Jacobian matrix plays a key role in the analysis, design, and control of robots. For example, it can be used for the performance analysis and evaluation of parallel mechanisms (PMs). However, the Jacobian matrix of a PM generally varies with the poses of the moving platform in the workspace. This leads to a nonconstant performance index of the PM. PMs with a constant Jacobian matrix have simple kinematics and are easy to design and control. This paper proposes a method for obtaining PMs with a constant Jacobian matrix. First, the criteria for detecting invariance of a Jacobian matrix are obtained based on the screw theory. An approach to the synthesis of PMs with a constant Jacobian matrix is then proposed. Using this approach, PMs with a constant Jacobian matrix are synthesized in two steps: the limb design and the combination of the limbs. Several PMs with a constant Jacobian matrix are obtained. In addition to the translational parallel mechanisms (TPMs) with a constant Jacobian matrix in the literature, the mixed-motion PMs whose moving platform can both translate and rotate with a constant Jacobian matrix are newly identified. The input/output velocity analysis of several PMs is presented to verify that Jacobian matrix of these PMs is constant.

References

References
1.
Yan
,
J.
, and
Huang
,
Z.
,
1985
, “
Kinematical Analysis of Multi-Loop Spatical Mechanism
,”
J. Southern China Inst. Technol.
,
13
(
4
), pp.
18
27
.
2.
Gosselin
,
C.
, and
Angeles
,
J.
,
1990
, “
Singularity Analysis of Closed Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
,
6
(
3
), pp.
281
290
.
3.
Kong
,
X.
, and
Gosselin
,
C.
,
2002
, “
Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3DOF Translational Parallel Manipulator
,”
Int. J. Rob. Res.
,
21
(
9
), pp.
791
798
.
4.
Joshi
,
S. A.
, and
Tsai
,
L.
,
2002
, “
Jacobian Analysis of Limited-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
254
258
.
5.
Liu
,
Y.
,
Liu
,
H.
, and
Huang
,
T.
,
2011
, “
Type Synthesis of 6R Serial Manipulators Using Manipulability Index
,”
Chin. J. Mech. Eng.
,
47
(
3
), pp.
8
13
.
6.
Dong
,
G.
,
Sun
,
T.
,
Song
,
Y.
,
Gao
,
H.
, and
Lian
,
B.
,
2016
, “
Mobility Analysis and Kinematic Synthesis of a Novel 4-DoF Parallel Manipulator
,”
Robotica
,
34
(
05
), pp.
1010
1025
.
7.
Zi, B.
,
Sun, H.
, and
Zhang, D.
, 2017, “
Design, Analysis and Control of a Winding Hybrid-Driven Cable Parallel Manipulator
,”
Robotics and Computer-Integrated Manufacturing
,
48
(3), pp. 196–208.
8.
Zi, B.
, and
Li, Y.
, 2017, “
Conclusions in Theory and Practice for Advancing the Applications of Cable-Driven Mechanisms
,”
Chin. J. Mech. Eng.
30
(4), pp. 763–765.
9.
Daniali
,
H.
,
Zsombor-Murray
,
P. J.
, and
Angeles
,
J.
,
1995
, “
Singularity Analysis of a General Class of Planar Parallel Manipulators
,”
IEEE International Conference on Robotics and Automation
, Nagoya, Japan, May 21–27, Paper No. ICRA 1050-4729, pp.
1547
1552
.
10.
St-Onge
,
B. M.
, and
Gosselin
,
C. M.
,
2000
, “
Singularity Analysis and Representation of the General Gough-Stewart Platform
,”
Int. J. Rob. Res.
,
19
(
3
), pp.
271
288
.
11.
Park
,
F. C.
, and
Kim
,
J. W.
,
1999
, “
Singularity Analysis of Closed Kinematic Chains
,”
ASME J. Mech. Des.
,
121
(
1
), pp.
32
38
.
12.
Liu
,
G.
,
Lou
,
Y.
, and
Li
,
Z.
,
2003
, “
Singularities of Parallel Manipulators: A Geometric Treatment
,”
IEEE Trans. Rob. Autom.
