Research Papers: Design of Mechanisms and Robotic Systems

Kinematically Redundant Planar Parallel Mechanisms for Optimal Singularity Avoidance

[+] Author and Article Information
Mats Isaksson

Electrical and Computer Engineering Department,
Colorado State University,
Fort Collins, CO 80523
e-mail: mats.isaksson@gmail.com

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 11, 2016; final manuscript received December 21, 2016; published online February 8, 2017. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 139(4), 042302 (Feb 08, 2017) (9 pages) Paper No: MD-16-1501; doi: 10.1115/1.4035677 History: Received July 11, 2016; Revised December 21, 2016

A parallel mechanism possesses several advantages compared to a similar-sized serial mechanism, including the potential for higher accuracy and reduced moving mass, the latter enabling increased load capacity and higher acceleration. One of the most important issues affecting a parallel mechanism is the potential of parallel singularities. Such configurations strongly affect the performance of a parallel mechanism, both in the actual singularity and in its vicinity. For example, both the stiffness of a mechanism and the efficiency of the power transmission to the tool platform are related to the closeness to singular configurations. A mechanism with a mobility larger than the mobility of its tool platform is referred to as a kinematically redundant mechanism. It is well known that introducing kinematic redundancy enables a mechanism to avoid singular configurations. In this paper, three novel kinematically redundant planar parallel mechanisms are proposed. All three mechanisms provide planar translations of the tool platform in two degrees-of-freedom, in addition to infinite rotation of the platform around an axis normal to the plane of the translations. The unique feature of the proposed mechanisms is that, with the appropriate inverse kinematics solutions, all configurations in the entire workspace feature optimal singularity avoidance. It is demonstrated how it is sufficient to employ five actuators to achieve this purpose. In addition, it is shown how including more than five actuators significantly reduces the required actuator motions for identical motions of the tool platform, thereby reducing the cycle times for typical applications.

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


Lee, J. , Yi, B. J. , Oh, S. R. , and Suh, I . H. , 1998, “ Optimal Design of a Five-Bar Finger With Redundant Actuation,” IEEE International Conference on Robotics and Automation (ICRA’98), May 20, pp. 2068–2074.
O'Brien, J. F. , and Wen, J. T. , 1999, “ Redundant Actuation for Improving Kinematic Manipulability,” IEEE International Conference on Robotics and Automation (ICRA’99), May 10–15, pp. 1520–1525.
Nokleby, S. B. , Fisher, R. , Podhorodeski, R. P. , and Firmani, F. , 2005, “ Force Capabilities of Redundantly-Actuated Parallel Manipulators,” Mech. Mach. Theory, 40(5), pp. 578–599. [CrossRef]
Yi, Y. , McInroy, J. E. , and Chen, Y. , 2006, “ Fault Tolerance of Parallel Manipulators Using Task Space and Kinematic Redundancy,” IEEE Trans. Rob., 22(5), pp. 1017–1021. [CrossRef]
Isaksson, M. , Marlow, K. , Maciejewski, A. , and Eriksson, A. , 2016, “ Novel Fault-Tolerance Indices for Redundantly Actuated Parallel Robots,” ASME J. Mech. Des., (Accepted).
Wang, J. , and Gosselin, C. M. , 2004, “ Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms,” ASME J. Mech. Des., 126(1), pp. 109–118. [CrossRef]
Merlet, J.-P. , 1996, “ Redundant Parallel Manipulators,” Lab. Rob. Autom., 8(1), pp. 17–24. [CrossRef]
Gosselin, C. , and Angeles, J. , 1990, “ Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Marquet, F. , Krut, S. , Company, O. , and Pierrot, F. , 2001, “ ARCHI: A New Redundant Parallel Mechanism—Modeling, Control and First Results,” IEEE/RSJ International Conference on Robotics and System (IROS'01), Oct. 29–Nov. 3, pp. 183–188.
Kock, S. , Oesterlein, R. , and Brogårdh, T. , 2003, “ Industrial Robot,” Patent No. WO 03/066289.
Liu, G. F. , Wu, Y. L. , Wu, X. Z. , Kuen, Y. Y. , and Li, Z. X. , 2001, “ Analysis and Control of Redundant Parallel Manipulators,” IEEE International Conference on Robotics and Automation (ICRA’01), May 21–26, pp. 3748–3754.
Isaksson, M. , 2011, “ A Family of Planar Parallel Manipulators,” IEEE International Conference on Robotics and Automation (ICRA’11), May 9–13, pp. 2737–2744.
Isaksson, M. , and Watson, M. , 2013, “ Workspace Analysis of a Novel 6-DOF Parallel Manipulator With Coaxial Actuated Arms,” ASME J. Mech. Des., 135(10), p. 104501. [CrossRef]
Isaksson, M. , Eriksson, A. , Brogardh, T. , Watson, M. , and Nahavandi, S. , 2015, “ A Method for Extending Planar Axis-Symmetric Parallel Manipulators to Spatial Mechanisms,” Mech. Mach. Theory, 83(1), pp. 1–13. [CrossRef]
Gosselin, C. , Laliberte, T. , and Veillette, A. , 2015, “ Singularity-Free Kinematically Redundant Planar Parallel Mechanisms With Unlimited Rotational Capability,” IEEE Trans. Rob., 31(2), pp. 457–467. [CrossRef]
Mohamed, M. G. , and Gosselin, C. M. , 2005, “ Design and Analysis of Kinematically Redundant Parallel Manipulators With Configurable Platforms,” IEEE Trans. Rob., 21(3), pp. 277–287. [CrossRef]
Ebrahimi, I. , Carretero, J. A. , and Boudreau, R. , 2008, “ A Family of Kinematically Redundant Planar Parallel Manipulators,” ASME J. Mech. Des., 130(6), p. 062306. [CrossRef]
Alizade, R. I. , Tagiyev, N. R. , and Duffy, J. , 1994, “ A Forward and Reverse Displacement Analysis of a 6-DOF In-Parallel Manipulator,” Mech. Mach. Theory, 29(1), pp. 115–124. [CrossRef]
Reboulet, C. , 1996, “ Parallel-Structure Manipulator Device for Displacing and Orienting an Object in a Cylindrical Work Space,” U.S. Patent No. WO 03/066289.
Wang, J. , Wu, C. , and Liu, X.-J. , 2010, “ Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index,” Mech. Mach. Theory, 45(10), pp. 1462–1476. [CrossRef]
Ball, R. S. , 1900, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, UK.
Hunt, K. H. , 1978, Kinematic Geometry of Mechanisms, University Press, Oxford, UK.
Sutherland, G. , and Roth, B. , 1973, “ A Transmission Index for Spatial Mechanisms,” ASME J. Eng. Ind., 95(2), pp. 589–597. [CrossRef]
Chen, C. , and Angeles, J. , 2007, “ Generalized Transmission Index and Transmission Quality for Spatial Linkages,” Mech. Mach. Theory, 42(9), pp. 1225–1237. [CrossRef]
Liu, X.-J. , Wu, C. , and Wang, J. , 2012, “ A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators,” ASME J. Mech. Rob., 4(4), p. 041001. [CrossRef]
Marlow, K. , Isaksson, M. , Dai, J. S. , and Nahavandi, S. , 2016, “ Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed- Loop Sub-Chains,” ASME J. Mech. Des., 138(6), p. 062302. [CrossRef]
Marlow, K. , Isaksson, M. , and Nahavandi, S. , 2016, “ Motion/Force Transmission Analysis of Planar Parallel Mechanisms With Closed-Loop Subchains,” ASME J. Mech. Rob., 8(4), p. 041019. [CrossRef]
Xie, F. , Liu, X.-J. , and Li, J. , 2014, “ Performance Indices for Parallel Robots Considering Motion/Force Transmissibility,” Intelligent Robotics and Applications, Springer International Publishing, Switzerland, pp. 35–43.
Liu, X.-J. , Chen, X. , and Nahon, M. , 2014, “ Motion/Force Constrainability Analysis of Lower-Mobility Parallel Manipulators,” ASME J. Mech. Rob., 6(3), p. 031006. [CrossRef]
Liu, H. , Wang, M. , Huang, T. , Chetwynd, D. G. , and Kecskeméthy, A. , 2015, “ A Dual Space Approach For Force/Motion Transmissibility Analysis of Lower Mobility Parallel Manipulators,” ASME J. Mech. Rob., 7(3), p. 034504. [CrossRef]
Phakatkar, H. G. , 2006, Theory of Machines and Mechanisms I, N. Prakashan , ed., Pune, India.


