Graphical Abstract Figure
Schematic diagram of limited positions of PKM
Abstract
At present, the design of parallel kinematic mechanism (PKM) generally starts from type synthesis based on the motion pattern and then the dimensions are synthesized based on performance requirements. The synthesized type of PKM with optimal load-bearing capacity is hard to determine because the above type synthesis is just based on the motion pattern and the number of synthesized types of PKM is huge. Therefore, this paper aims to investigate a force-motion coupled mechanism synthesis method for heavy-load PKM with optimal motion performance and load-bearing capacity. First, the optimal load-bearing conditions for PKM are derived, namely, the wrench screw of a limb is parallel to the external force acting on the moving platform and is reciprocal with the wrench of the actuator. Furthermore, a novel force-motion coupled type synthesis method is proposed, in which the wrench of the limb is added to the constrained screw system. In this situation, the synthesized PKM is singular. Therefore, dimension synthesis is carried out based on the workspace, and a near-singular 6-PHSS PKM is then synthesized. Finally, a novel multi-DoF forming machine with a forming force of 6000 kN is developed. Compared with the Stewart platform (6-UPS PKM), the maximum forces of the actuator and limb of the new near-singular 6-PHSS PKM were reduced by 80% and 10%, respectively, validating the proposed force-motion coupled synthesis method for heavy-load PKM.
References
1.
Weck
, M.
, and Staimer
, D.
, 2002
, “Parallel Kinematic Machine Tools—Current State and Future Potentials
,” CIRP Ann.
, 51
(2
), pp. 671
–683
. 2.
Meng
, X. D.
, Gao
, F.
, Wu
, S. F.
, and Ge
, Q. J.
, 2014
, “Type Synthesis of Parallel Robotic Mechanisms: Framework and Brief Review
,” Mech. Mach. Theory
, 78
(8
), pp. 177
–186
. 3.
Russo
, M.
, Zhang
, D.
, Liu
, X. J.
, and Xie
, Z. H.
, 2024
, “A Review of Parallel Kinematic Machine Tools: Design, Modeling, and Applications
,” Int. J. Mach. Tools Manuf.
, 196
(3
), p. 104118
. 4.
Zhang
, D.
, and Gosselin
, C. M.
, 2002
, “Kinetostatic Analysis and Design Optimization of the Tricept Machine Tool Family
,” ASME J. Manuf. Sci. Eng.
, 124
(3
), pp. 725
–733
. 5.
Xu
, L. M.
, Chai
, X. X.
, and Ding
, Y.
, 2024
, “Design of a 2RRU-RRS Parallel Kinematic Mechanism for an Inner-Cavity Machining Hybrid Robot
,” ASME J. Mech. Rob.
, 16
(5
), p. 054501
. 6.
Xie
, F.
, Li
, T.
, and Liu
, X.
, 2013
, “Type Synthesis of 4-DOF Parallel Kinematic Mechanisms Based on Grassmann Line Geometry and Atlas Method
,” Chin. J. Mech. Eng.
, 26
(6
), pp. 1073
–1081
. 7.
Wang
, C.
, Fang
, Y.
, and Guo
, S.
, 2015
, “Multi-Objective Optimization of a Parallel Ankle Rehabilitation Robot Using Modified Differential Evolution Algorithm
,” Chin. J. Mech. Eng.
, 28
(4
), pp. 702
–715
. 8.
Yang
, X. S.
, Zhao
, Z. L.
, Xiong
, H.
, Li
, Q. C. A.
, and Lou
, Y. J.
, 2021
, “Kinematic Analysis and Optimal Design of a Novel Schonflies-Motion Parallel Manipulator With Rotational Pitch Motion for Assembly Operations
,” ASME J. Mech. Rob.
, 13
(4
), p. 040910
. 9.
Kong
, X. W.
, and Gosselin
, C. M.
, 2004
, “Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory
,” ASME J. Mech. Des.
, 126
(1
), pp. 101
–108
. 10.
Yang
, S.
, Sun
, T.
, and Huang
, T.
, 2017
, “Type Synthesis of Parallel Mechanisms Having 3T1R Motion With Variable Rotational Axis
,” Mech. Mach. Theory
, 109
(3
), pp. 220
–230
. 11.
Liu
, Y.
, Li
, Y.
, Yao
, Y.-a.
, and Kong
, X.
