Hostname: page-component-76c49bb84f-ndtt8 Total loading time: 0 Render date: 2025-07-14T02:16:10.986Z Has data issue: false hasContentIssue false
  • English
  • Français

Type synthesis of closed-loop robots for machining and manufacturing of complex quadric surfaces

Published online by Cambridge University Press:  18 June 2025

Jiahao Song ,
Shuofei Yang Open the ORCID record for Shuofei Yang [Opens in a new window] ,
Yunwen Zhang ,
Zhengjun Fang  and
Tianrui Zou
Jiahao Song
Affiliation:
College of Engineering, China Agricultural University, Beijing 100083, China
Shuofei Yang*
Affiliation:
College of Engineering, China Agricultural University, Beijing 100083, China
Yunwen Zhang
Affiliation:
College of Engineering, China Agricultural University, Beijing 100083, China
Zhengjun Fang
Affiliation:
College of Engineering, China Agricultural University, Beijing 100083, China
Tianrui Zou
Affiliation:
College of Engineering, China Agricultural University, Beijing 100083, China
*
Corresponding author: Shuofei Yang; Email: shuofei.yang@cau.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a general approach to synthesizing closed-loop robots for machining and manufacturing of complex quadric surfaces, such as toruses, helicoids, and helical tubes. The proposed approach begins by employing finite screw theory to describe the motion sets generated by prismatic, rotational, and helical joints. Subsequently, generatrices and generating lines are put forward and combined for type synthesis of serial kinematic limbs capable of generating single-DoF translations along spatial curves and two-DoF translations on complex quadric surfaces. Following this manner, the two-DoF translational motion patterns on these complex quadric surfaces are algebraically defined and expressed as finite screw sets. Type synthesis of close-loop robots having the newly defined motion patterns can thus be carried out based upon analytical computations of finite screws. As application of the presented approach, closed-loop robots for machining toruses are synthesized, resulting in four-DoF and five-DoF standard and derived limbs together with their corresponding assembly conditions. Additionally, brief descriptions of robots for machining helicoids and helical tubes are provided, along with a comprehensive list of all the feasible limbs for these kinds of robots. The robots synthesized in this paper have promised applications in machining and manufacturing of spatial curves and surfaces, enabling precise control of machining trajectories ensured by mechanism structures and achieving high precision with low cost.

Keywords

finite screwtype synthesismechanism analysisrobot designcomplex quadric surface

Information

Type
Research Article
Information
Robotica , First View , pp. 1 - 29
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Song, Y. M., Xian, W., Huo, X. M. and Qi, Y., “Type synthesis of parallel mechanism with 3T/3R motion patterns,” Mech. Mach. Theory 186, 105349 (2023).10.1016/j.mechmachtheory.2023.105349CrossRefGoogle Scholar
Liu, K., Kong, X. W. and Yu, J. J., “Algebraic synthesis and input-output analysis of 1-DoF multi-loop linkages with a constant transmission ratio between two adjacent parallel, intersecting or skew axes,” Mech. Mach. Theory 190, 105467 (2023).10.1016/j.mechmachtheory.2023.105467CrossRefGoogle Scholar
