Graphical Abstract Figure
Abstract
A class of 5 degree-of-freedom (DoF) hybrid robots consisting of one translational and two rotational (1T2R) parallel module and 2 T serial module is presented for assembling in the aircraft cabin. The 1T2R parallel modules are with three limb topologies (PRS, RRS, and internal closed loop) and two layouts (symmetrical and “T” shape). Herein, P, R, and S denote prismatic, rotational, and spherical joints. This article presents the multi-objective optimization of the hybrid robot regarding different limb topology, limb layout, and corresponding dimensions as design variables. Considering demands from the in-cabin assembling, kinematic, linear stiffness along z-axis and total mass of the robot are the objectives. The Pareto fronts and cooperative equilibrium point (CEP) indicate that the robot with 3-PRS and 3-RRS parallel module have better performances than the one with internal closed loop. The overall performances of robot with symmetrical layout are superior than the one with “T” shape layout. In addition, two optimization methods are compared. One is to separately optimize six robots with specific topology and layout. The other is to optimize all design variables in a model. It is found that six robots have their own performance zones. Therefore, final optimums of two methods are close to each other. But optimization in one model is able to eliminate unfeasible topologies in the early stage of searching and thus is more efficient. Optimal module is 3-PRS with symmetrical layout. Experiments on the physical prototype validate performances of the optimal robot.
References
1.
Ma
, T.
, Xu
, X.
, Chai
, Z. W.
, Wang
, T.
, Shen
, X. T.
, and Sun
, T.
, 2023
, “A Wearable Biofeedback Device for Monitoring Tibial Load During Partial Weight-Bearing Walking
,” IEEE Trans. Neural Syst. Rehabil. Eng.
, 31
, pp. 3428
–3436
. 2.
Yang
, C.
, Geng
, S.
, Walker
, I.
, Branson
, D. T.
, Liu
, J.
, Dai
, J. S.
, and Kang
, R.
, 2020
, “Geometric Constraint-Based Modeling and Analysis of a Novel Continuum Robot With Shape Memory Alloy Initiated Variable Stiffness
,” Int. J. Rob. Res.
, 39
(14
), pp. 1602
–1634
. 3.
Cui
, J.
, Wang
, P.
, Sun
, T.
, Ma
, S.
, Liu
, S.
, Kang
, R.
, and Guo
, F.
, 2022
, “Design and Experiments of a Novel Quadruped Robot With Tensegrity Legs
,” Mech. Mach. Theory
, 171
, p. 104781
. 4.
Meißner
, D. W. I. J.
, Schmatz
, M. S. F.
, Beuß
, D. I. F.
, Sender
, D. W. I. J.
, Flügge
, I. W.
, and Gorr
, D. K. F. E.
, 2018
, “Smart Human-Robot-Collaboration in Mechanical Joining Processes
,” Proc. Manuf.
, 24
, pp. 264
–270
. 5.
Clean Aviation
, “It's About Time: Human/Robot Collab Zips Up Production Rates,” https://clean-aviation.eu/its-about-time-humanrobot-collab-zips-up-production-rates, Accessed March 26, 2024.6.
Muijs
, L.
, and Snijders
, M.
, 2017
, “Collaborative Robot Applications at GKN Aerospace’s Fokker Business,” SAE Technical Paper No. 2017-01-2091.7.
Yang
, D.
, Xie
, F. G.
, and Liu
, X. J.
, 2022
, “Velocity Constraints Based Approach for Online Trajectory Planning of High-Speed Parallel Robots
,” Chin. J. Mech. Eng.
, 35
(1
), p. 127
. 8.
She
, C. H.
, and Huang
, Z. T.
, 2008
, “Postprocessor Development of a Five-Axis Machine Tool With Nutating Head and Table Configuration
,” Int. J. Adv. Manuf. Technol.
, 38
(7–8
), pp. 728
–740
. 9.
Sun
, T.
, and Yang
, S. F.
, 2019
, “An Approach to Formulate the Hessian Matrix for Dynamic Control of Parallel Robots
,” IEEE/ASME Trans. Mechatron.
, 24
(1
), pp. 271
–281
. 10.
Yang
, S. F.
, Sun
, T.
, and Huang
, T.
