Forward and inverse kinematic analyses of a developed and evaluated bricklaying gantry-based parallel robot manipulator

Gantry robots are still used in wide application areas, especially pick and place applications. However, their kinematic modeling is associated with transforming positions and velocitiesin several base frames to each other. Generally, there are two types of kinematics as regards position, forward (direct) kinematics and inverse kinematics. Forward kinematics deals with determing the position (spot/location) and orientation of the end-effector while given the joint variables. Thus, the inverse kinematics is associated with finding the joint variables while given the position and orientation of the end-effector. Hence, this research presents a study in the field of forward and inverse kinematics modeling on the aforementioned robot through an attempt to provide a better solution enhancing kinematics simplicity. In this study, mathematical functions and equations were used, including the likes of algebra, trigonometry, geometry and a knowledge of motion mechanics was also applied. This study used a two-method kinematic analysis procedure for the forward kinematics. The results shows a range of values for the displacements and orientation of the links. Two experimental procedures gave a maximum difference of 0.03rad/s and 0.47rad using the first setup and 0.001rad/s and 0.016rad using the second setup, in the displacement and orientation of the links respectively. The inverse kinematics gave a displacent result of A(5mm), B(8.61mm), and C(7mm) and orientation of A' (71.53^0), B(90.11^0) and C' (125.61^0).

[1]      M. Javaid, A. Haleem, R. P. Singh, and R. Suman, “Substantial capabilities of robotics in enhancing industry 4.0 implementation,” Cognitive Robotics, vol. 1, pp. 58–75, Jan. 2021, doi: 10.1016/J.COGR.2021.06.001.

[2]      S. Luhar and I. Luhar, “Additive Manufacturing in the Geopolymer Construction Technology: A Review,” The Open Construction & Building Technology Journal, vol. 14, no. 1, pp. 150–161, Aug. 2020, doi: 10.2174/1874836802014010150.

[3]      O. Adepoju, “Robotic Construction Technology,” Springer Tracts in Civil Engineering, pp. 141–169, 2022, doi: 10.1007/978-3-030-85973-2_7/COVER.

[4]      T. Bruckmann, H. Mattern, A. Spengler, C. Reichert, A. Malkwitz, and M. König, “Automated Construction of Masonry Buildings using Cable-Driven Parallel Robots”.

[5]      F. P. Bos et al., “The realities of additively manufactured concrete structures in practice,” Cem Concr Res, vol. 156, p. 106746, Jun. 2022, doi: 10.1016/J.CEMCONRES.2022.106746.

[6]      C. Y. Lai, D. E. Villacis Chavez, and S. Ding, “Transformable parallel-serial manipulator for robotic machining,” International Journal of Advanced Manufacturing Technology, vol. 97, no. 5–8, pp. 2987–2996, Jul. 2018, doi: 10.1007/S00170-018-2170-Z/METRICS.

[7]      C. Yang, W. Ye, and Q. Li, “Review of the performance optimization of parallel manipulators,” Mech Mach Theory, vol. 170, p. 104725, Apr. 2022, doi: 10.1016/j.mechmachtheory.2022.104725.

[8]      R. Simoni, P. R. Rodriguez, P. Cieslak, L. Weihmann, and A. P. Carboni, “Design and kinematic analysis of a 6-DOF foldable/deployable Delta parallel manipulator with spherical wrist for an I-AUV,” OCEANS 2019 - Marseille, OCEANS Marseille 2019, vol. 2019-June, Jun. 2019, doi: 10.1109/OCEANSE.2019.8867496.

[9]      M. O. Afolayan, D. S. Yawas, C. O. Folayan, and S. Y. Aku, “Mechanical Description of a Hyper-Redundant Robot Joint Mechanism Used for a Design of a Biomimetic Robotic Fish,” Journal of Robotics, vol. 2012, pp. 1–16, 2012, doi: 10.1155/2012/826364.

[10]    Z. A. Karam and M. A. Neamah, “Design, Implementation, Interfacing and Control of Internet of Robot Things for Assisting Robot,” International Journal of Computing and Digital Systems, vol. 11, no. 1, pp. 387–399, 2022, doi: 10.12785/IJCDS/110132.

[11]    B. K. Panda, S. S. Panigrahi, G. Mishra, and V. Kumar, “Robotics for general material handling machines in food plants,” Transporting Operations of Food Materials within Food Factories: Unit Operations and Processing Equipment in the Food Industry, pp. 341–372, Jan. 2023, doi: 10.1016/B978-0-12-818585-8.00005-2.

[12]    J. Gunnar, “Dynamical Analysis and System Identification of the Gantry-Tau Parallel Manipulator,” 2005, Accessed: May 13, 2023. [Online]. Available: https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5322

[13]    “Robotic gantry with end effector for product lifting,” Nov. 2018.

[14]    C. Ye, N. Chen, L. Chen, and C. Jiang, “A variable-scale modular 3D printing robot of building interior wall,” Proceedings of 2018 IEEE International Conference on Mechatronics and Automation, ICMA 2018, pp. 1818–1822, Oct. 2018, doi: 10.1109/ICMA.2018.8484433.

[15]    A. N. Oyedeji, U. A. Umar, L. S. Kuburi, A. A. Edet, and Y. Mukhtar, “Development and performance evaluation of an oil palm harvesting robot for the elimination of ergonomic risks associated with oil palm harvesting,” Journal of Agricultural Engineering, vol. 53, no. 3, Sep. 2022, doi: 10.4081/JAE.2022.1388.

