Implementation of Gibbs-Appell method in dynamic analysis of a novel serial-parallel hybrid robot PP-(3RSS-PS)

Document Type : Original Article

Authors

S. Nader Nabavi ¹

javad Enferadi ²

¹ Department of Mechanical Engineering, University of Bojnord, Bojnord, Iran

² Mechanical Engineering Department, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

10.22067/jacsm.2023.83429.1193

Abstract

This paper introduces a conceptual design of a new hybrid robot, named PP-(3RSS-PS), specifically intended for motion simulation. The presented robot offers several notable advantages, including a simple and compact structural design that optimizes its large workspace. The modular X and Y axes are engineered to facilitate extended acceleration phases, while the power transmission system's hollow shaft design enables unlimited yaw motion. In certain applications like aerial maneuvers, dogfights, and helicopter operations, the ability to achieve unlimited yaw motion holds significant importance for delivering precise and immersive simulations. To establish the relationship between joint space and Cartesian space parameters, comprehensive kinematic, Jacobian, and dynamic analyses of the robot are performed. These preliminary relations lay the foundation for subsequent investigations, such as optimization studies. The Gibbs-Appell formulation is employed to derive the dynamic equations, leveraging its computational efficiency over the Lagrange method. To validate the analytical model, a simulation using MSC-ADAMS software is conducted. This simulation incorporates six predefined trajectories adopted from an industrial motion simulator. Successful validation of the results would not only confirm the accuracy of the analytical model but also motivate further research in search of an exceptional alternative motion simulator.

Keywords

Hybrid robot

Robot synthesis

Dynamic

Gibbs-Appell

Motion simulator

Subjects

• Robotics

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References

[1]    M. Shahinpoor, "Kinematics of a parallel‐serial (Hybrid) manipulator," Journal of Robotic Systems, vol. 9, no. 1, pp. 17-36, )1992(.

[2]    R. Ricard and C. Gosselin, "On the development of hybrid planar manipulators," IEEE in Proceedings of 36th Midwest Symposium on Circuits and Systems, pp. 398-401, (1993).

[3]    S. Lee and S. Kim, "Efficient inverse kinematics for serial connections of serial and parallel manipulators," IEEE in Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'93), vol. 3, pp. 1635-1641, (1993).

[4]    A. Campos, C. Budde, and J. Hesselbach, "A type synthesis method for hybrid robot structures," Mechanism and Machine Theory, vol. 43, no. 8, pp. 984-995, )2008(.

[5]    K. Etemadi-Zanganeh and J. Angeles, "Instantaneous kinematics of general hybrid parallel manipulators," 1995.

[6]    S. Kim and W. Kim, "On the structure of the macro-micro neurosurgical robots in stereotactic surgery," Hanyang Medical Reviews, vol. 36, no. 4, pp. 254-261, )2016(.

[7]    D. Zhang, J. Chen, W. Li, D. B. Salinas, and G.-Z. Yang, "A microsurgical robot research platform for robot-assisted microsurgery research and training," International Journal of Computer Assisted Radiology and Surgery, vol. 15, no. 1, pp. 15-25, )2020(.

[8]    G. Tosolin, J. Cartró, and V. Sharma, "Development of model predictive motion planning and control for autonomous vehicles," Springer in 10th International Munich Chassis Symposium 2019, pp. 323-340, (2020).

[9]    Y. Feng, J. Fan, B. Tao, S. Wang, J. Mo, Y. Wu, Q. Liang, and X. Chen, "An image-guided hybrid robot system for dental implant surgery, " International Journal of Computer Assisted Radiology and Surgery, vol. 17. no.1, pp.15-26, (2022).

[10] C. Dong, H. Liu, J. Xiao, and T. Huang,, "Dynamic modeling and design of a 5-DOF hybrid robot for machining,," Mechanism and Machine Theory, vol. 165, p.104438, (2021).

[11] H. D. Yang and A. T. Asbeck,  "Design and characterization of a modular hybrid continuum robotic manipulator, " IEEE/ASME Transactions on Mechatronics, vol. 25, no.6, pp.2812-2823, (2020).

