A novel CAD variation geometric approach is proposed for designing the computer v-a (velocity-acceleration) simulation mechanisms of parallel manipulators with 3-, 4-, 5-linear driving limbs. Some common math foundations, computer aided geometry constraints, and dimension driving technique, and definitions for designing the velocity-acceleration simulation mechanism are presented. The v-a simulation mechanisms of parallel manipulators with 3-, 4-, 5-linear driving limbs are created. When modifying the driving dimension of the driving limbs, the configurations of the v-a simulation mechanisms are varied correspondingly, and the velocity, angular velocity, acceleration, and angular acceleration of the moving platform are solved automatically and visualized dynamically. The results show that the computer aided geometric approach is not only fairly quick and straightforward, but is also advantageous from viewpoint of accuracy and repeatability.

1.
Stewart
,
D.
, 1965, “
A Platform With Six Degrees of Freedom
,”
Proc. Inst. Mech. Eng.
0020-3483,
180
(
15
), pp.
371
386
.
2.
Hunt
,
K. H.
, 1983, “
Structural Kinematics of In-Parallel Actuated Robot Arms
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
105
(
4
), pp.
705
712
.
3.
Huang
,
Z.
,
Kong
,
L. F.
, and
Fang
,
Y. F.
, 1997,
Theory on parallel robotics and control
,
Machinery Industry Press
,
Beijing, China
.
4.
Huang
,
Z.
, and
Li
,
Qinchuan
, 2002, “
Type Synthesis Principle of Minor-Mobility Parallel Manipulators
,”
Sci. China, Ser. E: Technol. Sci.
1006-9321,
45
(
3
), pp.
241
248
.
5.
Tsai
,
L. W.
, and
Tahmasebi
,
F.
, 1993, “
Synthesis and Analysis of a New Class of Six-Degree of Freedom Parallel Minimanipulators
,”
J. Rob. Syst.
0741-2223,
10
(
5
), pp.
561
580
.
6.
Gao
,
F.
,
Li
,
W.
, and
Zhao
,
X.
, 2002, “
New Kinematic Structures for and 5-DOF Parallel Manipulator Designs
,”
Mech. Mach. Theory
0094-114X,
37
, pp.
1395
1411
.
7.
Tsai
,
L. W.
, and
Joshi
,
S.
, 2000, “
Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator
,”
ASME J. Mech. Des.
1050-0472,
122
(
4
), pp.
439
446
.
8.
Huang
,
Z.
, and
Fang
,
Y. F.
, 1996, “
Kinematic Characteristics Analysis of 3-DOF In-Parallel Actuated Pyramid Mechanisms
,”
Mech. Mach. Theory
0094-114X,
31
(
8
), pp.
1009
1018
.
9.
Huang
,
Z.
, and
Wang
,
J.
, 2001, “
Identification of Principal Screws of 3-DOF Parallel Manipulators by Quadric Degeneration
,”
Mech. Mach. Theory
0094-114X,
36
(
8
), pp.
893
911
.
10.
Wang
,
S.-C.
,
Hikita
,
H.
,
Kubo
,
H.
,
Zhao
,
Y.-S.
,
Huang
,
Z.
, and
Ifukube
,
T.
, 2003, “
Kinematics and Dynamics of Degree-of-Freedom Fully Parallel Manipulator With Elastic Joints
,”
Mech. Mach. Theory
0094-114X,
38
(
4
), pp.
439
461
.
11.
Gosselin
,
C. M.
, 1993, “
On The Direct Kinematics of Spherical 3-DOF Parallel Manipulators
,”
Int. J. Robot. Res.
0278-3649,
12
(
4
), pp.
394
402
.
12.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1994, “
The Optimum Kinematic Design of a Spherical 3-DOF Parallel Manipulator
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
116
(
4
), pp.
1141
1147
.
13.
Kim
,
H. S.
, and
Tsai
,
L.-W.
, 2003, “
Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator
,”
ASME J. Mech. Des.
1050-0472,
125
(
1
), pp.
92
97
.
14.
Sreentvasan
,
S. V.
, and
Waldron
,
K. J.
, 1994, “
Closed-Form Direct Displacement Analysis Of 6-6 Stewart Platform
,”
Mech. Mach. Theory
0094-114X,
29
(
2
), pp.
855
864
.
15.
Dasgupta
,
B.
, and
Mruthyunjaya
,
T. S.
, 1996, “
A Constructive Predictor-Corrector Algorithm for the Direct Position Kinematic Problem for a General 6-6 Stewart Platform
,”
Mech. Mach. Theory
0094-114X,
31
(
6
), pp.
