43
(
4
), pp.
491
505
.10.1016/j.mechmachtheory.2007.03.008
22.
Hardage
,
D. S.
, and
Wiens
,
G. J.
,
1999
, “
Modal Analysis and Modeling of a Parallel Kinematic Machine
,”
ASME Manuf. Eng. Div.
,
10
, pp.
857
862
.
23.
Zhou
,
Z. L.
,
Jeff
,
X.
, and
Chris
,
K. M.
,
2006
, “
Modeling of a Fully Flexible 3PRS Manipulator for Vibration Analysis
,”
ASME J. Mech. Des.
,
128
(
2
), pp.
403
412
.10.1115/1.2167655
24.
Zhang
,
J.
,
Li
,
Y. G.
, and
Huang
,
T.
,
2010
, “
Dynamic Modeling and Eigenvalue Evaluation of a 3-DOF PKM Module
,”
Chin. J. Mech. Eng.
,
23
(
2
), pp.
166
173
.10.3901/CJME.2010.02.166
25.
Gausselin
,
C. M.
, and
Zhang
,
D.
,
2002
, “
Stiffness Analysis of Parallel Mechanisms Using a Lumped Model
,”
Int. J. Rob. Autom.
,
17
(
1
), pp.
17
27
.
26.
Simaan
,
N.
, and
Shoham
,
M.
,
2003
, “
Geometric Interpretation of the Derivatives of Parallel Robots' Jacobian Matrix With Application to Stiffness Control
,”
ASME J. Mech. Des.
,
125
(
1
), pp.
33
42
.10.1115/1.1539514
27.
Wang
,
Y. Y.
,
Liu
,
H. T.
, and
Huang
,
T.
,
2009
, “
Stiffness Modeling of the Tricept Robot Using the Overall Jacobian Matrix
,”
ASME J. Mech. Rob.
,
1
(
2
), p.
021002
.10.1115/1.3046131
28.
Ruggiu
,
M.
,
2012
, “
Cartesian Stiffness Matrix Mapping of a Translational Parallel Mechanism With Elastic Joints
,”
Int. J. Adv. Rob. Syst.
,
195
(
9
), pp.
1
8
.10.5772/52145
29.
Dai
,
J. S.
, and
Ding
,
X. L.
,
2006
, “
Compliance Analysis of a Three-Legged Rigidly-Connected Platform Device
,”
ASME J. Mech. Des.
,
128
(
4
), pp.
755
764
.10.1115/1.2202141
30.
Ding
,
X. L.
, and
Dai
,
J. S.
,
2008
, “
Characteristic Equation-Based Dynamic Analysis of Vibration Bowl Feeders With Three Spatial Compliant Legs
,”
IEEE Trans. Autom. Sci. Eng.
,
5
(
1
), pp.
164
175
.10.1109/TASE.2007.910301
You do not currently have access to this content.