Electronical and Mechanical System Modeling of Robot Dynamics Using a Mass/Pulley Model

Subject Areas : journal of Artificial Intelligence in Electrical Engineering

عطالله رجب پور ¹ , امیر زارعی ² , آرزو رجب پور ³ , فاطمه احمدی ⁴

1 -
2 -
3 -
4 -

Received: 2015-07-23 Accepted : 2015-07-23 Published : 2013-11-01

Keywords: Mass matrix, inertia matrix, MP model, pulley, differential transmission, mechanical system representation, robot dynamics, impedance, equivalent electric circuit,

Abstract :

The well-known electro-mechanical analogy that equates current, voltage, resistance, inductance and capacitance to force, velocity, damping, spring constant and mass has a shortcoming in that mass can only be used to simulate a capacitor which has one terminal connected to ground. A new model that was previously proposed by the authors that combines a mass with a pulley (MP) is shown to simulate a capacitor in the general case. This new MP model is used to model the off-diagonal elements of a mass matrix so that devices whose effective mass is coupled between more than one actuator can be represented by a mechanical system diagram that is topographically parallel to its equivalent electric circuit model. Specific examples of this technique are presented to demonstrate how a mechanical model can be derived for both a serial and a parallel robot with both two and three degrees of freedom. The technique, however, is extensible to any number of degrees of freedom

References:

[1] Brune, O., 1931. "Synthesis of a finite twoterminal network whose driving-point impedance is a prescribed function of frequency". J. Math. Physics. vol. 10, pp. 191- 236.

[2] Craig, J.J., 2005. “Introduction to Robotics Mechanics and Control”. 3rd ed., Pearson Prentice Hall.

[3] Eppinger, S., Seering, W., 1992. “Three Dynamic Problems in Robot Force Control”. IEEE Trans. Robotics & Auto., V. 8, No. 6, pp. 751-758.

[4] Fairlie-Clarke, A.C., 1999. “Force as a Flow Variable”. Proc. Instn. Mech. Engrs., V. 213, Part I, pp. 77-81. Foster, R. M., 1924. "A reactance theorem". Bell System Tech. J., vol. 3, pp. 259-267.

[5] Hamill, D.C., 1993. "Lumped Equivalent Circuits of Magnetic Components: The Gyrator-Capacitor Approach". IEEE Transactions on Power Electronics, vol. 8, pp. 97.

[6] Hayward, V., Choksi, J., Lanvin, G., Ramstein, C., 1994. “Design and Multi-Objective Optimization of a Linkage for a Haptic Interface”. Proc. of ARK „94, 4th Int. Workshop on Advances in Robot Kinematics (Ljubliana, Slovenia), pp. 352-359.

[7] Paynter, H.M., 1961. Analysis and Design of Engineering Systems. MIT Press.

[8] Sass, L., McPhee, J., Schmitke, C., Fisette, P., Grenier, D., 2004. "A Comparison of Different Methods for Modelling Electromechanical Multibody Systems". Multibody System Dynamics, vol. 12, pp. 209-250

[9] ligent Robots & Systems, (Raleigh, NC), pp. 1103,-1110.

[10] Stocco, L., Yedlin, M., Sept. 2006. “Closing the Loop on the Electro-Mechanical System Analogy”. Submitted to: IEEE J. Circuits & Systems.

[11] Tilmans, H.A.C., 1996. "Equivalent circuit representation of electromechanical transducers: I. Lumpedparameter systems". J. Micromech. Microeng, vol. 6, pp. 157-176.

[12] van Amerongen, J., Breedveld, P., 2003. "Modelling of physical systems for the design and control of mechatronic systems". Annual Reviews in Control, vol. 27, pp. 87-117. Yamakita, M., Shibasato, H., Furuta, K., 1992. “Tele- Virtual Reality of Dynamic Mechanical Model”. Proc. IEEE/RSJ Int. Conf. Int.