Most multimode parallel robots can change operation modes by passing through constraint singularities. This paper deals with a comprehensive kinematic study of a three degrees-of-freedom (DOF) multimode three-PRPiR parallel robot developed at Heriot-watt University. This robot is able to reach several operation modes without crossing any constraint singularity by using lockable Pi and R joints. Here, a Pi joint may act as a 1DOF planar parallelogram if its lockable P (prismatic) joint is locked or a 2DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation mode and four 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation mode are dealt with in detail. The joint space and workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. It is shown that the robot is able to change assembly mode in one operation mode by passing through another operation mode.
Issue Section:
Design Innovation Paper
References
1.
Fanghella
, P.
, Galletti
, C.
, and Gianotti
, E.
, 2006
, “Parallel Robots That Change Their Group of Motion
,” Advances in Robot Kinematics
, Springer
, Dordrecht The Netherlands
, pp. 49
–56
.2.
Refaat
, S.
, Hervé
, J. M.
, Nahavandi
, S.
, and Trinh
, H.
, 2007
, “Two-Mode Overconstrained Three-DOFs Rotational-Translational Linear-Motor-Based Parallel Kinematics Mechanism for Machine Tool Applications
,” Robotica
, 25
(4
), pp. 461
–466
.3.
Kong
, X.
, Gosselin
, C.
, and Richard
, P. L.
, 2007
, “Type Synthesis of Parallel Mechanisms With Multiple Operation Modes
,” ASME J. Mech. Des.
, 129
(6
), pp. 595
–601
.4.
Li
, Q.
, and Hervé
, J. M.
, 2009
, “Parallel Mechanisms With Bifurcation of Schoenflies Motion
,” IEEE Trans. Rob.
, 25
(1
), pp. pp. 158
–164
.5.
Gogu
, G.
, 2011
, “Maximally Regular T2R1-Type Parallel Manipulators With Bifurcated Spatial Motion
,” ASME J. Mech. Rob.
, 3
(1
), p. 011010
.6.
Ruggiu
, M.
, and Kong
, X.
, 2012
, “Mobility and Kinematic Analysis of a Parallel Mechanism With Both PPR and Planar Operation Modes
,” Mech. Mach. Theory
, 55
, pp. 77
–90
.7.
Kong
, X.
, 2012
, “Type Synthesis of Variable Degrees-of-Freedom Parallel Manipulators With Both Planar and 3T1R Operation Modes,” ASME
Paper No. DETC2012-70621.8.
Kong
, X.
, 2013
, “Type Synthesis of 3-DOF Parallel Manipulators With Both a Planar Operation Mode and a Spatial Translational Operation Mode
,” ASME J. Mech. Rob.
, 5
(4
), p. 041015
.9.
Kong
, X.
, and Yu
, J.
, 2015
, “Type Synthesis of Two-Degrees-of-Freedom 3-4R Parallel Mechanisms With Both Spherical Translation Mode and Sphere-on-Sphere Rolling Mode
,” ASME J. Mech. Rob.
, 7
(4
), p. 041018
.10.
Gan
, D.
, and Dai
, J. S.
, 2013
, “Geometry Constraint and Branch Motion Evolution of 3-PUP Parallel Mechanisms With Bifurcated Motion
,” Mech. Mach. Theory
, 61
, pp. 168
–183
.11.
Zeng
, Q.
, and Ehmann
, K. F.
, 2014
, “Design of Parallel Hybrid-Loop Manipulators With Kinematotropic Property and Deployability
,” Mech. Mach. Theory
, 71
, pp. 1
–26
.12.
Ye
, W.
, Fang
, Y.
, Zhang
, K.
, and Guo
, S.
, 2014
, “A New Family of Reconfigurable Parallel Mechanisms With Diamond Kinematotropic Chain
,” Mech. Mach. Theory
, 74
, pp. 1
–9
.13.
Ding
, X.
, Kong
, X.
, and Dai
, J. S.