Kong, X. W. and Gosselin, C. M., Type Synthesis of Parallel Mechanisms (Springer, Berlin, 2007).Google Scholar
Wang, R., Xiong, X. Y., Zhang, J. Z. and Yuan, R. L., “Configuration design of movable heavy-duty reconfigurable posture adjustment platform with dual motion modes,” Robotica 42(7), 2281–2308 (2024).10.1017/S026357472400064XCrossRefGoogle Scholar
Du, Z. Q., Li, J., Meng, Q. M., Ye, P. D. and Shen, H. P., “Symbolic position analysis for three 6-DOF parallel mechanisms and new insight,” Robotica 42(5), 1628–1648 (2024).10.1017/S0263574724000432CrossRefGoogle Scholar
Lin, R. F., Guo, W. Z. and Cheng, S. S., “Type synthesis of novel 1R, 2R, 1R1T, and 2R1T hybrid RCM mechanisms based on topological arrangement and modular design method,” Mech. Mach. Theory 200, 105692 (2024).10.1016/j.mechmachtheory.2024.105692CrossRefGoogle Scholar
Sun, T., Lian, B. B., Yang, S. F. and Song, Y. M., “Kinematic calibration of serial and parallel robots based on finite and instantaneous screw theory,” IEEE Trans. Robot. 36(3), 816–834 (2020).10.1109/TRO.2020.2969028CrossRefGoogle Scholar
Wang, J. Y., Kong, X. W. and Yu, J. J., “Design of deployable mechanisms based on Wren parallel mechanism units,” ASME J. Mech. Des. 144(6), 063302 (2022).10.1115/1.4053282CrossRefGoogle Scholar
Meng, J., Liu, G. F. and Li, Z. X., “A geometric theory for analysis and synthesis of sub-6 DoF parallel manipulators,” IEEE Trans. Robot. 23(4), 625–649 (2007).10.1109/TRO.2007.898995CrossRefGoogle Scholar
Huo, X. M., Song, Z. H. and Sun, T., “A machine learning-based approach for automatic motion/constraint and mobility analysis of parallel robots,” Robotica 42(7), 2403–2429 (2024).10.1017/S0263574724000808CrossRefGoogle Scholar
Zhou, J. Z., Kulkarni, P., Zhao, X. C. and Agrawal, S. K., “Design of a traction neck brace with two degrees-of-freedom via a novel architecture of a spatial parallel mechanism,” Robotica 42(12), 4136–4149 (2024).10.1017/S0263574724000882CrossRefGoogle Scholar
Zhang, K. T., Fang, Y. F., Fang, H. R. and Dai, J. S., “Geometry and constraint analysis of the three-spherical kinematic chain based parallel mechanism,” ASME J. Mech. Robot. 2(3), 031014 (2010).10.1115/1.4001783CrossRefGoogle Scholar
Dai, J. S. and Wang, D. L., “Theoretical foundation of metamorphic mechanism and its synthesis,” Chin. J. Mech. Eng. 43(8), 32–42 (2007).Google Scholar
Yao, W. and Dai, J. S., “Dexterous manipulation of origami cartons with robotic fingers based on the interactive configuration space,” ASME J. Mech. Des. 130(2), 022303 (2008).10.1115/1.2813783CrossRefGoogle Scholar
Dai, J. S. and Jones, J. R., “A linear algebraic procedure in obtaining reciprocal screw systems,” J. Robot. Syst. 20(7), 401–412 (2003).10.1002/rob.10094CrossRefGoogle Scholar
Shen, H. P., Yang, T. L., Li, J., Zhang, D., Deng, J. M. and Liu, A. X., “Evaluation of topological properties of parallel manipulators based on the topological characteristic indexes,” Robotica 38(8), 1381–1399 (2020).10.1017/S0263574719001528CrossRefGoogle Scholar
Feng, H. J., Chen, Y., Dai, J. S. and Gogu, G., “Kinematic study of the general plane-symmetric Bricard linkage and its bifurcation variations,” Mech. Mach. Theory 116, 89–104 (2017).10.1016/j.mechmachtheory.2017.05.019CrossRefGoogle Scholar