[12] J. Enferadi and K. Jafari, "A Kane’s based algorithm for closed-form dynamic analysis of a new design of a 3RSS-S spherical parallel manipulator," Multibody System Dynamics, vol. 49, pp. 377-394, (2020).

[13] R. Kelaiaia, O. Company, and A. Zaatri, "Multiobjective optimization of a linear Delta parallel robot," Mechanism and Machine Theory, vol. 50, pp. 159-178, (2012).

[14] J. Enferadi and R. Nikrooz, "The performance indices optimization of a symmetrical fully spherical parallel mechanism for dimensional synthesis," Journal of Intelligent & Robotic Systems, vol. 90, no. 3-4, pp. 305-321, (2018).

[15] S. N. Nabavi, M. Shariatee, J. Enferadi, and A. Akbarzadeh, "Parametric design and multi-objective optimization of a general 6-PUS parallel manipulator," Mechanism and Machine Theory, vol. 152, p. 103913, (2020).

[16] S. N. Nabavi, A. Akbarzadeh, J. Enferadi, and I. Kardan, "A homogeneous payload specific performance index for robot manipulators based on the kinetic energy," Mechanism and Machine Theory, vol. 130, pp. 330-345, (2018).

[17] Z. Gao and D. Zhang, "Performance analysis, mapping, and multiobjective optimization of a hybrid robotic machine tool," IEEE Transactions on Industrial Electronics, vol. 62, no. 1, pp. 423-433, (2014).

[18] S. Kucuk, "Dexterous workspace optimization for a new hybrid parallel robot manipulator," Journal of Mechanisms and Robotics, vol. 10, no. 6, (2018).

[19] O. Ibrahim and W. Khalil, "Inverse and direct dynamic models of hybrid robots," Mechanism and Machine Theory, vol. 45, no. 4, pp. 627-640, (2010).

[20] S. N. Nabavi, A. Akbarzadeh, and J. Enferadi, "Closed-Form Dynamic Formulation of a General 6-P US Robot," Journal of Intelligent & Robotic Systems, vol. 96, no. 3-4, pp. 317-330, (2019).

[21] J. Gallardo-Alvarado, C. R. Aguilar-Nájera, L. Casique-Rosas, J. M. Rico-Martínez, and M. N. Islam, "Kinematics and dynamics of 2 (3-RPS) manipulators by means of screw theory and the principle of virtual work," Mechanism and Machine Theory, vol. 43, no. 10, pp. 1281-1294, (2008).

[22] Y. Wu, Z. Yang, Z. Fu, J. Fei, and H. Zheng, "Kinematics and dynamics analysis of a novel five-degrees-of-freedom hybrid robot," International Journal of Advanced Robotic Systems, vol. 14, no. 3, p. 1729881417716634, (2017).

[23] Y. Yun and Y. Li, "Modeling and control analysis of a 3-PUPU dual compliant parallel manipulator for micro positioning and active vibration isolation," Journal of Dynamic Systems, Measurement, and Control, vol. 134, no. 2, (2012).

[24] D. Zhang, Y. Xu, J. Yao, and Y. Zhao, "Design of a novel 5-DOF hybrid serial-parallel manipulator and theoretical analysis of its parallel part," Robotics and Computer-Integrated Manufacturing, vol. 53, pp. 228-239, (2018).

[25] J. W. Gibbs, "On the fundamental formulae of dynamics," American Journal of Mathematics, vol. 2, no. 1, pp. 49-64, )1879(.

[26] P. Appell, "Sur les mouvements de roulment; equations du mouvement analougues a celles de Lagrange," Comptes Rendus, vol. 129, pp. 317-320, )1899(.

[27] M. Shariatee, A. Akbarzadeh, and N. Nabavi, "Design of a Pneumatic Weight Compensation System for the FUM Stewart Robot," IEEE in 2017 5th RSI International Conference on Robotics and Mechatronics (ICRoM), , pp. 624-629, (2017).