, 2016
, Advances in Reconfigurable Mechanisms and Robots II
, Springer International Publishing
, London.14.
Coste
, M.
, and Demdah
, K. M.
, 2015
, “Extra Modes of Operation and Self Motions in Manipulators Designed for Schoenflies Motion
,” ASME J. Mech. Rob.
, 7
(4
), p. 041020
.15.
Nurahmi
, L.
, Caro
, S.
, Wenger
, P.
, Schadlbauer
, J.
, and Husty
, M.
, 2016
, “Reconfiguration Analysis of a 4-RUU Parallel Manipulator
,” Mech. Mach. Theory
, 96
(Pt. 2
), pp. 269
–289
.16.
Gan
, D.
, Dai
, J. S.
, and Liao
, Q.
, 2009
, “Mobility Change in Two Types of Metamorphic Parallel Mechanisms
,” ASME J. Mech. Rob.
, 1
(4
), p. 041007
.17.
Zhang
, K. T.
, Dai
, J. S.
, and Fang
, Y. F.
, 2012
, “Geometric Constraint and Mobility Variation of Two 3-SPS Metamorphic Parallel Mechanisms
,” ASME J. Mech. Rob.
, 135
(1
), p. 011001
.18.
Kong
, X.
, and Jin
, Y.
, 2016
, “Type Synthesis of 3-DOF Multi-Mode Translational/Spherical Parallel Mechanisms With Lockable Joints
,” Mech. Mach. Theory
, 96
(Pt. 2), pp. 323
–333
.19.
Carbonari
, L.
, Callegari
, M.
, Palmieri
, G.
, and Palpacelli
, M.-C.
, 2014
, “A New Class of Reconfigurable Parallel Kinematic Machines
,” Mech. Mach. Theory
, 79
, pp. 173
–183
.20.
Walter
, D. R.
, Husty
, M. L.
, and Pfurner
, M.
, 2009
, “Chapter A: Complete Kinematic Analysis of the SNU 3-UPU Parallel Manipulator
,” Contemporary Mathematics
, Vol. 496
, American Mathematical Society
, Providence, RI
, pp. 331
–346
.21.
Kong
, X.
, 2014
, “Reconfiguration Analysis of a 3-DOF Parallel Mechanism Using Euler Parameter Quaternions and Algebraic Geometry Method
,” Mech. Mach. Theory
, 74
, pp. 188
–201
.22.
Kong
, X.
, 2016
, “Reconfiguration Analysis of a 4-DOF 3-RER Parallel Manipulator With Equilateral Triangular Base and Moving Platform
,” Mech. Mach. Theory
, 98
, pp. 180
–189
.23.
Kong
, X.
, 2016
, “Reconfiguration Analysis of a Variable Degrees-of-Freedom Parallel Manipulator With Both 3-DOF Planar and 4-DOF 3T1R Operation Modes,” ASME
Paper No. DETC2016-59203.24.
Chablat
, D.
, Jha
, R.
, Rouillier
, F.
, and Moroz
, G.
, 2014
, “Non-Singular Assembly Mode Changing Trajectories in the Workspace for the 3-RPS Parallel Robot
,” Advances in Robot Kinematics
, Springer International Publishing, Cham, Switzerland, pp. 149
–159
.25.
Chablat
, D.
, Jha
, R.
, Rouillier
, F.
, and Moroz
, G.
, 2014
, “Workspace and Joint Space Analysis of the 3-RPS Parallel Robot,” ASME
Paper No. DETC2014-34593.26.
Zhang
, C.
, 2015
, “Improvement of a Disassembly-Free Reconfigurable Parallel Manipulator,” M.Sc. dissertation
, Heriot-Watt University, Edinburgh, UK.27.
Nenchez
, D. N.
, and Uchiyama
, M.
, 1995
, “Singularity-Consistent Path Tracking: A Null Space Based Approach
,” IEEE
International Conference on Robotics and Automation
, Nagoya, Japan, May 21–27, pp. 2482
–2489
.28.
