Analysis of the Dynamic Forces of 3D Printer with 4 Degrees of Freedom

Subject Areas : robotics

sajjad  pakzad ¹ (Faculty of Design, Tabriz Islamic Art University, Iran)
ebrahim  imani ² (Faculty of Design, Tabriz Islamic Art University, Iran Department of PDTA, Sapienza University of Rome, Rome, Italy)

Received: 2019-10-15 Accepted : 2020-02-05 Published : 2020-06-01

Keywords: Dynamic, Force Analysis, MATLAB, 3D Printer,

Abstract :

The use of parallel mechanisms in the structure of 3D printers are developing. Parallel mechanisms have excellent capabilities in terms of accuracy, stiffness and high load-bearing capacity. This article studies a 3D printer with four degrees of freedom that has three degrees of linear freedom and one degree of rotational freedom. The advantages of this printer are greater than conventional Cartesian printers, including higher print speed and stiffness, and there are also higher degrees of freedom for manoeuvrability. In this paper, the Newton-Euler analytical method is used to analyse the inverse dynamics and identify the driving forces required by the 3D nozzle motion. By coding the inverse dynamic equations in the MATLAB software environment, the driving forces diagrams are extracted based on the printer's nozzle motion. To validate the inverse dynamics relationships, simulations with the Simmechanic model of MATLAB software have been performed. Through changing the speed of movement of the printer nozzle and also change of the velocity and acceleration of drives, the forces required for the drive also change. The effect of changes in print speed of a specific geometry on the driving forces is also studied. As well as, choosing the optimum print speed with regard to the motor driver power and the dynamics of the forces applied to the drivers and the less print time are the most important factors that are discussed in this article.

References:

[1]     Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley, 1999.

[2]     Wu, J., Yin, Z., A Novel 4-DOF Parallel Manipulator H4 in Parallel Manipulators, Towards New Applications, Huapeng Wu, I-Tech Education and Publishing, 2008, pp. 405–448.

[3]     Stewart, D., A Platform with Six Degrees of Freedom, Proceedings of the Institution of Mechanical Engineers, Vol. 180, 1965, pp. 371–386.

[4]     Merlet, J. P., Parallel Robots. Springer, 2006.

[5]     Geng, Z., Haynes, L. S., Lee, J. D., and Carroll, R. L., On the Dynamic Model and Kinematic Analysis of a Class of Stewart Platforms, Robotics and Autonomous Systems, Vol. 9, No. 4, 1992, pp. 237–254.

[6]     Lebret, G., Liu, K., and Lewis, F. L., Dynamic Analysis and Control of a Stewart Platform Manipulator, Journal of Robotic Systems, Vol. 10, No. 3, 1993, pp. 629–655.

[7]     Pang, H., Shahinpoor, M., Inverse Dynamics of a Parallel Manipulator, Journal of Robotic Systems, Vol. 11, No. 8, 1994, pp. 693–702.

[8]     Caccavale, F., Siciliano, B., and Villani, L., The Tricept Robot: Dynamics and Impedance Control, IEEE/ASME Transactions on Mechatronics, Vol. 8, No. 2, 2003, pp. 263–268.

[9]     Abdellatif, H., Heimann, B., Computational Efficient Inverse Dynamics of 6-DOF Fully Parallel Manipulators by Using the Lagrangian Formalism, Mechanism and Machine Theory, Vol. 44, No. 1, 2009, pp. 192–207.

[10]  Do, W. Q. D., Yang, D. C., Inverse Dynamic Analysis and Simulation of a Platform Type of Robot, Journal of Robotic Systems, Vol. 5, No. 3, 1988, pp. 209–227.

[11]  Reboulet, C., Berthomieu, T., Dynamic Models of a Six Degree of Freedom Parallel Manipulators, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments, Pisa, Italy, 1991.

[12]  Ji, Z., Study of the Effect of Leg Inertia in Stewart Platforms, Proceedings IEEE International Conference on Robotics and Automation, Atlanta, GA, USA, 1993.

[13]  Harib, K. H., Dynamic Modeling, Identification and Control of Stewart Platform-Based Machine Tools, the Ohio State University, Columbus, Ohio, 1997.

[14]  Dasgupta, B., Mruthyunjaya, T. S., A Newton-Euler Formulation for The Inverse Dynamics of the Stewart Platform Manipulator, Mechanism and Machine Theory, Vol. 33, No. 8, 1998, pp. 1135–1152.

