Abstract
Machines and mechanisms realize processes, from the shaping process of a milling machine to the motion process of an automotive system. The dynamics of a machine generated by a properly chosen set of constraints in combination with an appropriate drive system is designed to meet the prescribed requirements of the process, which is done by projecting the machine equations of motion on the process dynamics. We get a set of nonlinear relations, which represent the machine motion in terms of the required process motion. A well-known example is the projection of arbitrarily many robot degrees of freedom on one given path degree of freedom resulting in a set for evaluating possible motion spaces, now supplemented also by constraint force spaces, helpful for design and optimization. For multidimensional processes, things become more complex but feasible. This paper presents a corresponding approach applying multibody system theory in combination with transformations from the machine side to the process side and vice versa. Practical aspects are discussed and examples given.
Similar content being viewed by others
References
Abraham, R., Marsden, J.E.: Foundations of Mechanics. Westview, Perseus Books Group, Cambridge (1978)
Angeles, J.: Fundamentals of Robotic Mechanical Systems. Springer, New York (1997)
Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edn. Springer, New York (1989)
Bobrow, J.E., Dubowsky, S., Gibson, J.S.: Time optimal control of robotic manipulators along specified paths. Int. J. Robot. Res. 4, 3–17 (1985)
Bremer, H.: Elastic Multibody Dynamics. Springer, New York (2008)
Dresig, H., Vul’fson, I.I.: Dynamik der Mechanismen. Springer, New York (1989)
Dubowsky, S., Shiller, Z.: Optimal dynamic trajectories for robotic manipulators. In: Proceedings of 5th Symposium on Theory and Practice of Robotics and Manipulators (1985)
Duschek, A., Hochrainer, A.: Grundzüge der Tensorrechnung in analytischer Darstellung. Springer, New York (1960)
Jacobi, C.G.J.: Vorlesungen über Dynamik. Edited by A. Clebsch, Berlin (1866)
Johanni, R.: Optimale Bahnplanung bei Robotern. Fortschritt-Berchte VDI, Reihe 18, Nr. 51, VDI-Verlag, Düsseldorf (1988)
Nolte, D.D.: Introduction to Modern Dynamics. Oxford University Press, Oxford (2015)
Pfeiffer, F.: Optimal Trajectory Planning for Manipulators, Systems and Control Encyclopedia. Pergamon Press, Oxford (1990)
Pfeiffer, F.: Mechanical System Dynamics. Springer, Heidelberg (2008)
Pfeiffer, F., Schindler, Th: Introduction to Dynamics. Springer, Berlin (2015)
Rajeev, S.G.: Advanced Mechanics. Oxford University Press, Oxford (2013)
Richter, K.: Kraftregelung elastischer Roboter. Fortschritt-Berichte VDI, Reihe 8, Nr. 259, VDI-Verlag, Düsseldorf (1991)
Wittenburg, J.: Kinematics. Springer, Heidelberg (2016)
Woernle, C.: Mehrkörpersysteme, 2nd edn. Springer, Berlin (2016)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Pfeiffer, F. Motion spaces of machine–process combinations. Arch Appl Mech 89, 2115–2132 (2019). https://doi.org/10.1007/s00419-019-01564-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-019-01564-7