Innocenti
, C.
, and Parenti-Castelli
, V.
, 1998
, “Singularity-Free Evolution From One Configuration to Another in Serial and Fully-Parallel Manipulators
,” ASME J. Mech. Des.
, 120
(1
), pp. 73
–79
.29.
Zein
, M.
, Wenger
, P.
, and Chablat
, D.
, 2008
, “Non-Singular Assembly-Mode Changing Motions for 3-RPR Parallel Manipulators
,” Mech. Mach. Theory
, 43
(4
), pp. 480
–490
.30.
Chablat
, D.
, and Wenger
, P.
, 1998
, “Working Modes and Aspects in Fully-Parallel Manipulator
,” IEEE
International Conference on Robotics and Automation
, Leuven, Belgium, May 16–20, pp. 1964
–1969
.31.
Company
, O.
, and Pierrot
, F.
, 2002
, “Modelling and Design Issues of a 3-Axis Parallel Machine-Tool
,” Mech. Mach. Theory
, 37
(11
), pp. 1325
–1345
.32.
Chablat
, D.
, and Wenger
, P.
, 2003
, “Architecture Optimization of a 3-DOF Parallel Mechanism for Machining Applications, the Orthoglide
,” IEEE Trans. Rob. Autom.
, 19
(3
), pp. 403
–410
.33.
Chablat
, D.
, Wenger
, P.
, Majou
, F.
, and Merlet
, J. P.
, 2004
, “An Interval Analysis Based Study for the Design and the Comparison of 3-DOF Parallel Kinematic Machines
,” Int. J. Rob. Res.
, 23
(6
), pp. 615
–624
.34.
Kong
, X.
, and Gosselin
, C. M.
, 2005
, “Type Synthesis of 3-DOF PPR-Equivalent Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain
,” ASME J. Mech. Des.
, 127
(6
), pp. 1113
–1121
.35.
Chablat
, D.
, Kong
, X.
, and Zhang
, C.
, 2017
, “Kinematics, Workspace and Singularity Analysis of a Multi-Mode Parallel Robot,” ASME
Paper No. DETC2017-67284.36.
Pashkevich
, A.
, Chablat
, D.
, and Wenger
, P.
, 2006
, “Kinematics and Workspace Analysis of a Three-Axis Parallel Manipulator: The Orthoglide
,” Robotica
, 24
(1
), pp. 39
–49
.37.
Gosselin
, C.
, and Angeles
, J.
, 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
, 6
(3
), pp. 281
–290
.38.
Wenger
, P.
, and Chablat
, D.
, 1997
, “Definition Sets for the Direct Kinematics of Parallel Manipulators
,” Eighth International Conference in Advanced Robotics
(ICAR
), Monterey, CA, July 7–9, pp. 859
–864
.39.
Siropa
, 2010, “A Library for Manipulator Singularities Analysis,” INRIA/CNRS, Paris, France, accessed, Jan. 30, 2018, http://siropa.gforge.inria.fr/doc/files/Siropa/modeling-mpl.html40.
Pashkevich
, A.
, Wenger
, P.
, and Chablat
, D.
, 2005
, “Design Strategies for the Geometric Synthesis of Orthoglide-Type Mechanisms
,” Mech. Mach. Theory
, 40
(8
), pp. 907
–930
.41.
Collins
, G. E.
, 1975
, Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition
, Springer, Berlin
.42.
Manubens
, M.
, Moroz
, G.
, Chablat
, D.
, Wenger
, P.
, and Rouiller
, F.
, 2012
, “Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators
,” ASME J. Mech. Rob.
, 4
(4
), p. 041003.43.
Lazard
, D.
, and Rouillier
, F.
, 2007
, “Solving Parametric Polynomial Systems
,” J. Symbolic Comput.
, 42
(6
), pp. 636
–667
.Copyright © 2018 by ASME
You do not currently have access to this content.