, 2020
, “Type Synthesis of Multi-Mode Mobile Parallel Mechanisms Based on Refined Virtual Chain Approach
,” Mech. Mach. Theory
, 152
(10
), p. 103908
. 12.
Li
, X.
, Qu
, H. B.
, and Guo
, S.
, 2023
, “Kinematic Performance and Static Analysis of a Two-Degree-of-Freedom 3-RPS/US Parallel Manipulator With Two Passive Limbs
,” ASME J. Mech. Rob.
, 15
(2
), p. 021014
. 13.
Zeng
, Q.
, and Fang
, Y.
, 2012
, “Structural Synthesis and Analysis of Serial–Parallel Hybrid Mechanisms With Spatial Multi-Loop Kinematic Chains
,” Mech. Mach. Theory
, 49
(3
), pp. 198
–215
. 14.
Li
, Q.
, and Herve
, J. M.
, 2014
, “Type Synthesis of 3-DOF RPR-Equivalent Parallel Mechanisms
,” IEEE Trans. Rob.
, 30
(6
), pp. 1333
–1343
. 15.
Zhang
, X.
, Mu
, D. J.
, Zhang
, Y. T.
, You
, H. H.
, and Wang
, H. R.
, 2019
, “Type Synthesis of Multi-Loop Spatial Mechanisms With Three Translational Output Parameters Based on Virtual-Loop Theory and Assur Groups
,” Robotica
, 37
(6
), pp. 1104
–1119
. 16.
Kong
, X. W.
, 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
. 17.
Chen
, J.
, San
, H.
, Wu
, X.
, Chen
, M.
, and He
, W.
, 2019
, “Structural Design and Characteristic Analysis for a 4-Degree-of-Freedom Parallel Manipulator
,” Adv. Mech. Eng.
, 11
(5
), p. 1687814019850995
. 18.
Mohamed
, M. G.
, and Duffy
, J.
, 1985
, “A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators
,” ASME J. Mech.,Transm., Autom., Des.
, 107
(2
), pp. 226
–229
. 19.
Huang
, Z.
, and Li
, Q. C.
, 2002
, “General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators
,” Int. J. Rob. Res.
, 21
(2
), pp. 131
–145
. 20.
Xu
, Y.
, Yao
, J.
, and Zhao
, Y.
, 2012
, “Type Synthesis of Spatial Mechanisms for Forging Manipulators
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 226
(9
), pp. 2320
–2330
. 21.
Borges Dos Santos
, J. V.
, Simoni
, R.
, Carboni
, A. P.
, and Martins
, D.
, 2020
, “A New Method for Type Synthesis of Parallel Mechanisms Using Screw Theory and Features of Genetic Algorithms
,” J. Braz. Soc. Mech. Sci. Eng.
, 42
(12
), p. 615
. 22.
Song
, J. K.
, Zhao
, C.
, Zhao
, K.
, Yan
, W. J.
, and Chen
, Z. M.
, 2023
, “Singularity Analysis and Dimensional Synthesis of a 2R1 T 3-UPU Parallel Mechanism Based on Performance Atlas
,” ASME J. Mech. Rob.
, 15
(1
), p. 011001
. 23.
Yue
, J.
, Lin
, C.
, Jiang
, S.
, Li
, W.
, Gao
, F.
, and Chen
, W.
, 2024
, “Design, Analysis and Optimization of a Novel Redundant (6+1)-Degree-of-Freedom Parallel Mechanism With Configurable Platform
,” Mech. Mach. Theory
, 192
(2
), p. 105550
. 24.
Gao
, Z.
, Zhang
, D.
, and Ge
, Y.
, 2010
, “Design Optimization of a Spatial Six Degree-of-Freedom Parallel Manipulator Based on Artificial Intelligence Approaches
,” Rob. Comput. Integr. Manuf.
, 26
(2
), pp. 180
–189
. 25.
Sun
, J.
, Shao
, L.
, Fu
, L.
, Han
, X.
, and Li
, S.
, 2020
, “Kinematic Analysis and Optimal Design of a Novel Parallel Pointing Mechanism
,” Aerosp. Sci. Technol.
, 104
(9
), p. 105931
. 26.
Meng
, Q.
, Liu
, X.-J.
, and Xie
, F.
, 2022
, “Design and Development of a Schönflies-Motion Parallel Robot With Articulated Platforms and Closed-Loop Passive Limbs
,” Rob. Comput. Integr. Manuf.
