Abstract
This study presents a novel approach to the design of a 3T1R parallel-based machine tool by incorporating local and global dexterity indices. The methodology focuses on the synthesis of geometric dimensions to optimize the mechanism’s performance. Initially, the paper provides a brief overview of the inverse kinematics of the mechanism and develops a 2-degrees-of-freedom (2-DoF) design based on the desired workspace, which is defined as the largest enclosed operational area. The research also evaluates the kinematic precision and distance singularity of the manipulator using global and local dexterity indices. Subsequently, the optimal dimensions for the individual components of the 3T1R parallel-based machine tool are determined by combining two 2-DoF mechanisms that have undergone design improvements. The study then discusses various conditions related to each component and establishes enhanced dimensions for the 3T1R manipulator to achieve the desired workspace. The design process considers the appropriate range of global and local dexterity indices to improve the performance of the 3T1R manipulator components within the targeted workspace. With this enhanced design, the 3T1R manipulator is capable of achieving four degrees of motion at any given position, while avoiding singular points outside the workspace boundaries. This methodology can be applied to a wide range of parallel-based machine tools.
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References
Merlet JP (2006) Parallel robots. Springer Science & Business Media, p 128
Liu X-J et al (2004) A new approach to the design of a DELTA robot with a desired workspace. J Intell Rob Syst 39:209–225
Kong X, Gosselin CM, Richard PL (2007) Type synthesis of parallel mechanisms with multiple operation modes, pp 595–601
Bonev IA, Ryu J (2001) A new approach to orientation workspace analysis of 6-DOF parallel manipulators. Mech Mach Theory 36(1):15–28
Pedrammehr S (2018) Dynamic modelling of hexarot parallel mechanisms for design and development (Doctoral dissertation). Deakin University, Australia
Lu Y, Hu B (2007) Analyzing kinematics and solving active/constrained forces of a 3SPU+ UPR parallel manipulator. Mech Mach Theory 42(10):1298–1313
Karimi A, Masouleh MT, Cardou P (2014) Singularity-free workspace analysis of general 6-UPS parallel mechanisms via convex optimization. Mech Mach Theory 80:17–34
Rahmani A, Ghanbari A, Pedrammehr S (2014) Kinematic analysis for hybrid 2-(6-UPU) manipulator using wavelet neural network. Adv Mater Res 1016:726–730
Kaloorazi M-HF, Masouleh MT, Caro S (2015) Determination of the maximal singularity-free workspace of 3-DOF parallel mechanisms with a constructive geometric approach. Mech Mach Theory 84:25–36
Gosselin C (1990) Determination of the workspace of 6-DOF parallel manipulators, pp 331–336
Merlet JP (1992) Geometrical determination of the workspace of a constrained parallel manipulator. Advances in Robot Kinematics, pp 326–329
Yang TL, Liu A, Shen H, Hang L, Luo Y, Jin Q (2018) Topology design of robot mechanisms. Springer, pp 35–80
Xie F et al (2014) Type synthesis of 2T1R-type parallel kinematic mechanisms and the application in manufacturing. Robot Comput-Integr Manuf 30(1):1–10
Peng S et al (2023) Configuration design and dimensional synthesis of an asymmetry 2R1T parallel mechanism. Robotica 41(2):713–734
Tajaril MJ, Pedrammehr S, Qazani MR, Nategh MJ (2017) The effects of joint clearance on the kinematic error of the hexapod tables. In Proceedings of the 5th RSI International Conference on Robotics and Mechatronics (ICRoM 2017), Tehran, Iran, pp 39–44.