Qin, Y., Dai, J. S. and Gogu, G., “Multi-furcation in a derivative queer-square mechanism,” Mech. Mach. Theory 81, 36–53 (2014).10.1016/j.mechmachtheory.2014.06.006CrossRefGoogle Scholar
Zhao, T. S., Dai, J. S. and Huang, Z., “Geometric synthesis of spatial parallel manipulators with fewer than six degrees of freedom,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 216(12), 1175–1185 (2002).10.1243/095440602321029418CrossRefGoogle Scholar
Liu, H. H. and Dai, J. S., “Carton manipulation analysis using configuration transformation,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 216(5), 543–555 (2002).10.1243/0954406021525331CrossRefGoogle Scholar
Gan, D. M., Liao, Q. Z., Dai, J. S. and Wei, S. M., “Forward displacement analysis of the general 6-6 Stewart mechanism using Gröbner bases,” Mech. Mach. Theory 44(9), 1640–1647 (2009).10.1016/j.mechmachtheory.2009.01.008CrossRefGoogle Scholar
Leal, E. R. and Dai, J. S., “From Origami to a New Class of Centralized 3-DOF Parallel Mechanisms,” Proceedings of the ASME. 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (2007) pp. 1183–1193.Google Scholar
Salerno, M., Zhang, K., Menciassi, A. and Dai, J. S., “A Novel 4-DOFs Origami Enabled, SMA Actuated, Robotic End-Effector for Minimally Invasive Surgery,” Proceedings of 2014 IEEE International Conference on Robotics and Automation (2014) pp. 2844–2849.Google Scholar
Xing, Y. S., Wei, J., Zhu, Y. H., Yang, M. N., Lv, W. L., Guo, S. J. and Dai, J. S., “Lie algebra-based high-order constraint analysis of a novel multi-loop metamorphic mechanism derived from four-bar linkage for lower limb exoskeletons,” Mech. Mach. Theory 209, 105994 (2025).10.1016/j.mechmachtheory.2025.105994CrossRefGoogle Scholar
Gao, C. Q., Kang, X., Lei, H., Xu, P. and Li, B., “Design and analysis of a novel large-span two-fold deployable mechanism,” Mech. Mach. Theory 186, 105352 (2023).10.1016/j.mechmachtheory.2023.105352CrossRefGoogle Scholar
Saglia, J. A., Tsagarakis, N. G., Dai, J. S. and Caldwell, D. G., “Control Strategies for Ankle Rehabilitation Using a High Performance Ankle Exerciser,” Proceedings of 2010 IEEE International Conference on Robotics and Automation (2010) pp. 2221–2227.Google Scholar
Wang, R. Q., Song, Y. Q. and Dai, J. S., “Reconfigurability of the origami-inspired integrated 8R kinematotropic metamorphic mechanism and its evolved 6R and 4R mechanisms,” Mech. Mach. Theory 161, 104245 (2021).10.1016/j.mechmachtheory.2021.104245CrossRefGoogle Scholar
Dai, J. S. and Jones, J. R., “Configuration Transformations in Metamorphic Mechanisms of Foldable/Erectable Kinds,” Proceedings of 10th World Congress on the Theory of Machine and Mechanisms (1999).10.1115/DETC98/MECH-5902CrossRefGoogle Scholar
Aimedee, F., Gogu, G., Dai, J. S., Bouzgarrou, C. and Bouton, N., “Systematization of morphing in reconfigurable mechanisms,” Mech. Mach. Theory 96, 215–224 (2016).10.1016/j.mechmachtheory.2015.07.009CrossRefGoogle Scholar
Li, D. L., Dai, J. S., Zhang, Q. X. and Jin, G. G., “Structure synthesis of metamorphic mechanisms based on the configuration transformations,” Chin. J. Mech. Eng. 38(7), 12–16 (2002).10.3901/JME.2002.09.012CrossRefGoogle Scholar
