Mechanical System Modelling of Robot Dynamics Using a Mass/Pulley Model

journal of Artificial Intelligence in Electrical Engineering

مقاله 1، دوره 2، شماره 5، مرداد 2013، صفحه 1-10   

چکیده

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.

کلیدواژه‌ها

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

مراجع

Brown, O., 1931. "Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency". J. Math. Physics. vol. 10, pp. 191-236.
Craig, J.J., 2005. “Introduction to Robotics Mechanics and Control”. 3rd ed., Pearson Prentice Hall.
Eppinger, S., Seering, W., 1992. “Three Dynamic Problems in Robot Force Control”. IEEE Trans. Robotics & Auto., V. 8, No. 6, pp. 751-758.
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.
Hamill, D.C., 1993. "Lumped Equivalent Circuits of Magnetic Components: The Gyrator-Capacitor Approach". IEEE Transactions on Power Electronics, vol. 8, pp. 97.
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.
Paynter, H.M., 1961. Analysis and Design of Engineering Systems. MIT Press.
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.
Stocco, L., Yedlin, M., Sept. 2006. “Closing the Loop on the Electro-Mechanical System Analogy”. Submitted to: IEEE J. Circuits & Systems.
Tilmans, H.A.C., 1996. "Equivalent circuit representation of electromechanical transducers: I. Lumpedparameter systems". J. Micromech. Microeng, vol. 6, pp. 157-176.
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. Intel
ligent Robots & Systems, (Raleigh, NC), pp. 1103,-1110