799
811
.
16.
Alizade
,
R. I.
,
Tagiyev
,
N. R.
, and
Duffy
,
J.
, 1994, “
A Forward and Reverse Displacement Analysis of a 6-DOF In-Parallel Manipulators
,”
Mech. Mach. Theory
0094-114X,
29
(
1
), pp.
115
124
.
17.
Luck
,
K.
, 1994, “
Computer-Aided Mechanism Synthesis Based on the Burmester Theory
,”
Mech. Mach. Theory
0094-114X,
29
(
6
), pp.
877
886
.
18.
Matone
,
R.
, and
Roth
,
B.
, 1999, “
In-Parallel Manipulators: A Framework on How to Model Actuation Schemes and a Study of Their Effects on Singular Postures
,”
ASME J. Mech. Des.
1050-0472,
121
(
1
), pp.
2
8
.
19.
Tsai
,
M.-S.
,
Shiau
,
T.-N.
,
Tsai
,
Y.-J.
, and
Chang
,
T.-H.
, 2003, “
Direct Kinematics Analysis of 3-PRS Parallel Mechanism
,”
Mech. Mach. Theory
0094-114X,
38
(
1
), pp.
71
83
.
20.
Sheth
,
P. N.
, 1972, “
A Digital Computer Based Simulation Procedure for Multiple Degree of Freedom Mechanical Systems With Geometric Constraints
,” Ph.D. dissertation, University of Wisconsin, University Microfilm No. 73–2565.
21.
Gosselin
,
C. M.
,
Pereault
,
L.
, and
Vaillancourt
,
Ch.
, 1995, “
Simulation and Computer-Aided Kinematic Design of Three-Degree-of Freedom Spherical Parallel Manipulators
,”
J. Rob. Syst.
0741-2223,
12
(
12
), pp.
857
869
.
22.
Furlong
,
T. J.
,
Vance
,
J. M.
, and
Larochelle
,
P. M.
, 1999, “
Spherical Mechanism Synthesis in Virtual Reality
,”
ASME J. Mech. Des.
1050-0472,
121
(
4
), pp.
515
520
.
23.
Deng
,
Y. M.
,
Britton
,
G. A.
, and
Tor
,
S. B.
, 2000, “
Constraint-Based Functional Design Verification for Conceptual Design
,”
CAD
0010-4485,
32
(
14
), pp.
889
899
.
24.
Ge
,
Q. J.
, and
Sirchia
,
M.
, 1999, “
Computer Aided Geometric Design of two Parameters Free Form Motion
,”
ASME J. Mech. Des.
1050-0472,
121
(
4
), pp.
9
14
.
25.
Lu
,
L.
, 2004, “
Using CAD Functionalities for the Kinematics Analysis of Spatial Parallel Manipulators With 6-Linearly Driven Limbs
,”
Mech. Mach. Theory
0094-114X,
39
(
1
), pp.
41
60
.
26.
Beng
,
H.
, 2001,
Application Guiding of SolidWorks 2000
,
Metallurgical Industry Press
,
Bejing, China
.
27.
Lu
,
Y.
, and
Leinonen
,
T.
, 2002, “
Computer Aided Geometric Approach of Approximate Dimensional Synthesis With Four-bar Linkage
,”
Journal of Computer Aided Design and Graphics
,
14
(
6
), pp.
547
552
.
28.
Lu
,
Y.
, and
Leinonen
,
T.
, 2002, “
Computer Simulation Approach of Manufacturing Complicated Shape on Orthogonal 6-Rod Virtual Machine Tool
,”
Int. J. Mach. Tools Manuf.
0890-6955,
42
(
3
), pp.
441
447
.
29.
Zhang
,
D.
,
Wang
,
L.
, and
Lang
,
S. Y. T.
, 2005, “
Parallel Kinematic Machines: Design, Analysis and Simulation in an Integrated Virtual Environment
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
580
588
.
30.
Yi
,
L.
, 2002, “
Computer Simulation Applied to an Orthogonal Three-Rod Machine Tool for Machining a Complicated Three-dimensional Surface
,”
Int. J. Mach. Tools Manuf.
0890-6955,
42
(
11
), pp.
1277
1284
.
31.
Senin
,
N.
,
Wallace
,
D. R.
, and
Borland
,
N.
, 2003, “
Distributed Object-Based Modeling in Design Simulation Marketplace
,”
ASME J. Mech. Des.
1050-0472,
125
(
1
), pp.
2
13
.
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