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Unified Kinematics of Prismatically Actuated Parallel Delta Robots

Published online by Cambridge University Press:  15 February 2019

Eray A. Baran ,
Ozhan Ozen ,
Dogacan Bilgili  and
Asif Sabanovic
Eray A. Baran*
Affiliation:
Mechatronics Engineering, Istanbul Bilgi University, Istanbul, Turkey
Ozhan Ozen
Affiliation:
Gerontechnology & Rehabilitation, ARTORG Center for Biomedical Engineering Research, University of Bern, Bern, Switzerland
Dogacan Bilgili
Affiliation:
Mechatronics Engineering, Sabanci University, Istanbul, Turkey
Asif Sabanovic
Affiliation:
Mechatronics Engineering, Sabanci University, Istanbul, Turkey
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper presents a unified formulation for the kinematics, singularity and workspace analyses of parallel delta robots with prismatic actuation. Unlike the existing studies, the derivations presented in this paper are made by assuming variable angles and variable link lengths. Thus, the presented scheme can be used for all of the possible linear delta robot configurations including the ones with asymmetric kinematic chains. Referring to a geometry-based derivation, the paper first formulates the position and the velocity kinematics of linear delta robots with non-iterative exact solutions. Then, all of the singular configurations are identified assuming a parametric content for the Jacobian matrix derived in the velocity kinematics section. Furthermore, a benchmark study is carried out to determine the linear delta robot configuration with the maximum cubic workspace among symmetric and semi-symmetric kinematic chains. In order to show the validity of the proposed approach, two sets of experiments are made, respectively, on the horizontal and the Keops type of linear delta robots. The experiment results for the confirmation of the presented kinematic analysis and the simulation results for the determination of the maximum cubic workspace illustrate the efficacy and the flexible applicability of the proposed framework.

Keywords

Linear Delta RobotUnified KinematicsAsymmetric Delta RobotMaximum Symmetric WorkspaceGeneralized Singularities
Type
Articles
Information
Robotica , Volume 37 , Issue 9 , September 2019 , pp. 1513 - 1532
Copyright
© Cambridge University Press 2019 

