Taking the 3DOF parallel mechanism within the Tricept robot as an example, this paper presents an analytical approach for the stiffness modeling of parallel kinematic machines having a properly constrained passive limb. The stiffness model is formulated using the 6×6overall Jacobian. It takes particular interest in the precise formulation of the bending stiffness matrix of the properly constrained passive limb by considering the compatibility conditions of the system. Stiffness evaluation of a sample Tricept robot is carried out using two global indices obtained from singular value decomposition of the compliance matrix.

1.
Tsai
,
L. W.
, 1999,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators
,
Wiley
,
New York
.
2.
Huang
,
T.
,
Li
,
M.
,
Wu
,
M. L.
,
Mei
,
J. P.
,
Zhao
,
X. M.
, and
Hu
,
S. J.
, 2005, “
The Criteria for Conceptual Design of Reconfigurable PKM Modules—Theory and Application
,”
Chin. J. Mech. Eng.
0577-6686,
41
(
8
), pp.
36
41
.
3.
Neumann
,
K. E.
, 1988, “
Robot
,” U.S. Patent No. 4732525.
4.
Neumann
,
K. E.
, 2001, “
System and Method for Controlling a Robot
,” U.S. Patent No. 6301525.
6.
Tonshoff
,
H. K.
,
Grendel
,
H.
, and
Kaak
,
R.
, 1999, “
Structure and Characteristics of the Hybrid Manipulator George V
,”
Parallel Kinematic Machines
,
C. R.
Boer
,
L.
Molinari-Tosatti
, and
K. S.
Smith
, eds.,
Springer-Verlag
,
London
, pp.
365
376
.
7.
Zielinski
,
C.
,
Mianowski
,
K.
,
Nazarczuk
,
K.
, and
Szynkiewicz
,
W.
, 2003, “
A Prototype Robot for Polishing and Milling Large Objects
,”
Ind. Robot
,
30
(
1
), pp.
67
76
. 0143-991X
8.
Huang
,
T.
,
Li
,
M.
, and
Li
,
Z. X.
, 2004, “
A 5-DOF Hybrid Robot
,” Patent Cooperation Treaty (PCT), International Application No. PCT/CN2004/000479, pending.
9.
Huang
,
T.
,
Li
,
M.
,
Zhao
,
X. M.
,
Mei
,
J. P.
,
Chetwynd
,
D. G.
, and
Hu
,
S. J.
, 2005, “
Conceptual Design and Dimensional Synthesis for a 3-DOF Module of the TriVariant—A Novel 5-DOF Reconfigurable Hybrid Robot
,”
IEEE Trans. Rob. Autom.
,
21
(
3
), pp.
449
456
. 1546-1904
10.
Li
,
M.
,
Huang
,
T.
,
Mei
,
J. P.
,
Zhao
,
X. M.
,
Chetwynd
,
D. G.
, and
Hu
,
S. J.
, 2005, “
Dynamic Formulation and Performance Comparison of the 3-DOF Modules of Two Reconfigurable PKMs —The Tricept and the TriVariant
,”
ASME J. Mech. Des.
0161-8458,
127
(
6
), pp.
1129
1136
.
11.
Liu
,
H. T.
,
Huang
,
T.
,
Mei
,
J. P.
,
Zhao
,
X. M.
,
Chetwynd
,
D. G.
,
Li
,
M.
, and
Hu
,
S. J.
, 2007, “
Kinematic Design of a 5-DOF Hybrid Robot With Large Workspace/Limb-Stroke Ratio
,”
ASME J. Mech. Des.
0161-8458,
129
(
5
), pp.
530
537
.
12.
Joshi
,
S.
, and
Tsai
,
L. W.
, 2003, “
A Comparison Study of Two 3-DOF Parallel Manipulators: One With Three and the Other With Four Supporting Legs
,”
IEEE Trans. Rob. Autom.
1042-296X,
19
(
2
), pp.
200
209
.
13.
Zhang
,
D.
, and
Gosselin
,
C. M.
, 2001, “
Kinetostatic Modeling of N-DOF Parallel Mechanisms With a Passive Constraining Leg and Prismatic Actuators
,”
ASME J. Mech. Des.
0161-8458,
123
(
3
), pp.
375
384
.
14.
Zhang
,
D.
, and
Gosselin
,
C. M.
, 2002, “
Kinetostatic Modeling of Parallel Mechanisms With a Passive Constraining Leg and Revolute Actuators
,”
Mech. Mach. Theory
0094-114X,
37
(
6
), pp.
599
617
.
15.
Zhang
,
D.
, and
Gosselin
,
C. M.
, 2002, “
Kinetostatic Analysis and Design Optimization of the Tricept Machine Tool Family
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
124
(
3
), pp.
725
733
.
16.
Zhang
,
D.
,
Xi
,
F.
,
Mechefske
,
C. M.
, and
Langb
,
S. Y. T.
, 2004, “
Analysis of Parallel Kinematic Machine With Kinetostatic Modeling Method
,”
Rob. Comput.-Integr. Manufact.
0736-5845,
20
(
2
), pp.
151
165
.
17.
Zhang
,
D.
, 2005, “
On Stiffness Improvement of the Tricept Machine Tool
,”
Robotica
,
23
(
3
), pp.
377
386
. 0263-5747
18.
Majou
,
F.
,
Gosselin
,
C.
, and
Wenger
,
P.
, 2007, “
Parametric Stiffness Analysis of the Orthoglide
,”
Mech. Mach. Theory
0094-114X,
42
(
3
), pp.
296
311
.
19.
Joshi
,
S.
, and
Tsai
,
L. W.
, 2002, “
Jacobian Analysis of Limited-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
0161-8458,
124
(
2
), pp.
254
258
.
You do not currently have access to this content.