Abstract
This paper introduces a novel compact three-degree-of-freedom (DOF) parallel robot that will be used as a leg of a 9-DOF kinematically redundant parallel robot. First, the kinematic model of the robot is established based on geometric constraint conditions. Then, the inverse and forward kinematic problems are solved. The inverse problem is straightforward, while the forward problem can be solved analytically by three different approaches. Afterward, a singularity analysis is presented based on the Jacobian matrices derived from the kinematic model. The mathematical conditions for singularities are obtained and their geometric interpretation is given. Finally, the workspace of the robot is analyzed and is shown to correspond to a portion of a torus. The analysis reveals that the robot can have a singularity-free workspace of significant size relative to its footprint provided that some simple limitations are introduced at the design stage.
Issue Section:
Research Papers
References
1.
Gosselin
, C.
, and Schreiber
, L.-T.
, 2018
, “Redundancy in Parallel Mechanisms: A Review
,” Appl. Mech. Rev.
, 70
(1
), p. 010802
. 2.
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
. 3.
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
. 4.
Kotlarski
, J.
, Abdellatif
, H.
, Ortmaier
, T.
, and Heimann
, B.
, 2009
, “Enlarging the Useable Workspace of Planar Parallel Robots Using Mechanisms of Variable Geometry
,” 2009 ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots
, London, UK
, June 22–24
, IEEE
, pp. 63
–72
.5.
Boudreau
, R.
, and Nokleby
, S.
, 2012
, “Force Optimization of Kinematically-Redundant Planar Parallel Manipulators Following a Desired Trajectory
,” Mech. Mach. Theory
, 56
, pp. 138
–155
. 6.
Kotlarski
, J.
, Heimann
, B.
, and Ortmaier
, T.
, 2011
, “Experimental Validation of the Influence of Kinematic Redundancy on the Pose Accuracy of Parallel Kinematic Machines
,” 2011 IEEE International Conference on Robotics and Automation
, Shanghai, China
, May 9–13
, IEEE
, pp. 1923
–1929
.7.
Wen
, K.
, Nguyen
, T. S.
, Harton
, D.
, Laliberté
, T.
, and Gosselin
, C.
, 2021
, “A Backdrivable Kinematically Redundant (6+3)-Degree-of-Freedom Hybrid Parallel Robot for Intuitive Sensorless Physical Human–Robot Interaction
,” IEEE Trans. Rob.
, 37
(4
), pp. 1222
–1238
. 8.
Wen
, K.
, and Gosselin
, C.
, 2019
, “Kinematically Redundant Hybrid Robots With Simple Singularity Conditions and Analytical Inverse Kinematic Solutions
,” IEEE Rob. Autom. Lett.
, 4
(4
), pp. 3828
–3835
. 9.
Gosselin
, C.
, Allan
, J.
, and Laliberté
, T.
, 1999
, “A New Architecture for a High-Performance 6-DOF Parallel Mechanism
,” Proceedings of the IFTOMM 10th World Congress on the Theory of Machine and Mechanisms
, Oulu, Finland
, June 20–24
, pp. 1140
–1145
.10.
Kong
, X.
, and Gosselin
, C. M.
, 2007
, Type Synthesis of Parallel Mechanisms
, Vol. 33
, Springer
, Berlin/Heidelberg
.11.
Gogu
, G.
, 2008
, Structural Synthesis of Parallel Robots
, Vol. 930
, Springer
, Dordrecht, The Netherlands
.12.
Angeles
, J.
, 2004
, “The Qualitative Synthesis of Parallel Manipulators
,” ASME J. Mech. Des.
, 126
(4
), pp. 617
–624
. 13.
Liu
, X.-J.
, and Kim
, J.
, 2005
, “A New Spatial Three-DOF Parallel Manipulator With High Rotational Capability
,” IEEE/ASME Trans. Mechatron.
, 10
(5
), pp. 502
–512
. 14.
Xie
, F.
, Liu
, X.-J.
, and Wang
, J.
