Abstract
A 6-P-RR-R-RR parallel-kinematics machine (PKM) with axially offset RR-joints is the subject of this article. Different from the universal joint, an axial offset between the two axes of the RR-joint is included. The offset is intended to prevent joint interference, while enlarging the workspace of the whole PKM. Compared with a 6-PUS PKM, the kinematics of the PKM introduced here is significantly more complex due to the axial offsets. The displacement analysis is conducted numerically, and velocity and acceleration analyses are conducted symbolically. The accuracy and effectiveness of the proposed formulation are verified by numerical simulation in adams. In addition, the workspace, singularity, and dexterity analyses of this new type of PKM are conducted and then compared with those of the 6-PUS mechanism.
Issue Section:
Research Papers
References
1.
Gough
, V. E.
, 1957
, “Contribution to Discussion of Papers on Research in Automobile Stability, Control and Tyre Performance
,” Proc. Automob. Div. Inst. Mech. Eng.
, 171
, pp. 392
–395
.2.
Stewart
, D.
, 1965
, “A Platform With Six Degrees of Freedom
,” Proc. Inst. Mech. Eng.
, 180
(1
), pp. 371
–386
. 3.
Duffy
, J.
, 1996
, Statics and Kinematics With Applications to Robotics
, Cambridge University Press
, Cambridge, UK
.4.
Hunt
, K. H.
, and Primrose
, E. J. F.
, 1993
, “Assembly Configurations of Some In-Parallel-Actuated Manipulators
,” Mech. Mach. Theory
, 28
(1
), pp. 31
–42
. 5.
Tsai
, L.-W.
, 1999
, Robot Analysis: The Mechanics of Serial and Parallel Manipulators
, John Wiley & Sons
, Hoboken, NJ
.6.
Merlet
, J.-P.
, 2005
, Parallel Robots
, Vol. 128, Springer-Verlag New York Inc.
, New York
.7.
Angeles
, J.
, 2014
, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms
, Springer
, Cham, Switzerland
.8.
Angeles
, J.
, 2004
, “The Qualitative Synthesis of Parallel Manipulators
,” ASME J. Mech. Des.
, 126
(4
), pp. 617
–624
. 9.
Gosselin
, C. M.
, 1990
, “Stiffness Mapping for Parallel Manipulators
,” IEEE Trans. Rob. Autom.
, 6
(3
), pp. 377
–382
. 10.
Gosselin
, C. M.
, and Wang
, J.
, 2000
, “Static Balancing of Spatial Six-Degree-of-Freedom Parallel Mechanisms With Revolute Actuators
,” J. Rob. Syst.
, 17
(3
), pp. 159
–170
. 11.
Li
, P.
, Han
, H.
, Liu
, C.
, Ren
, B.
, Wu
, Q.
, and Xu
, Z.
, 2023
, “Workspace Analysis of Axial Offset Joint Based on Parameterization
,” Robotica
, 41
(9
), pp. 2882
–2906
. 12.
Gloess
, R.
, and Lula
, B.
, 2010
, “Challenges of Extreme Load Hexapod Design and Modularization for Large Ground-Based Telescopes,” Modern Technologies in Space- and Ground-Based Telescopes and Instrumentation
, E.
Atad-Ettedgui
and D.
Lemke
, eds., Vol. 7739, SPIE
, San Diego, CA
, pp. 689
–699
.13.
Großmann
, K.
, and Kauschinger
, B.
, 2012
, “Eccentric Universal Joints for Parallel Kinematic Machine Tools: Variants and Kinematic Transformations
,” Prod. Eng. Res. Dev.
, 6
(4
), pp. 521
–529
.14.
Hu
, B.
, and Lu
, Y.
, 2008
, “Analyses of Kinematics, Statics, and Workspace of a 3-RRPRR Parallel Manipulator and Its Three Isomeric Mechanisms
,” Proc. Inst. Mech. Eng., Part C
, 222
(9
), pp. 1829
–1837
. 15.
Ji
, P.
, and Wu
, H.
, 2003
, “Kinematics Analysis of an Offset 3-UPU Translational Parallel Robotic Manipulator
,” Robot. Auton. Syst.
, 42
(2
), pp. 117
–123
. 16.
Tsai
, L.-W.
, 1996
, “Kinematics of a Three-DoF Platform With Three Extensible Limbs,” Recent Advances in Robot Kinematics
, J.
Lenarčič
and V.
Parenti-Castelli
, eds., Springer
, Dordrecht, Netherlands
, pp. 401
–410
.17.
Dalvand
, M. M.
, and Shirinzadeh
, B.
, 2011
, “Forward Kinematics Analysis of Offset 6-RRCRR Parallel Manipulators
,” Proc. Inst. Mech. Eng., Part C
, 225
(12
), pp. 3011
–3018
. 18.
Dalvand
, M. M.
, and Shirinzadeh
, B.
, 2012
, “Kinematics Analysis of 6-DOF Parallel Micro-Manipulators With Offset U-Joints: A Case Study
,” Int. J. Intell. Mechatron. Robot. (IJIMR)
, 2
(1
), pp. 28
–40
. 19.
Dalvand
, M. M.
, Shirinzadeh
, B.
, and Nahavandi
, S.
, 2013
, “Inverse Kinematics Analysis of 6-RRCRR Parallel Manipulators
,” 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, IEEE
, pp. 644
–648
.20.
Yu
, Y.
, Xu
, Z.
, Wu
, Q.
, Yu
, P.
, He
, S.
, and Wang
, G.