[16]    J. Meena, T. K. Sunil Kumar, and T. R. Amal, “Design and Implementation of a Multi-purpose End-effector Tool for Industrial Robot,” 2021 International Symposium of Asian Control Association on Intelligent Robotics and Industrial Automation, IRIA 2021, pp. 70–76, Sep. 2021, doi: 10.1109/IRIA53009.2021.9588746.

[17]    K. Mohamed, H. Elgamal, and A. Elsharkawy, “Dynamic analysis with optimum trajectory planning of multiple degree-of-freedom surgical micro-robot,” Alexandria Engineering Journal, vol. 57, no. 4, pp. 4103–4112, Dec. 2018, doi: 10.1016/J.AEJ.2018.10.011.

[18]    E. V. Gaponenko, D. I. Malyshev, and L. Behera, “Approximation of the parallel robot working area using the method of nonuniform covering,” J Phys Conf Ser, vol. 1333, no. 5, p. 052005, Oct. 2019, doi: 10.1088/1742-6596/1333/5/052005.

[19]    A. M. Hoover, E. Steltz, and R. S. Fearing, “RoACH: An autonomous 2.4g crawling hexapod robot,” 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, pp. 26–33, 2008, doi: 10.1109/IROS.2008.4651149.

[20]    R. V. Martinez et al., “Robotic Tentacles with Three-Dimensional Mobility Based on Flexible Elastomers,” Advanced Materials, vol. 25, no. 2, pp. 205–212, Jan. 2013, doi: 10.1002/ADMA.201203002.

[21]    Z. Zou et al., “Real-time Full-stack Traffic Scene Perception for Autonomous Driving with Roadside Cameras,” Proc IEEE Int Conf Robot Autom, pp. 890–896, 2022, doi: 10.1109/ICRA46639.2022.9812137.

[22]    H. A. Sonar, J.-L. Huang, and J. Paik, “Soft Touch using Soft Pneumatic Actuator–Skin as a Wearable Haptic Feedback Device,” Advanced Intelligent Systems, vol. 3, no. 3, p. 2000168, Mar. 2021, doi: 10.1002/AISY.202000168.

[23]    L. Ljung, “System Identification,” pp. 163–173, 1998, doi: 10.1007/978-1-4612-1768-8_11.

[24]    M. Hofer and R. D’Andrea, “Design, Modeling and Control of a Soft Robotic Arm,” IEEE International Conference on Intelligent Robots and Systems, pp. 1456–1463, Dec. 2018, doi: 10.1109/IROS.2018.8594221.

[25]    S. Gale, H. Rahmati, J. T. Gravdahl, and H. Martens, “Improvement of a Robotic Manipulator Model Based on Multivariate Residual Modeling,” Front Robot AI, vol. 4, p. 28, Jul. 2017, doi: 10.3389/FROBT.2017.00028/BIBTEX.

[26]    B. Alkali “Design and Development of Parallel and Serial Robot Manipulators for Bottle Capping Process” 2014. A Ph.D. Thesis, Department of Mechanical Engineering, Ahmadu Bello             University, Zaria.

[27]    M. W. Spong, Vidyasagar and M. Wiley. Robot Dynamics and Control. Prentice-Hall Int., London, 1989.

[28]    L. Sciavicco and B. Siciliano. Modeling and Control of Robotic Manipulators. The Math Works Inc., Sherborn, MA, USA, Springer, 2000.

[29]    A. C. Mark. Obstacle avoidance in Multi-Robotic System. Robots and Autonomous. Canada: 3rd Edition, John Wiley and Sons Inc, 1998.

[30]    G. D. Nicholas & A. Edward (2009). Kinematic Modeling of six Degree of Freedom Tri-stage Micro-Positioned. Proceedings of the American Society of Precision Engineering, 16th Annual Meeting, (pp. 200-203).

[31]    Z. G. Woldu. Design and Control of a Five bar Linkage Parallel Manipulator with Flexible Arms. Milan, Spain: An M.Sc. Thesis, Polytechnic Di Milano, Spain, 2010.

[32]    M. Donya, Y. Aghil, B. Shanaz, & M. Hessam (2008). Design Fabrication and Hydrodynamic          Analysis of a Biomimetic Robot Fish (Vol. 4). International Journal of Mechanics.

[33]    H. I. Musa, U. A. Umar, M. O. Afolayan, and O. N. Ayodeji (2023). Development and Performance Evaluation of a Bricklaying gantry-Based Parallel Robot Manipulator. Journal of Engineering, Science and Computing (JESC). The Islamic University Journal of Applied Sciences Volume V, Issue I, jesc.iu.edu.sa/Main/Article/112, pp. 71 – 90, July 2023.

[34]    A. I. I. Mahir and M. K. Mohammed (2015). Gantry Robot Kinematic Analysis User Interface Based on Visual Basic and MATLAB.International Journal of Science and Research (IJSR). ISSN (online): 2319-7064. Mechanical Engineering Department, Tianjin Univerity of Technology and Education, Tianjin 300222, China.

[35]    A. Rosyid, C. Steanini and B. El-Khasawneh (2022). A Reconfigurable Parallel Robot for On-Structure Machining of Large Structures. Robotics 2022, 11, 110. https:/ /doi.org/10.3390/robotics11050110. https:/ /www.mdpi.com/journal/robotics.

[36]    V. Swaminath and D. Chablat (2023). Mapping the Tilt and Torsion Angles for a 3-SPS-U Parallel Mechanism. Robotics 2023, 12, 50. https:/ /doi.org/10.3390/robotics12020050. https:/ /www.mdpi.com/journal/robotics.