, 2012
, “A 3-DOF Parallel Manufacturing Module and Its Kinematic Optimization
,” Rob. Comput.-Integr. Manuf.
, 28
(3
), pp. 334
–343
. 15.
Carretero
, J.
, Podhorodeski
, R.
, Nahon
, M.
, and Gosselin
, C. M.
, 2000
, “Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator
,” ASME J. Mech. Des.
, 122
(1
), pp. 17
–24
. 16.
Gojtan
, G.
, Furtado
, G.
, and Hess-Coelho
, T.
, 2013
, “Error Analysis of a 3-DOF Parallel Mechanism for Milling Applications
,” ASME J. Mech. Rob.
, 5
(3
), p. 034501
. 17.
Conconi
, M.
, and Carricato
, M.
, 2009
, “A New Assessment of Singularities of Parallel Kinematic Chains
,” IEEE Trans. Rob.
, 25
(4
), pp. 757
–770
. 18.
Gosselin
, C.
, Angeles
, J.
, et al., 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
, 6
(3
), pp. 281
–290
. 19.
Ball
, R. S.
, 1998
, A Treatise on the Theory of Screws
, Cambridge University Press
, Cambridge
.20.
Gibson
, C.
, and Hunt
, K.
, 1990
, “Geometry of Screw Systems—1: Screws: Genesis and Geometry
,” Mech. Mach. Theory
, 25
(1
), pp. 1
–10
. 21.
Merlet
, J.-P.
, 1989
, “Singular Configurations of Parallel Manipulators and Grassmann Geometry
,” Int. J. Rob. Res.
, 8
(5
), pp. 45
–56
. 22.
Hao
, F.
, and McCarthy
, J. M.
, 1998
, “Conditions for Line-Based Singularities in Spatial Platform Manipulators
,” J. Rob. Syst.
, 15
(1
), pp. 43
–55
. 23.
Merlet
, J.-P.
, 2005
, Parallel Robots
, Vol. 128
, Springer Science & Business Media
, Dordrecht, The Netherlands
.24.
Wen
, K.
, and Gosselin
, C. M.
, 2020
, “Forward Kinematic Analysis of Kinematically Redundant Hybrid Parallel Robots
,” ASME J. Mech. Rob.
, 12
(6
), p. 061008
. 25.
Bonev
, I. A.
, Ryu
, J.
, Kim
, S.-G.
, and Lee
, S.-K.
, 2001
, “A Closed-Form Solution to the Direct Kinematics of Nearly General Parallel Manipulators With Optimally Located Three Linear Extra Sensors
,” IEEE Trans. Rob. Autom.
, 17
(2
), pp. 148
–156
. 26.
Chiu
, Y.-J.
, and Perng
, M.-H.
, 2001
, “Forward Kinematics of a General Fully Parallel Manipulator With Auxiliary Sensors
,” Int. J. Rob. Res.
, 20
(5
), pp. 401
–414
. 27.
Schreiber
, L.-T.
, and Gosselin
, C.
, 2018
, “Kinematically Redundant Planar Parallel Mechanisms: Kinematics, Workspace and Trajectory Planning
,” Mech. Mach. Theory
, 119
, pp. 91
–105
. 28.
Li
, W.
, and Angeles
, J.
, 2017
, “A Novel Three-Loop Parallel Robot With Full Mobility: Kinematics, Singularity, Workspace, and Dexterity Analysis
,” ASME J. Mech. Rob.
, 9
(5
), p. 051003
. 29.
Adkins
, F. A.
, and Haug
, E. J.
, 1997
, “Operational Envelope of a Spatial Stewart Platform
,” ASME J. Mech. Des.
, 119
(2
), pp. 330
–332
. 30.
Gosselin
, C.
, and Angeles
, J.
, 1989
, “The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator
,” J. Mech. Trans. Autom. Des.
, 111
(2
), pp. 202
–207
. 31.
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
. Copyright © 2022 by ASME
You do not currently have access to this content.