[15]  Dasgupta, B., Mruthyunjaya, T. S., Closed-Form Dynamic Equations of the General Stewart Platform through the Newton–Euler Approach, Mechanism and Machine Theory, Vol. 33, No. 7, 1998, pp. 993–1012.

[16]  Dasgupta, B., Mruthyunjaya, T. S., Erratum to ‘Closed-Form Dynamic Equations of the General Stewart Platform through the Newton — Euler Approach’ [Mechanism and Machine Theory 33 (7) 993–1012], Mechanism and Machine Theory, Vol. 35, No. 4, 2000, p. III.

[17]  Riebe, S., Ulbrich, H., Modelling and Online Computation of the Dynamics of a Parallel Kinematic with Six Degrees-Of-Freedom, Archive of Applied Mechanics, Vol. 72, No. 11-12, 2003, pp. 817–829.

[18]  Guo, H. B., Li, H. R., Dynamic Analysis and Simulation of a Six Degree of Freedom Stewart Platform Manipulator, Proceedings of The Institution of Mechanical Engineers Part C-journal of Mechanical Engineering Science, Vol. 220, 2006, pp. 61–72.

[19]  Khalil, W., Ibrahim, O., General Solution for The Dynamic Modeling of Parallel Robots, Journal of Intelligent and Robotic Systems, Vol. 49, No. 1, 2007, pp. 19–37.

[20]  Wang, J., Wu, J., Wang, L., and Li, T., Simplified Strategy of the Dynamic Model of A 6-UPS Parallel Kinematic Machine for Real-Time Control, Mechanism and Machine Theory, Vol. 42, No. 9, 2007, pp. 1119–1140.

[21]  Mahmoodi, A., Menhaj, M. B., and Sabzehparvar, M., An Efficient Method for Solution of Inverse Dynamics of Stewart Platform, Aircraft Engineering and Aerospace Technology, Vol. 81, No. 5, 2009, pp. 398–406.

[22]  Clavel, R., Conception d’un Robot Parallèle Rapide À 4 Degrés De Liberté, Lausanne, EPFL, Thesis, 1991.

[23]  Wang, J., Gosselin, C. M., A New Aproach for the Dynamic Analysis of Parallel Manipulators, Multibody System Dynamics, Vol. 2, No. 3, 1998, pp. 317–334.

[24]  Gallardo, J., Rico, J. M., Frisoli, A., Checcacci, D., and Bergamasco, M., Dynamics of Parallel Manipulators by Means of Screw Theory, Mechanism and Machine Theory, Vol. 38, No. 11, 2003, pp. 1113–1131.

[25]  Tsai, L. W., Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work, Journal of Mechanical Design, Vol. 122, No. 1, 2000, pp. 3.

[26]  Nguyen, C. C., Pooran, F. J., Dynamic Analysis of A 6 dof Ckcm Robot End-Effector for Dual-Arm Telerobot Systems, Robotics and Autonomous Systems, Vol. 5, No. 4, 1989, pp. 377–394.

[27]  Fujimoto, K.; Kinoshita, Y.; Maeda, K.; Tadokoro, S., and Takamori, T., Derivation and Analysis of Equations of Motion for 6-DOF Direct-Drive Wrist Joint, Proceedings IROS '91: IEEE/RSJ International Workshop on Intelligent Robots and Systems '91, Osaka, Japan, 1991, pp. 2–7.

[28]  Miller, K., Clavel, R., The Lagrange-Based Model of Delta-4 Robot Dynamics, Robotersysteme, No. 8, 1992, pp. 49–54.

[29]  Liu, K., Lewis, F., Lebret, G., and Taylor, D., The Singularities and Dynamics of a Stewart Platform Manipulator, Journal of Intelligent and Robotic Systems, Vol. 8, No. 3, 1993, pp. 287–308.

[30]  Miller, K., Optimal Design and Modeling of Spatial Parallel Manipulators, The International Journal of Robotics Research, Vol. 23, No. 2, 2004, pp. 127–140.

[31]  Kebria, P., Abazari, M. R., and Abdi, H., Simmechanics Model Development for Gantry-Tau Robot.

[32]  Craig, J. J., Introduction to Robotics: Mechanics and Control, Pearson Prentice Hall, Upper Saddle River, Vol. 3, 2005.