Ye W, Li Q (2019) Type synthesis of lower mobility parallel mechanisms: a review. Chin J Mech Eng 32:1–11
Boudreau R, CM Gosselin (1998) The synthesis of planar parallel manipulators with a genetic algorithm. In International design engineering technical conferences and computers and information in engineering conference. Am Soc Mech Eng 80302:V01AT01A032
Laribi M, Romdhane L, Zeghloul S (2007) Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace. Mech Mach Theory 42(7):859–870
Wang J, Wu J, Li T, Liu X (2009) Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy. Publ Robot 27(1):51–57
Huang T, Li M, Zhao XM, Mei JP, Chetwynd DG, Hu SJ (2005) Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant-a novel 5-DOF reconfigurable hybrid robot. IEEE Trans Robot 21(3):449–456
Karimi A, Masouleh MT, Cardou P (2016) Avoiding the singularities of 3-RPR parallel mechanisms via dimensional synthesis and self-reconfigurability. Mech Mach Theory 99:189–206
Schappler M, Jahn P, Raatz A, Ortmaier T (2021) Combined structural and dimensional synthesis of a parallel robot for cryogenic handling tasks. in Annals of Scientific Society for Assembly, Handling and Industrial Robotics 2022. Springer, pp 65–77
Che L et al (2020) Dimensional synthesis for a Rec4 parallel mechanism with maximum transmission workspace. Mech Mach Theory 153:104008
Zhao X et al (2019) Kinematic analysis and dimensional synthesis of a three-degrees-of-freedom hybrid-drive parallel mechanism. Proc Inst Mech Eng C J Mech Eng Sci 233(8):2728–2752
Song J, Zhao C, Zhao K, Yan W, Chen Z (2023) Singularity analysis and dimensional synthesis of a 2R1T 3-UPU parallel mechanism based on performance atlas. J Mech Robot 15(1):011001
Rao ABK, Rao PM, Saha SK (2005) Dimensional design of hexaslides for optimal workspace and dexterity. IEEE Trans Rob 21(3):444–449
Fomin A et al (2021) Dimensional (parametric) synthesis of the hexapod-type parallel mechanism with reconfigurable design. Machines 9(6):117
Liu XJ, Guan L, Wang J (2007) Kinematics and closed optimal design of a kind of PRRRP parallel manipulator, pp 558–563
Le HN, Le XH (2018) Geometrical design of a RUU type delta robot based on the predescribed workspace. in 2018 4th International Conference on Green Technology and Sustainable Development (GTSD). IEEE, pp 359–364
Yang C, Li Q, Ye W (2022) Dimensional synthesis method of parallel manipulators based on the principle component analysis. Mech Mach Theory 176:104980
Di Gregorio R (2022) Dimensional synthesis of a novel 3-URU translational manipulator implemented through a novel method. Robotics 11(1):10
Di Gregorio R (2021) Direct position analysis of a particular translational 3-URU manipulator. J Mech Robot 13(6):061007
Ji W, Z Xie, X Chai (2021) Kinematics and dimensional synthesis of a novel 2RPU-PUR parallel manipulator. in Intelligent Robotics and Applications: 14th International Conference, ICIRA, Yantai, China, Proceedings, Part II 14. 2021. Springer, pp 754–765
Dastjerdi AH, Sheikhi MM, Masouleh MT (2020) A complete analytical solution for the dimensional synthesis of 3-DOF delta parallel robot for a prescribed workspace. Mech Mach Theory 153:103991
Laryushkin P, Fomin A, Antonov A (2023) Kinematic and singularity analysis of a 4-DOF Delta-type parallel robot. J Braz Soc Mech Sci Eng 45(4):218
Toz M, Han H, Angeles J (2024) Workspace, singularity and dexterity analyses of a six-dof SDelta robot with an orthogonal base platform. J Mech Robot 16(7)
Puglisi LJ et al (2012) Dimensional synthesis of a spherical parallel manipulator based on the evaluation of global performance indexes. Robot Auton Syst 60(8):1037–1045
Rezania V, Ebrahimi S (2017) Dexterity characterization of the RPR parallel manipulator based on the local and global condition indices. J Mech Sci Technol 31:335–344
Kucuk S (2009) A dexterity comparison for 3-DOF planar parallel manipulators with two kinematic chains using genetic algorithms. Mechatronics 19(6):868–877
Wu J, Yin Z (2008) A novel 4-DOF parallel manipulator H4. Parallel manipulators, towards new applications, IntechOpen. https://doi.org/10.5772/5441
Gosselin C (1991) and J. Angeles, A global performance index for the kinematic optimization of robotic manipulators
Meng Q, Liu X-J, Xie F (2022) Design and development of a Schönflies-motion parallel robot with articulated platforms and closed-loop passive limbs. Robot Comput-Integr Manuf 77:102352
Mahboubkhah M, Barari A (2019) Design and development of a novel 4-DOF parallel kinematic coordinate measuring machine (CMM). Int J Comput Integr Manuf 32(8):750–760
Gan D, Dai JS, Dias J, Umer R, Seneviratne L (2015) Singularity-free workspace aimed optimal design of a 2T2R parallel mechanism for automated fiber placement. Publ J Mech Robot 7(4):041022
Badescu M, J Morman, and C Mavroidis (2002) Workspace optimization of 3-UPU parallel platforms with joint constraints. in Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292).