, 2017
, “Type Synthesis of Parallel Mechanisms Having 3T1R Motion with Variable Rotational Axis
,” Mech. Mach. Theory
, 109
, pp. 220
–230
. 11.
Lian
, B. B.
, Feng
, P.
, Wu
, J.
, Ma
, J. T.
, Zhang
, Y.
, and Song
, Y. M.
, 2024
, “Light-Weight Design of Five-Degree-of-Freedom Hybrid Robot for Assembling in the Cabin
,” ASME J. Mech. Rob.
, 16
(3
), p. 031010
. 12.
Sun
, T.
, Yang
, S. F.
, Huang
, T.
, and Dai
, J. S.
, 2018
, “A Finite and Instantaneous Screw Based Approach for Topology Design and Kinematic Analysis of 5‐Axis Parallel Kinematic Machines
,” Chin. J. Mech. Eng.
, 33
(1
), p. 44
. 13.
Yang
, S.
, Sun
, T.
, Huang
, T.
, Li
, Q.
, and Gu
, D.
, 2016
, “A Finite Screw Approach to Type Synthesis of Three-DOF Translational Parallel Mechanisms
,” Mech. Mach. Theory
, 104
, pp. 405
–419
. 14.
Sun
, T.
, Yang
, S.
, Huang
, T.
, and Dai
, J. S.
, 2017
, “A Way of Relating Instantaneous and Finite Screws Based on the Screw Triangle Product
,” Mech. Mach. Theory
, 108
, pp. 75
–82
. 15.
Li
, S.
, Wang
, H.
, Meng
, Q.
, and Dai
, J. S.
, 2016
, “Task-Based Structure Synthesis of Source Metamorphic Mechanisms and Constrained Forms of Metamorphic Joints
,” Mech. Mach. Theory
, 96
, pp. 334
–345
. 16.
Sun
, T.
, Yang
, S. F.
, and Lian
, B. B.
, 2020
, Finite and Instantaneous Screw Theory in Robotic Mechanism
, Springer Nature
, Singapore
.17.
Viegas
, C.
, Tavakoli
, M.
, and Almeida
, A. T.
, 2017
, “A Novel Grid-Based Reconfigurable Spatial Parallel Mechanism With Large Workspace
,” Mech. Mach. Theory
, 115
, pp. 149
–167
. 18.
Li
, Q. C.
, Chen
, Z.
, Chen
, Q. H.
, Wu
, C. Y.
, and Hu
, X. D.
, 2011
, “Parasitic Motion Comparison of 3-PRS Parallel Mechanism With Different Limb Arrangements
,” Robot. Comput. Integr. Manuf.
, 27
(2
), pp. 389
–396
. 19.
Hess-Coelho
, T. A.
, 2006
, “Topological Synthesis of a Parallel Wrist Mechanism
,” ASME J. Mech. Des.
, 128
(1
), pp. 230
–235
. 20.
Li
, Q. C.
, and Herve
, J. M.
, 2008
, “Structural Shakiness of Nonoverconstrained Translational Parallel Mechanisms With Identical Limbs
,” IEEE Trans. Robot.
, 25
(1
), pp. 25
–36
. 21.
Yang
, T.-L.
, Liu
, A.-X.
, Jin
, Q.
, Luo
, Y.-F.
, Shen
, H.-P.
, and Hang
, L.-B.
, 2009
, “Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms
,” ASME J. Mech. Des.
, 131
(2
), p. 021001
. 22.
Hu
, B.
, 2016
, “Kinematically Identical Manipulators for the Exechon Parallel Manipulator and Their Comparison Study
,” Mech. Mach. Theory
, 103
, pp. 117
–137
. 23.
Nayak
, A.
, Caro
, S.
, and Wenger
, P.
, 2018
, “Comparison of 3-[PP] S Parallel Manipulators Based on Their Singularity Free Orientation Workspace, Parasitic Motions and Complexity
,” Mech. Mach. Theory
, 129
, pp. 293
–315
. 24.
Huo
, X.
, Lian
, B.
, Wang
, P.
, Song
, Y.
, and Sun
, T.
, 2023
, “Topology and Dimension Synchronous Optimization of 1T2R Parallel Robots
,” Mech. Mach. Theory
, 187
, p. 105385
. 25.