,
19
(
4
), pp.
579
594
.
13.
Kong
,
X.
, and
Gosselin
,
C.
,
2002
,
Type Synthesis of Linear Translational Parallel Manipulators
,
Springer
,
Berlin
.
14.
Kong
,
X.
, and
Gosselin
,
C.
, “
A Class of 3-DOF Translational Parallel Manipulators With Linear Input-Output Equations
,”
Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
, Oct. 3–4, Paper No. FIFRD1047-0582, pp.
25
32
.
15.
Kong
,
X.
, and
Gosselin
,
C. M.
,
2003
, “
Type Synthesis of Input-Output Decoupled Parallel Manipulators
,”
Trans. Can. Soc. Mech. Eng.
,
28
(
2A
), pp.
185
196
.
16.
Carricato
,
M.
, and
Parenti-Castelli
,
V.
,
2002
, “
Singularity-Free Fully-Isotropic Translational Parallel Manipulators
,”
ASME
Paper No. DETC2002/MECH-34323
.
17.
Carricato
,
M.
,
2005
, “
Fully Isotropic Four-Degrees-of-Freedom Parallel Mechanisms for Schoenflies Motion
,”
Int. J. Rob. Res.
,
24
(
5
), pp.
397
414
.
18.
Kim
,
H. S.
, and
Tsai
,
L.
-
W.
,
2002
, “
Design Optimization of a Cartesian Parallel Manipulator
,”
ASME J. Mech. Des.
,
125
(
1
), pp.
43
51
.
19.
Zhang
,
W. J.
,
Zou
,
J.
,
Watson
,
L. G.
,
Zhao
,
W.
,
Zong
,
G. H.
, and
Bi
,
S. S.
,
2002
, “
The Constant-Jacobian Method for Kinematics of a Three-DOF Planar Micro-Motion Stage
,”
J. Rob. Syst.
,
19
(
2
), pp.
63
72
.
20.
Lu
,
T.
-
F.
,
Handley
,
D. C.
, and
Yong
,
Y.
-
K.
,
2004
, “
Position Control of a 3 DOF Compliant Micro-Motion Stage
,”
Eighth Control, Automation, Robotics and Vision Conference
(
ICARCV
), Kunming, China, Dec. 6–9, Paper No. ICARCV 2474-2953, pp.
1274
1278
.
21.
Tsai
,
L. W.
,
1999
,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators
,
Wiley
,
New York
.
22.
Kong
,
X.
,
1999
, “
Detection of Input Interference in Spatial Linkages
,”
J. Mech. Transm.
,
23
(
4
), pp.
23
25
.
23.
Zhao
,
T.
, and
Huang
,
Z.
,
2000
, “
Theory and Application of Selecting Actuating Components of Spatial Parallel Mechanisms
,”
Chin. J. Mech. Eng.
,
36
(
10
), pp.
81
85
.
24.
Huang
,
Z.
,
Zhao
,
Y.
, and
Zhao
,
T.
,
2014
,
Advanced Spatial Mechanism
,
High Education Press
,
Beijing, China
.
25.
Kong
,
X.
,
Gosselin
,
C.
, and
Rhichard
,
P.-L.
,
2006
, “
Type Synthesis of Parallel Mechanisms With Multiple Operation Modes
,”
ASME
Paper No. DETC2006-99628
.
26.
Deng
,
J.
,
Yin
,
H.
,
Shen
,
H.
,
Li
,
J.
, and
Yang
,
T.
,
2013
, “
Type Synthesis and Applications for 0T-2R Parallel Mechanisms Based on POC Set Method
,”
China Mech. Eng.
,
24
(
24
), pp.
3386
3391
.
27.
Yu
,
J.
,
Jin
,
Z.
, and
Kong
,
X.
,
2017
, “
Identification and Comparison for Continuous Motion Characteristics of Three Two-Degree-of-Freedom Pointing Mechanisms
,”
ASME J. Mech. Rob.
,
9
(
5
), p.
051015
.
You do not currently have access to this content.