Akhbari S, Jond AZ, Mahboubkhah M (2018) Kinematic and workspace analyses of a novel 4-DOF parallel mechanism. In Proceedings of the 6th RSI International Conference on Robotics and Mechatronics (IcRoM), Tehran, Iran
Liu S, Huang T, Mei J, Zhao X, Wang P, Chetwynd DG (2012) Optimal design of a 4-DOF SCARA type parallel robot using dynamic performance indices and angular constraints, 031005
Gogu G (2007) Structural synthesis of fully-isotropic parallel robots with Schönflies motions via theory of linear transformations and evolutionary morphology. Eur J Mech-A/Solids 26(2):242–269
Liu X-J, Wang J (2003) Some new parallel mechanisms containing the planar four-bar parallelogram. Int J Robot Res 22(9):717–732
Huang Z, Q Li, H Ding (2012) Theory of parallel mechanisms. Springer Science & Business Media, 6
Zhao J-S, Zhou K, Feng Z-J (2004) A theory of degrees of freedom for mechanisms. Mech Mach Theory 39(6):621–643
Wang L, Xu H, Guan L (2015) Mobility analysis of parallel mechanisms based on screw theory and mechanism topology. Adv Mech Eng 7(11):1687814015610467
Kelaiaia R, Company O, Zaatri A (2012) Multiobjective optimization of a linear Delta parallel robot. Mech Mach Theory 50:159–178
Gosselin C (1990) Stiffness mapping for parallel manipulators. IEEE Trans Robot Autom 6(3):377–382
Patel S, Sobh T (2015) Manipulator performance measures-a comprehensive literature survey. J Intell Rob Syst 77:547–570
Aliakbari M et al (2022) Computer integrated work-space quality improvement of the C4 parallel robot CMM based on kinematic error model for using in intelligent measuring. Int J Comput Integr Manuf 35(4–5):444–461
Akhbari S, Mahboubkhah M, Karimi D, Barari A (2022) Experimental and analytical evaluation of tool path error using computer integrated nonlinear kinematical modeling for a 4-DOF parallel milling machine. Int J Comput Integr Manuf 35(4–5):527–555
Chen YY, Han XZ, Gao F, Wei ZH, Zhang Y (2015) Workspace analysis of a 2-dof planar parallel mechanism. in 2015 International Conference on Electrical, Automation and Mechanical Engineering. 2015. Atlantis Press, pp 192–195
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Zare Jond, A., Pedrammehr, S., Pakzad, S. et al. Exploring the geometric design of a 3T1R parallel-based machine tool to achieve a targeted workspace. Int J Adv Manuf Technol 130, 1799–1822 (2024). https://doi.org/10.1007/s00170-023-12701-6
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DOI: https://doi.org/10.1007/s00170-023-12701-6