Gregorio, R. D., “A geometric and analytic technique for the determination of the instantaneous screw axes in single-DOF spatial mechanisms,” Mech. Mach. Theory 184, 105297 (2023).10.1016/j.mechmachtheory.2023.105297CrossRefGoogle Scholar
Castillo, C., López-Martínez, J., García-Vallejo, D. and Blanco-Claraco, J. L., “Synthesis of 1-DOF mechanisms for exact regular polygonal path generation based on non-circular gear transmissions,” Mech. Mach. Theory 198, 105657 (2024).10.1016/j.mechmachtheory.2024.105657CrossRefGoogle Scholar
Gregorio, R. D., “Singularity analysis of spatial single-DOF mechanisms based on the locations of the instantaneous screw axes,” Mech. Mach. Theory 189, 105438 (2023).10.1016/j.mechmachtheory.2023.105438CrossRefGoogle Scholar
Zhang, X., Kang, X. and Li, B., “Origami-inspired design of a single-degree-of-freedom reconfigurable wing with lockable mechanisms,” ASME J. Mech. Robot. 16(7), 071008 (2024).10.1115/1.4063456CrossRefGoogle Scholar
Guo, F., Sun, T., Wang, P. F., Liu, S. B. and Song, Y. M., “Synchronous design method of stiffness and topology for parallel flexible mechanisms with various joints,” Mech. Mach. Theory 180, 105137 (2023).10.1016/j.mechmachtheory.2022.105137CrossRefGoogle Scholar
Yao, L. G., Gu, B., Haung, S. J., Wei, G. W. and Dai, J. S., “Mathematical modeling and simulation of the external and internal double circular-arc spiral bevel gears for the nutation drive,” ASME J. Mech. Des. 132(2), 021008 (2010).10.1115/1.4001003CrossRefGoogle Scholar
Chen, X. C., Liu, J. X., Dong, J. A., Zhang, Z. H., Guo, Y., Xiao, B. and Chen, Z. M., “Analysis and optimization design of motion characteristics for a 3-PUU/R parallel ankle joint rehabilitation mechanism,” Robotica 42(10), 3450–3479 (2024).10.1017/S0263574724001462CrossRefGoogle Scholar
Ding, X. L., Yang, Y. and Dai, J. S., “Topology and kinematic analysis of color-changing ball,” Mech. Mach. Theory 46(1), 67–81 (2011).10.1016/j.mechmachtheory.2010.08.010CrossRefGoogle Scholar
Kang, X., Lin, Q., Feng, H. J. and Li, B., “Double-level reconfigurable variation of Bennett-induced 8R mechanism and its evolved metamorphic 7R mechanism family,” Mech. Mach. Theory 205, 105879 (2025).10.1016/j.mechmachtheory.2024.105879CrossRefGoogle Scholar
Kong, X. W., “Kinematic analysis of a 6R single-loop overconstrained spatial mechanism for circular translation,” Mech. Mach. Theory 93, 163–174 (2015).10.1016/j.mechmachtheory.2015.07.005CrossRefGoogle Scholar
Wang, K., Li, J., Shen, H. P., You, J. J. and Yang, T. L., “Inverse dynamics of a 3-DOF parallel mechanism based on analytical forward kinematic,” Chin. J. Mech. Eng. 35(1), 119 (2022).10.1186/s10033-022-00781-6CrossRefGoogle Scholar
Li, J., Zhu, Z. Q., Shen, H. P. and Chablat, D., “Topological design and kinematic analysis of novel three-translation parallel mechanism,” Chin. J. Mech. Eng. 53(9), 425–433,442 (2022).Google Scholar
López-Custodio, P. C., Müller, A., Rico, J. M. and Dai, J. S., “A synthesis method for 1-DOF mechanisms with a cusp in the configuration space,” Mech. Mach. Theory 132, 154–175 (2019).10.1016/j.mechmachtheory.2018.09.008CrossRefGoogle Scholar
López-Custodio, P. C. and Dai, J. S., “Design of a variable-mobility linkage using the Bohemian dome,” ASME J. Mech. Des. 141(9), 092303 (2019).10.1115/1.4042845CrossRefGoogle Scholar
