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Role of Automated Symbolic Generation of Equations of Motion in Mechanism and Robotics Education

[+] Author Affiliations
Hrishi Shah, Sumit Tripathi, Leng-Feng Lee, Venkat Krovi

State University of New York at Buffalo, Buffalo, NY

Paper No. DETC2010-28994, pp. 995-1002; 8 pages
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4410-6 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME


In recent years there has been a significant increase in the variety and complexity of Articulated-Multi-Body-Systems (AMBS) used in various applications. There is also increased interest in the model-based design-refinement and controller-development, which is critically dependent upon availability of underlying plant-models. Kinematic and dynamic plant-models for AMBSs can be formulated by systematic application of physics postulates. This process, in its various variants, forms the basis of various mechanisms/robotics courses. However, the type and complexity of the example systems is often limited by the tractability of first generating and subsequently analyzing complex equations-of-motion. Nevertheless, using simpler examples alone may sometimes fail to capture important physical phenomena (e.g. gyroscopic, coriolis). Hence, we examine the use of some contemporary symbolic- and numeric-computation tools to assist with the automated symbolic equation generation and subsequent analysis. We examine a host of examples beginning with simple pendulum, double pendulum; building up to intermediate examples like the four-bar mechanism and finally examine the implementation of 3-P RR and 3-R RR planar parallel platform mechanisms. The principal underlying philosophy of our effort is to establish linkage between traditional modeling approaches and use of these contemporary tools. We also try to make a case for use of automatic symbolic computation and manipulation as a means for enhancing understanding of both basic and advanced AMBS concepts. Lastly, we document our efforts towards creation of self-paced tutorials and case-studies that serve to showcase the benefits.

Copyright © 2010 by ASME



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