Parallel tracking mechanism with varied axes has great potential in actuating antenna to track moving targets. Due to varied rotational axes, its finite motions have not been modeled algebraically. This makes its type synthesis remain a great challenge. Considering these issues, this paper proposes a conformal geometric algebra (CGA) based approach to model its finite motions in an algebraic manner and parametrically generate topological structures of available open-loop limbs. Finite motions of rigid body, articulated joints, and open-loop limbs are formulated by outer product of CGA. Then, finite motions of parallel tracking mechanism with varied axes are modeled algebraically by two independent rotations and four dependent motions with the assistance of kinematic analysis. Afterward, available four degrees-of-freedom (4-DoF) open-loop limbs are generated by using revolute joints to realize dependent motions, and available five degrees-of-freedom (5-DoF) open-loop limbs are obtained by adding one finite rotation to the generated open-loop limbs. Finally, assembly principles in terms of minimal number and combinations of available open-loop limbs are defined. Typical topological structures are synthesized and illustrated.

References

References
1.
Mauro
,
S.
,
Battezzato
,
A.
,
Biondi
,
G.
, and
Scarzella
,
C.
,
2015
, “
Design and Test of a Parallel Kinematic Solar Tracker
,”
Adv. Mech. Eng.
,
7
(
12
), pp.
1
16
.
2.
Vimal
,
K.
, and
Prince
,
S.
,
2015
, “
System Analysis for Optimizing Various Parameters to Mitigate the Effects of Satellite Vibration on Inter-Satellite Optical Wireless Communication
,”
IEEE International Conference on Signal Processing, Informatics, Communication and Energy Systems
(
SPICES
), Kozhikode, India, Feb. 19–21, pp.
1
4
.
3.
Shi
,
M. X.
,
2013
, “
Introduction to the Highly Reliable Antenna Pedestal of an Unmanned Weather Radar
,”
Electro-Mech. Eng.
,
29
(
1
), pp.
22
26
.
4.
Dunlop
,
G. R.
, and
Jones
,
T. P.
,
1999
, “
Position Analysis of a Two DOF Parallel Mechanism—The Canterbury Tracker
,”
Mech. Mach. Theory
,
34
(
4
), pp.
599
614
.
5.
Sofka
,
J.
, and
Skormin
,
V.
,
2006
, “
Integrated Approach to Electromechanical Design of a Digitally Controlled High Precision Actuator for Aerospace Applications
,”
IEEE Conference on Computer Aided Control System Design, IEEE International Conference on Control Applications, IEEE International Symposium on Intelligent Control
(
CACSD-CCA-ISIC
), Munich, Germany, Oct. 4–8, pp.
261
265
.
6.
Sofka
,
J.
,
Skormin
,
V.
,
Nikulin
,
V.
, and
Nicholson
,
D. J.
,
2006
, “
Omini-Wrist III—A New Generation of Pointing Devices—Part I: Laser Beam Steering Devices-Mathematical Modeling
,”
IEEE Trans. Aerosp. Electron. Syst.
,
42
(
2
), pp.
718
725
.
7.
Sofka
,
J.
,
Nikulin
,
V.
,
Skormin
,
V.
, and
Hughes
,
D. H.
,
2009
, “
Laser Communication Between Mobile Platforms
,”
IEEE Trans. Aerosp. Electron. Syst.
,
45
(
1
), pp.
336
346
.
8.
Yang
,
S. F.
,
Sun
,
T.
, and
Huang
,
T.
,
2017
, “
Type Synthesis of Parallel Mechanisms Having 3T1R Motion With Variable Rotational Axis
,”
Mech. Mach. Theory
,
109
, pp.
220
230
.
9.
Qi
,
Y.
,
Sun
,
T.
,
Song
,
Y. M.
, and
Jin
,
Y.
,
2015
, “
Topology Synthesis of Three-Legged Spherical Parallel Mechanisms Employing Lie Group Theory
,”
Proc. Inst. Mech. Eng. Part C
,
229
(
10
), pp.
1873
1886
.
10.
Sun
,
T.
,
Yang
,
S. F.
,
Huang
,
T.
, and
Dai
,
J. S.
,
2017
, “
A Way of Relating Instantaneous and Finite Screws Based on the Screw Triangle Product
,”
Mech. Mach. Theory
,
108
, pp.
75
82
.
11.
Yang
,
S. F.
,
Sun
,
T.
,
Huang
,
T.
,
Li
,
Q. C.
, and
Gu
,
D. B.
,
2016
, “
A Finite Screw Approach to Type Synthesis of Three-DoF Translational Parallel Mechanisms
,”
Mech. Mach. Theory
,
104
, pp.
405
419
.
12.
Huo
,
X. M.
,
Sun
,
T.
,
Song
,
Y. M.
,
Qi
,
Y.
, and
Wang
,
P. F.
,
2017
, “
An Analytical Approach to Determine Motions/Constraints of Serial Kinematic Chains Based on Clifford Algebra
,”
Proc. Inst. Mech. Eng. C
,
231
(
7
), pp.
1324
1338
.
13.
Bayro-Corrochano
,
E.
,
Reyes-Lozano
,
L.
, and
Zamora-Esquivel
,
J.
,
2006
, “
Conformal Geometric Algebra for Robotic Vision
,”
J. Math. Imaging Vis.
,
24
(
1
), pp.
55
81
.
14.
Hitzer
,
E. M. S.
,
2005
, “
Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity}
,”
Bull. Belg. Math. Soc.-Simon Stevin
,
11
(
5
), pp.
653
662
.
15.
Hildenbrand
,
D.
,
Zamora
,
J.
, and
Bayro-Corrochano
,
E.
,
2008
, “
Inverse Kinematics Computation in Computer Graphics and Robotics Using Conformal Geometric Algebra
,”
Adv. Appl. Clifford Algebra
,
18
(
3–4
), pp.
699
713
.
16.
Fu
,
Z. T.
,
Yang
,
W. Y.
, and
Yang
,
Z.
,
2013
, “
Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra
,”
ASME J. Mech. Rob.
,
5
(
3
), p.
031010
.
17.
Bonev
,
I. A.
,
2002
, “
Geometric Analysis of Parallel Mechanisms
,”
Ph.D. dissertation
, Laval University, Quebec City, QC, Canada.
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