Grahic Jump Location
Fig. 1

Different approaches to employing redundancy to provide the non-redundant mechanism in (a) with infinite rotation of the tool platform (black). The joints R (solid circle) and R (hollow circle) are actuated and passive revolute joints, respectively, while the joints P are actuated prismatic joints. In order to reduce the figure size, only a section of the circular guide-way in (f) is shown: (a) nonredundant, (b) redundantly actuated, (c) redundantly actuated, (d) kinematically redundant, (e) kinematically redundant, and (f) kinematically redundant.

Grahic Jump Location
Fig. 2

Three kinematically redundant planar parallel mechanisms providing planar translations in two DOFs in addition to infinite rotation around an axis perpendicular to the plane of the translations. The upper image in each figure provides a top view of the mechanism, while the lower image provides an approximate side view. As can be seen from the side views, the mechanisms are designed to avoid any collisions between different sections except for collisions between the manipulated platform and the guide-ways. The number of actuators in (a), (b), and (c) are five, six, and seven, respectively.

Grahic Jump Location
Fig. 3

(a) Notation for determining the OTI of the tool platform. The output twist $̂Oi of each chain is a zero pitch twist through the corresponding instantaneous center of rotation ICi, while fi are the direction vectors of the zero pitch actuation wrenches $̂Ai. The common perpendicular between $̂Ai and $̂Oi is denoted by ρOi, while the maximum value of ρOi is denoted by ρOmaxi. (b) Notation for determining the OTI of the closed-loop subchain of the mechanisms in Figs. 2(b) and 2(c). The used notations are the same as in (a).

Grahic Jump Location
Fig. 4

Simulations of the mechanisms in Fig. 2. (a) Pure rotation of the mechanism in Fig. 2(a). (b) Pure rotation of the mechanisms in Figs. 2(b) and 2(c). (c) Square path by the mechanism in Fig. 2(a). (d) Square path by the mechanism in Fig. 2(b). (e) Square path by the mechanism in Fig. 2(c). (f) Square path by the mechanisms in Figs. 2(a)2(c).

Grahic Jump Location
Fig. 5

Simulations of a square path and a platform rotation for the described 3-RPR and 4-RPR mechanisms. For the 3-RPR mechanism, κ is given by Eq. (25) and for the 4-RPR mechanism by Eq. (26). (a) Three actuators, rotation, (b) three actuators, square, (c) four actuators, rotation, and (d) four actuators, square.



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