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References

Pozhbelko, V., Kuts, E., “Structural synthesis and analysis of multiple-jointed mechanical systems and industrial application for robot manipulator,” Proc. Eng. 206 1774–1779 (2017).CrossRefGoogle Scholar
Zhakypov, Z., Uzunovic, T., Nergiz, A. O., Baran, E. A., Golubovic, E., Sabanovic, A., “Desktop Microfactory for High Precision Assembly and Machining,” Industrial Electronics (ISIE), 2014 IEEE 23rd International Symposium on IEEE, Istanbul, Turkey (2014) pp. 1192–1197.CrossRefGoogle Scholar
Dogar, M., Knepper, R. A., Spielberg, A., Choi, C., Christensen, H. I., Rus, D., “Towards Coordinated Precision Assembly with Robot Teams,” Experimental Robotics, vol. 109 (Springer, Cham, 2016) pp. 655–669.CrossRefGoogle Scholar
Pourkand, A., Zamani, N., Grow, D., “Mechanical model of orthopaedic drilling for augmented-haptics-based training,” Comput. Biol. Med. 89, 256–263 (2017).CrossRefGoogle ScholarPubMed
Feng, L., Di, P., Arai, F., “High-precision motion of magnetic microrobot with ultrasonic levitation for 3-d rotation of single oocyte,” Int. J. Robot. Res. 35 (12), 1445–1458 (2016).CrossRefGoogle Scholar
Li, Y., Ma, Y., Liu, S., Luo, Z., Mei, J., Huang, T., Chetwynd, D., “Integrated design of a 4-dof high-speed pick-and-place parallel robot,” CIRP Ann. Manuf. Technol. 63 (1), 185–188 (2014).CrossRefGoogle Scholar
Cammarata, A., “Optimized design of a large-workspace 2-dof parallel robot for solar tracking systems,” Mech. Mach. Theor. 83 175–186 (2015).CrossRefGoogle Scholar
Hosseini, M. A., Daniali, H., “Cartesian workspace optimization of tricept parallel manipulator with machining application,” Robotica 33 (9), 1948–1957 (2015).CrossRefGoogle Scholar
Kelaiaia, R., Zaatri, A., Chikh, L., et al., “Some investigations into the optimal dimensional synthesis of parallel robots,” Int. J. Adv. Manuf. Technol. 83 (9–12), 1525–1538 (2016).CrossRefGoogle Scholar
Wu, J., Chen, X., Wang, L., “Design and dynamics of a novel solar tracker with parallel mechanism,” IEEE/ASME Trans. Mechatron. 21 (1), 88–97 (2016).Google Scholar
Zhao, Y., Qiu, K., Wang, S., Zhang, Z., “Inverse kinematics and rigid-body dynamics for a three rotational degrees of freedom parallel manipulator,” Robot. Comput.-Integr. Manuf. 31 40–50 (2015).CrossRefGoogle Scholar
Seriani, S., Seriani, M., Gallina, P., “Workspace optimization for a planar cable suspended direct-driven robot,” Robot. Comput.-Integr. Manuf. 34 1–7 (2015).CrossRefGoogle Scholar
Shi, H., Duan, X., Su, H.-J., “Optimization of the Workspace of a Mems Hexapod Nanopositioner using an Adaptive Genetic Algorithm,” Robotics and Automation (ICRA), 2014 IEEE International Conference on IEEE, Hong Kong, China (2014) pp. 4043–4048.CrossRefGoogle Scholar
Ganesh, S. S., Rao, A. K., “Optimal workspace volume of two configurations of 3-dof pkm,” Indian J. Sci. Technol. 10 (46).Google Scholar
Kosinska, A., Galicki, M., Kedzior, K., “Designing and optimization of parameters of delta-4 parallel manipulator for a given workspace,” J. Robot. Syst. 20 (9), 539–548 (2003).CrossRefGoogle Scholar
Jamwal, P. K., Hussain, S., Xie, S. Q., “Three-stage design analysis and multicriteria optimization of a parallel ankle rehabilitation robot using genetic algorithm,” IEEE Trans. Automation Sci. Eng. 12 (4), 1433–1446 (2015).CrossRefGoogle Scholar
Shin, H., Moon, J.-H., “Design of a double triangular parallel mechanism for precision positioning and large force generation,” IEEE/ASME Trans. Mechatron. 19 (3), 862–871 (2014).CrossRefGoogle Scholar
Kelaiaia, R., Company, O., Zaatri, A., “Multiobjective optimization of a linear delta parallel robot,” Mech. Mach. Theor. 50 159–178 (2012).CrossRefGoogle Scholar
Zhang, D., Gao, Z., “Performance analysis and optimization of a five-degrees-of freedom compliant hybrid parallel micromanipulator,” Robot. Comput.-Integr. Manuf. 34 20–29 (2015).CrossRefGoogle Scholar
Yan, S., Ong, S., Nee, A., “Stiffness analysis of parallelogram-type parallelmanipulators using a strain energy method,” Robot. Comput.-Integr. Manuf. 37 13–22 (2016).CrossRefGoogle Scholar
Miller, K., “Maximization of workspace volume of 3-dof spatial parallel manipulators,” J. Mech. Design 124(2), 347–350 (2002).CrossRefGoogle Scholar
Xie, F., Liu, X.-J., Chen, X., Wang, J., “Optimum Kinematic Design of a 3-dof Parallel Kinematic Manipulator with Actuation Redundancy,” Intelligent Robotics and Applications. ICIRA 2011, Lecture Notes in Computer Science, vol. 7101 (Springer, Berlin-Heidelberg, 2011) pp. 250–259.CrossRefGoogle Scholar
