This paper presents methods to exploit the redundancy of a kinematically redundant spatial parallel mechanism with three redundant DOFs. The architecture of the mechanism is similar to the well-known Gough–Stewart (GS) platform and it retains its advantages, i.e., the members connecting the base to the moving platform are only subjected to tensile/compressive loads. The kinematic redundancy is exploited to avoid singularities and extend the rotational workspace. The architecture is described and the associated kinematic relationships are presented. Solutions for the inverse kinematics are given, as well as strategies to take into account the limitations of the mechanism such as mechanical interferences and velocity limits of the actuators while controlling the redundant degrees-of-freedom.
Issue Section:
Research Papers
References
1.
Advani
, S.
, Nahon
, M.
, Haeck
, N.
, and Albronda
, J.
, 1999
, “Optimization of Six-Degrees-of-Freedom Motion Systems for Flight Simulators
,” J. Aircr.
, 36
(5
), pp. 819
–826
.2.
Lin
, L.-C.
, and Tsay
, M.-U.
, 2000
, “Modeling and Control of Micropositioning Systems Using Stewart Platforms
,” J. Rob. Syst.
, 17
(1
), pp. 17
–52
.3.
Pierrot
, F.
, Reynaud
, C.
, and Fournier
, A.
, 1990
, “Delta: A Simple and Efficient Parallel Robot
,” Robotica
, 8
(2
), pp. 105
–109
.4.
Charles
, P. A.
, 1995
, “Octahedral Machine Tool Frame
,” U.S. Patent No. 5,392,663.5.
Pittens
, K. H.
, and Podhorodeski
, R. P.
, 1993
, “A Family of Stewart Platforms With Optimal Dexterity
,” J. Rob. Syst.
, 10
(4
), pp. 463
–479
.6.
Zanganeh
, K. E.
, and Angeles
, J.
, 1997
, “Kinematic Isotropy and the Optimum Design of Parallel Manipulators
,” Int. J. Rob. Res.
, 16
(2
), pp. 185
–197
.7.
Yun
, Y.
, and Li
, Y.
, 2010
, “Design and Analysis of a Novel 6-DOF Redundant Actuated Parallel Robot With Compliant Hinges for High Precision Positioning
,” Nonlinear Dyn.
, 61
(4
), pp. 829
–845
.8.
Merlet
, J.-P.
, 1996
, “Redundant Parallel Manipulators
,” Lab. Rob. Autom.
, 8
(1
), pp. 17
–24
.9.
Gosselin
, C.
, and Angeles
, J.
, 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
, 6
(3
), pp. 281
–290
.10.
Merlet
, J.-P.
, 1989
, “Singular Configurations of Parallel Manipulators and Grassmann Geometry
,” Int. J. Rob. Res.
, 8
(5
), pp. 45
–56
.11.
Bonev
, I.
, 2003
, “The True Origins of Parallel Robots
,” Parallemic, Montreal, QC, Canada, accessed Jan. 2, 2018, http://www.parallemic.org/Reviews/Review007.html12.
Gough
, V.
, and Whitehall
, S.
, 1962
, “Universal Tyre Test Machine
,” FISITA Ninth International Technical Congress
, London, Apr. 30–May 5, pp. 117
–137
.13.
Gosselin
, C.
, and Schreiber
, L.-T.
, 2018
, “Redundancy in Parallel Mechanisms: A Review
,” ASME Appl. Mech. Rev.
, 70
(1
), p. 010802
.14.
Gosselin
, C.
, Laliberté
, T.
, and Veillette
, A.
, 2015
, “Singularity-Free Kinematically Redundant Planar Parallel Mechanisms With Unlimited Rotational Capability
,” IEEE Trans. Rob.
, 31
(2
), pp. 457
–467
.15.
Schreiber
, L.-T.
, and Gosselin
, C.
, 2017
, “Kinematically Redundant Planar Parallel Mechanisms: Kinematics, Workspace and Trajectory Planning
,” Mech. Mach. Theory
, 119
, pp. 91
–105
.16.
Gosselin
, C.
, and Schreiber
, L.-T.
, 2016
, “Kinematically Redundant Spatial Parallel Mechanisms for Singularity Avoidance and Large Orientational Workspace
,” IEEE Trans. Rob.
, 32
(2
), pp. 286
–300
.17.
Merlet
, J.-P.
, 2006
, Parallel Robots
, 2nd ed., Vol. 128
, Springer
, Dordrecht, The Netherlands
.18.
Chiaverini
, S.
, 1997
, “Singularity-Robust Task-Priority Redundancy Resolution for Real-Time Kinematic Control of Robot Manipulators
,” IEEE Trans. Rob. Autom.
, 13
(3
), pp. 398
–410
.19.
Nakamura
, Y.
, Hanafusa
, H.
, and Yoshikawa
, T.
, 1987
, “Task-Priority Based Redundancy Control of Robot Manipulators
,” Int. J. Rob. Res.
, 6
(2
), pp. 3
–15
.20.
Tandirci
, M.
, Angeles
, J.
, and Ranjbaran
, F.
, 1992
, “The Characteristic Point and the Characteristic Length of Robotic Manipulators
,” ASME 22nd Biennial Mechanisms Conference, Scottsdale, AZ, Sept. 13–16, pp. 203–208.21.
Lin
, C.-C.
, and Chang
, W.-T.
, 2002
, “The Force Transmissivity Index of Planar Linkage Mechanisms
,” Mech. Mach. Theory
, 37
(12
), pp. 1465
–1485
.22.
Sutherland
, G.
, and Roth
, B.
, 1973
, “A Transmission Index for Spatial Mechanisms
,” J. Eng. Ind.
, 95
(2
), pp. 589
–597
.23.
Cardou
, P.
, Bouchard
, S.
, and Gosselin
, C.
, 2010
, “Kinematic-Sensitivity Indices for Dimensionally Nonhomogeneous Jacobian Matrices
,” IEEE Trans. Rob.
, 26
(1
), pp. 166
–173
.24.
Lu
, T.-T.
, and Shiou
, S.-H.
, 2002
, “Inverses of 2 x 2 Block Matrices
,” Comput. Math. Appl.
, 43
(1
), pp. 119
–129
.25.
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
.Copyright © 2019 by ASME
You do not currently have access to this content.