, 2017
, “Kinematic Analysis and Testing of a 6-RRRPRR Parallel Manipulator
,” Proc. Inst. Mech. Eng., Part C
, 231
(13
), pp. 2515
–2527
. 21.
Zhang
, Y.
, Han
, H.
, Xu
, Z.
, Han
, C.
, Yu
, Y.
, Mao
, A.
, and Wu
, Q.
, 2021
, “Kinematics Analysis and Performance Testing of 6-RR-RP-RR Parallel Platform With Offset RR-Hinges Based on Denavit-Hartenberg Parameter Method
,” Proc. Inst. Mech. Eng., Part C
, 235
(18
), pp. 3519
–3533
. 22.
Zhang
, Y.
, Han
, H.
, Zhang
, H.
, Xu
, Z.
, Xiong
, Y.
, Han
, K.
, and Li
, Y.
, 2022
, “Acceleration Analysis of 6-RR-RP-RR Parallel Manipulator With Offset Hinges by Means of a Hybrid Method
,” Mech. Mach. Theory
, 169
, p. 104661
. 23.
Wang
, J.
, and Masory
, O.
, 1993
, “On the Accuracy of a Stewart Platform. I. The Effect of Manufacturing Tolerances
,” 1993 IEEE International Conference on Robotics and Automation
, IEEE
, pp. 114
–120
. 24.
Daney
, D.
, 2003
, “Kinematic Calibration of the Gough Platform
,” Robotica
, 21
(6
), pp. 677
–690
. 25.
Aginaga
, J.
, Iriarte
, X.
, Plaza
, A.
, and Mata
, V.
, 2018
, “Kinematic Design of a New Four Degree-of-Freedom Parallel Robot for Knee Rehabilitation
,” ASME J. Mech. Des.
, 140
(9
), p. 092304
. 26.
Isaksson
, M.
, 2017
, “Kinematically Redundant Planar Parallel Mechanisms for Optimal Singularity Avoidance
,” ASME J. Mech. Des.
, 139
(4
), p. 042302
. 27.
Toz
, M.
, Han
, H.
, and Angeles
, J.
, 2024
, “Workspace, Singularity and Dexterity Analyses of a Six-dof SDelta Robot With an Orthogonal Base Platform
,” ASME J. Mech. Rob.
, 16
(7
), p. 071010
. 28.
Ruiz-García
, J.
, Chaparro-Altamirano
, D.
, Zavala-Yoe
, R.
, and Ramírez-Mendoza
, R.
, 2013
, “Direct and Inverse Dynamics Modeling of a 6-PUS Parallel Robot
,” 2013 International Conference on Mechatronics, Electronics and Automotive Engineering, IEEE
, pp. 21
–26
. 29.
Wu
, P.
, Xiong
, H.
, and Kong
, J.
, 2012
, “Dynamic Analysis of 6-SPS Parallel Mechanism
,” Int. J. Mech. Mater. Des.
, 8
(2
), pp. 121
–128
. 30.
Liu
, Y.
, Wu
, H.
, Yang
, Y.
, Zou
, S.
, Zhang
, X.
, and Wang
, Y.
, 2018
, “Symmetrical Workspace of 6-UPS Parallel Robot Using Tilt and Torsion Angles
,” Math. Probl. Eng.
, 2018
(1
), p. 6412030
. 31.
Liu
, G.
, Qu
, Z.
, Liu
, X.
, and Han
, J.
, 2014
, “Singularity Analysis and Detection of 6-UCU Parallel Manipulator
,” Robot. Cim-Int. Manuf.
, 30
(2
), pp. 172
–179
. 32.
Han
, H.
, Han
, C.
, Xu
, Z.
, Zhu
, M.
, Yu
, Y.
, and Wu
, Q.
, 2019
, “Kinematics Analysis and Testing of Novel 6-P-RR-R-RR Parallel Platform With Offset RR-Joints
,” Proc. Inst. Mech. Eng., Part C
, 233
(10
), pp. 3512
–3530
. 33.
Han
, H.
, and Angeles
, J.
, 2024
, “Dynamics of a Parallel-Kinematics Machine With Six Pairs of Offset Joints
,” ASME J. Mech. Rob.
, 16
(3
), p. 031015
. 34.
Lou
, Y.
, Liu
, G.
, and Li
, Z.
, 2008
, “Randomized Optimal Design of Parallel Manipulators
,” IEEE Trans. Autom. Sci. Eng.
, 5
(2
), pp. 223
–233
. 35.
Cheng
, H.
, and Gupta
, K. C.
, 1989
, “An Historical Note on Finite Rotations
,” ASME J. Appl. Mech.
, 56
(1
), pp. 139
–145
. 36.
Angeles
, J.
, 1988
, Rational Kinematics
(Springer Tracts in Natural Philosophy
), Vol. 34
, Springer
, New York
.37.
Siciliano
, B.
, and Khatib
, O.
, 2008
, Springer Handbook of Robotics
, Springer International Publishing
, Berlin & Heidelberg, Germany
.38.
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
. 39.
Li
, W.
, and Angeles
, J.
, 2018
, “Full-Mobility 3-CCC Parallel-Kinematics Machines: Forward Kinematics, Singularity, Workspace and Dexterity Analyses
,” Mech. Mach. Theory
, 126
, pp. 312
–328
. 40.
Wang
, C.
, and Wu
, H.
, 2013
, “Singularity Analysis of 6-PUS Vertical Parallel Mechanism
,” Key Eng. Mater.
, 568
, pp. 129
–134
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