, 77
(10
), p. 102352
. 27.
Ma
, Y.
, Tian
, Y.
, Liu
, X.
, and Lu
, C.
, 2023
, “Dynamic Modeling and Analysis of the 3-PRS Power Head Based on the Screw Theory and Rigid Multipoint Constraints
,” Sci. China Technol. Sci.
, 66
(7
), pp. 1869
–1882
. 28.
Dong
, C. L.
, Liu
, H. T.
, Huang
, T.
, and Chetwynd
, D. G.
, 2019
, “A Screw Theory-Based Semi-Analytical Approach for Elastodynamics of the Tricept Robot
,” ASME J. Mech. Rob.
, 11
(3
), p. 031005
. 29.
Jin
, X.
, Ye
, W.
, and Li
, Q.
, 2023
, “New Indices for Performance Evaluation of Cable-Driven Parallel Robots: Motion/Force Transmissibility
,” Mech. Mach. Theory
, 188
(10
), p. 105402
. 30.
Liu
, X.-J.
, Xie
, F.
, and Meng
, Q.
, 2020
, “Motion–Force Interaction Performance Analyses of Redundantly Actuated and Overconstrained Parallel Robots With Closed-Loop Subchains
,” ASME J. Mech. Des.
, 142
(10
), p. 103304
. 31.
Ma
, J.
, Lian
, B.
, Wang
, M.
, Dong
, G.
, Li
, Q.
, Wu
, J.
, and Yang
, Y.
, 2023
, “Optimal Design of a Parallel Assembling Robot with Large Payload-to-Mass Ratio
,” Rob. Comput. Integr. Manuf.
, 80
(4
), p. 102474
. 32.
Briot
, S.
, and Boyer
, F.
, 2023
, “A Geometrically Exact Assumed Strain Modes Approach for the Geometrico- and Kinemato-Static Modelings of Continuum Parallel Robots
,” IEEE Trans. Rob.
, 39
(2
), pp. 1527
–1543
. 33.
Teo
, T. J.
, Chen
, I. M.
, and Yang
, G.
, 2014
, “A Large Deflection and High Payload Flexure-Based Parallel Manipulator for UV Nanoimprint Lithography: Part II. Stiffness Modeling and Performance Evaluation
,” Precis. Eng.
, 38
(4
), pp. 872
–884
. 34.
Shneor
, Y.
, and Portman
, V. T.
, 2010
, “Stiffness of 5-Axis Machines With Serial, Parallel, and Hybrid Kinematics: Evaluation and Comparison
,” CIRP Ann.
, 59
(1
), pp. 409
–412
. 35.
Li
, S. H.
, Niu
, Y. Z.
, Xu
, J. L.
, and Yu
, H. B.
, 2024
, “A Novel Integrated Design Method of Parallel Mechanisms Based on Performance Requirements
,” ASME J. Mech. Rob.
, 16
(4
), p. 044502
. 36.
Zheng
, F. Y.
, Han
, X. H.
, Hua
, L.
, Zhuang
, W. H.
, and Huang
, B.
, 2024
, “Dynamic Error Prediction and Link Strain Feedback Control for a Novel Heavy Load Multi-DOF Envelope Forming Machine
,” Mech. Syst. Sig. Process.
, 216
(7
), p. 111494
. 37.
Han
, X.
, and Hua
, L.
, 2012
, “Investigation on Contact Parameters in Cold Rotary Forging Using a 3D FE Method
,” Int J. Adv. Manuf. Tech.
, 62
(9-12
), pp. 1087
–1106
. 38.
Zheng
, F. Y.
, Xin
, S.
, Han
, X. H.
, Hua
, L.
, Zhuang
, W. H.
, Hu
, X.
, and Chai
, F.
, 2024
, “Heavy-Load Nonapod: A Novel Flexible Redundant Parallel Kinematic Machine for Multi-DoF Forming Process
,” Int. J. Mach. Tools Manuf.
, 200
(8
), p. 104183
. 39.
Zheng
, F.
, Han
, X.
, Hua
, L.
, and Zhuang
, W.
, 2024
, “Hybrid Position-Force Feed Control of Heavy Load Forming Nonapod for Manufacturing Thin Wall and High Rib Parts
,” IEEE/ASME Trans. Mechatron.
, pp. 1
–13
. 