Chen
, K.
, Wang
, R.
, Niu
, Z.
, Wang
, P.
, and Sun
, T.
, 2023
, “Topology Design and Performance Optimization of Six-Limbs 5-DOF Parallel Machining Robots
,” Mech. Mach. Theory
, 185
, p. 105333
. 26.
Chen
, K.
, Wang
, M.
, Huo
, X.
, Wang
, P.
, and Sun
, T.
, 2023
, “Topology and Dimension Synchronous Optimization Design of 5-DoF Parallel Robots for In-Situ Machining of Large-Scale Steel Components
,” Mech. Mach. Theory
, 179
, p. 105105
. 27.
Sun
, T.
, and Huo
, X.
, 2018
, “Type Synthesis of 1T2R Parallel Mechanisms With Parasitic Motions
,” Mech. Mach. Theory
, 128
, pp. 412
–428
. 28.
Hu
, B.
, 2019
, “Terminal Position and Orientation Coupling in Lower Mobility Robots
,” ASME J. Mech. Robot.
, 11
(3
), p. 031008
. 29.
Hu
, B.
, 2014
, “Formulation of Unified Jacobian for Serial-Parallel Manipulators
,” Robot. Comput. Integr. Manuf.
, 30
(5
), pp. 460
–467
. 30.
Hu
, B.
, Huo
, Y.
, Gao
, J.
, and Zhang
, D.
, 2022
, “CGA-Based Approach for the Inverse Displacement of Serial-Parallel Manipulators
,” Mech. Mach. Theory
, 176
, p. 105011
. 31.
Hu
, B.
, Shi
, Y.
, Xu
, L.
, and Bai
, P.
, 2020
, “Reconsideration of Terminal Constraint/Mobility and Kinematics of 5-DOF Hybrid Manipulators Formed by One 2R1T PM and One RR SM
,” Mech. Mach. Theory
, 149
, p. 103837
. 32.
Hu
, B.
, Zhao
, J.
, and Cui
, H.
, 2019
, “Terminal Constraint and Mobility Analysis of Serial-Parallel Manipulators Formed by 3-RPS and 3-SPR PMs
,” Mech. Mach. Theory
, 134
, pp. 685
–703
. 33.
Dai
, J. S.
, 2014 and 2020
, Screw Algebra and Lie Groups and Lie Algebras, in “Modern Mathematics Series”
, Higher Education Press
, Beijing
.34.
Chen
, C.
, Peng
, F.
, Yan
, R.
, Li
, Y.
, Wei
, D.
, Fan
, Z.
, Tang
, X.
, and Zhu
, Z.
, 2019
, “Stiffness Performance Index Based Posture and Feed Orientation Optimization in Robotic Milling Process
,” Robot. Comput. Integr. Manuf.
, 55
, pp. 29
–40
. 35.
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
. 36.
Dai
, J. S.
, 2015
, “Euler-Rodrigues Formula Variations, Quaternion Conjugation and Intrinsic Connections
,” Mech. Mach. Theory
, 92
, pp. 144
–152
. 37.
Sun
, T.
, Liang
, D.
, and Song
, Y. M.
, 2018
, “Singular-Perturbation-Based Nonlinear Hybrid Control of Redundant Parallel Robot
,” IEEE Trans. Ind. Electron.
, 65
(4
), pp. 3326
–3336
. 38.
Deb
, K.
, Pratap
, A.
, Agarwal
, S.
, and Meyarivan
, T. A. M. T.
, 2002
, “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II
,” IEEE Trans. Evolut. Comput.
, 6
(2
), pp. 182
–197
. 39.
Qi
, Y.
, Sun
, T.
, and Song
, Y. M.
, 2018
, “Multi-Objective Optimization of Parallel Tracking Mechanism Considering Parameter Uncertainty
,” ASME J. Mech. Rob.
, 10
(4
), p. 041006
. 40.
Lian
, B. B.
, Wang
, X. V.
, and Wang
, L.
, 2019
, “Static and Dynamic Optimization of a Pose Adjusting Mechanism Considering Parameter Changes During Construction
,” Robot. Comput. Integr. Manuf.
, 59
(1
), pp. 267
–277
. 