Mousavi, M. A., Masouleh, M. T., Karimi, A., “On the maximal singularity-free ellipse of planar 3-rpr parallel mechanisms via convex optimization,” Robot. Comput.-Integr. Manuf. 30 (2), 218–227 (2014).CrossRefGoogle Scholar
Borras, J., Thomas, F., Torras, C., “New geometric approaches to the analysis and design of stewartgough platforms,” IEEE/ASME Trans. Mechatron. 19 (2), 445–455 (2014).CrossRefGoogle Scholar
Lopez, M., Castillo, E., Garca, G., Bashir, A., “Delta robot: inverse, direct, and intermediate- jacobians, Proceedings of the Institution of Mechanical Engineers, Part C:.” J. Mech. Eng. Sci. 220 (1), 103–109 (2006).CrossRefGoogle Scholar
Hsu, K., Karkoub, M., Tsai, M.-C., Her, M., “Modelling and index analysis of a delta-type mechanism,” Proc. Inst. Mech. Eng. Part K: J. Multi-body Dyn. 218 (3), 121–132 (2004).Google Scholar
Plitea, N., Szilaghyi, A., Pisla, D., “Kinematic analysis of a new 5-dof modular parallel robot for brachytherapy,” Robot. Comput.-Integr. Manuf. 31 70–80 (2015).CrossRefGoogle Scholar
Saafi, H., Laribi, M. A., Zeghloul, S., “Forward kinematic model improvement of a spherical parallel manipulator using an extra sensor,” Mech. Mach. Theor. 91 102–119 (2015).CrossRefGoogle Scholar
Bidokhti, H. S., Enferadi, J., “Direct Kinematics Solution of 3-rrr Robot by using Two Different Artificial Neural Networks,” Robotics and Mechatronics (ICROM), 2015 3rd RSI International Conference on IEEE, Tehran, Iran (2015) pp. 606–611.CrossRefGoogle Scholar
Yang, X., Wu, H., Li, Y., Chen, B., “A dual quaternion solution to the forward kinematics of a class of six-dof parallel robots with full or reductant actuation,” Mech. Mach. Theor. 107 27–36 (2017).CrossRefGoogle Scholar
Jin, Y., Bi, Z., Liu, H., Higgins, C., Price, M., Chen, W., Huang, T., “Kinematic analysis and dimensional synthesis of exechon parallel kinematic machine for large volume machining,” J. Mech. Robot. 7 (4), 041004 (2015).CrossRefGoogle Scholar
Xie, F., Liu, X.-J., You, Z., Wang, J., “Type synthesis of 2t1r-type parallel kinematic mechanisms and the application in manufacturing,” Robot. Comput.-Integr. Manuf. 30 (1), 1–10 (2014).CrossRefGoogle Scholar
Correa, J. E., Toombs, J., Toombs, N., Ferreira, P. M., “Laminated micro-machine: Design and fabrication of a flexure-based delta robot,” J. Manuf. Process. 24 370–375 (2016).CrossRefGoogle Scholar
Martini, A., Troncossi, M., Carricato, M., Rivola, A., “Static balancing of a parallel kinematics machine with linear-delta architecture: Theory, design and numerical investigation,” Mech. Mach. Theor. 90 128–141 (2015).CrossRefGoogle Scholar
Anzalone, G. C., Wijnen, B., Pearce, J.M., “Multi-material additive and subtractive prosumer digital fabrication with a free and open-source convertible delta reprap 3-d printer,” Rapid Prototyping J. 21 (5), 506–519 (2015).CrossRefGoogle Scholar
Baran, E. A., Kurt, T. E., Sabanovic, A., “Lightweight Design and Encoderless Control of a Miniature Direct Drive Linear Delta Robot,” Electrical and Electronics Engineering (ELECO), 2013 8th International Conference on IEEE, Bursa, Turkey (2013) pp. 502–506.CrossRefGoogle Scholar
Azulay, H., Mahmoodi, M., Zhao, R., Mills, J. K., Benhabib, B., “Comparative analysis of a new 3 pprs parallel kinematic mechanism,” Robot. Comput.-Integr. Manuf. 30 (4), 369–378 (2014).CrossRefGoogle Scholar
Yuan, W.-H., Tsai, M.-S., “A novel approach for forward dynamic analysis of 3-prs parallel manipulator with consideration of friction effect,” Robot. Comput.-Integr. Manuf. 30 (3), 315–325 (2014).CrossRefGoogle Scholar
Zeng, Q., Ehmann, K. F., Cao, J., “Tri-pyramid robot: Design and kinematic analysis of a 3-dof translational parallel manipulator,” Robot. Comput.-Integr. Manuf. 30 (6), 648–657 (2014).CrossRefGoogle Scholar
Pile, J., Simaan, N., “Modeling, design, and evaluation of a parallel robot for cochlear implant surgery,” IEEE/ASME Trans. Mechatron. 19 (6), 1746–1755 (2014).CrossRefGoogle Scholar
Li, Y., Xu, Q., “Design and development of a medical parallel robot for cardiopulmonary resuscitation,” IEEE/ASME Trans. Mechatron. 12 (3), 265–273 (2007).CrossRefGoogle Scholar
Li, Y., Xu, Q., “Kinematic analysis of a 3-prs parallel manipulator,” Robot. Comput.-Integr. Manuf. 23 (4), 395–408 (2007).CrossRefGoogle Scholar