López-Custodio, P. C., Müller, A., Kang, X. and Dai, J. S., “Tangential intersection of branches of motion,” Mech. Mach. Theory 147, 103730 (2020).10.1016/j.mechmachtheory.2019.103730CrossRefGoogle Scholar
Yang, S. F. and Li, Y. M., “Motion generators of quadric surfaces,” Mech. Mach. Theory 140, 446–456 (2019).10.1016/j.mechmachtheory.2019.06.006CrossRefGoogle Scholar
Selig, J. M. and Paola, V. D., “Some five dimensional persistent submanifolds of the study quadric,” Mech. Mach. Theory 196, 105632 (2024).10.1016/j.mechmachtheory.2024.105632CrossRefGoogle Scholar
Selig, J. M. and Di Paola, V., “Mechanisms generating line trajectories,” Mech. Mach. Theory 191, 105494 (2024).10.1016/j.mechmachtheory.2023.105494CrossRefGoogle Scholar
Sorgonà, O., Belfiore, N. P., Giannini, O. and Verotti, M., “Application of the ellipse of elasticity theory to the functional analysis of planar compliant mechanisms,” Mech. Mach. Theory 184, 105308 (2023).10.1016/j.mechmachtheory.2023.105308CrossRefGoogle Scholar
Stretti, D., Fanghella, P., Berselli, G. and Bruzzone, L., “Analytical expression of motion profiles with elliptic jerk,” Robotica 41(7), 1976–1990 (2023).10.1017/S0263574723000255CrossRefGoogle Scholar
He, Z., Fang, H. L., Bao, Y. F., Yang, F. F. and Zhang, J., “Smooth toolpath interpolation for a 5-axis hybrid machine tool,” Robotica 40(12), 4431–4454 (2022).10.1017/S026357472200100XCrossRefGoogle Scholar
Bulut, V., “The optimal path of robot end effector based on hierarchical clustering and Bézier curve with three shape parameters,” Robotica 40(9), 3266–3289 (2022).10.1017/S0263574722000182CrossRefGoogle Scholar
Wu, H. R. and Tang, Q., “Robotic spray painting path planning for complex surface: Boundary fitting approach,” Robotica 41(6), 1794–1811 (2023).10.1017/S0263574723000152CrossRefGoogle Scholar
De Benedictis, C. and Ferraresi, C., “Precise positioning in a robotized laser-cutting machine allowed by a three-V-shaped-groove kinematic coupling: A feasibility study,” Robotica 41(9), 2703–2712 (2023).10.1017/S0263574723000619CrossRefGoogle Scholar
Fomin, A., Antonov, A. and Glazunov, V., “Type synthesis, analysis, and prototyping of 4R1H mechanisms,” Robotica 42(12), 4200–4222 (2024).10.1017/S0263574724002005CrossRefGoogle Scholar
Spyrakos-Papastavridis, E. and Dai, J. S., “Minimally model-based trajectory tracking and variable impedance control of flexible-joint robots,” IEEE Trans. Ind. Electron. 68(7), 6031–6041 (2021).10.1109/TIE.2020.2994886CrossRefGoogle Scholar
Jiang, B. S., Huang, G. Y., Zhu, S. Q., Fang, H. R., Tian, X. Y., Xie, A. H., Zhang, L., Zhao, P. Y., Gu, J. J. and Kong, L. Y., “Type synthesis and trajectory planning of 5-DOF redundantly actuated parallel robots with large output rotational angles for large workpieces,” Robotica 42(1), 242–264 (2024).10.1017/S0263574723001467CrossRefGoogle Scholar
Cui, L. and Dai, J. S., “A darboux-frame-based formulation of spin-rolling motion of rigid objects with point contact,” IEEE Trans. Robot. 26(2), 383–388 (2010).10.1109/TRO.2010.2040201CrossRefGoogle Scholar
Dai, J. S., Holland, N. and Kerr, D. R., “Finite twist mapping and its application to planar serial manipulators with revolute joints,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 209(4), 263–271 (1995).10.1243/PIME_PROC_1995_209_153_02CrossRefGoogle Scholar