Technical Brief

Type Synthesis of Parallel Tracking Mechanism With Varied Axes by Modeling Its Finite Motions Algebraically

[+] Author and Article Information
Yang Qi, Yimin Song

Key Laboratory of Mechanism Theory
and Equipment Design,
Ministry of Education,
Tianjin University,
Tianjin 300350, China

Tao Sun

Key Laboratory of Mechanism Theory
and Equipment Design,
Ministry of Education,
Tianjin University,
Tianjin 300350, China
e-mail: stao@tju.edu.cn

1Corresponding author.

Manuscript received March 7, 2017; final manuscript received July 24, 2017; published online August 21, 2017. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 9(5), 054504 (Aug 21, 2017) (6 pages) Paper No: JMR-17-1055; doi: 10.1115/1.4037548 History: Received March 07, 2017; Revised July 24, 2017

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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


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. [CrossRef]
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.
Shi, M. X. , 2013, “ Introduction to the Highly Reliable Antenna Pedestal of an Unmanned Weather Radar,” Electro-Mech. Eng., 29(1), pp. 22–26.
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
Bonev, I. A. , 2002, “ Geometric Analysis of Parallel Mechanisms,” Ph.D. dissertation, Laval University, Quebec City, QC, Canada.


Grahic Jump Location
Fig. 1

General finite motion of arbitrary rigid body

Grahic Jump Location
Fig. 6

Typical topological structures of parallel tracking mechanisms with varied axes: (a) 2-RSR&4R, (b) 2-RSR&2-4R, (c) 3-RSR&SS, and (d) 4-(UR)R(RU)&SS

Grahic Jump Location
Fig. 2

Generation of available 4-DoF open-loop limb

Grahic Jump Location
Fig. 3

Generation of first type of available 5-DoF open-loop limb

Grahic Jump Location
Fig. 4

Generation of second type of available 5-DoF open-loop limb

Grahic Jump Location
Fig. 5

Generation of third type of available 5-DoF open-loop limb



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In