Abstract
Discussed in this paper is a method for the automatic generation of symbolic equations for multiple-loop mechanisms whose kinematics can be solved in closed form. The method is based on geometric and topological properties of the system which are invariant to coordinate transformations. It focuses on the treatment of the individual multibody loops as transmission elements which encompass the solution of the local nonlinear constraint equations and which can be assembled by linear equations to yield general mechanisms. The global processing is obtained as a combination of algorithms for generating the local kinematics of the individual loops, detecting a suitable set of independent loops, and finding an optimal “solution flow” in the resulting kinematical block-diagram which represents the order in which the equations are to be solved. An example processed by the current implementation of the method with the symbolic-computation language Mathematica illustrates the basic ideas and the scope of the approach.
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© 1993 Springer Science+Business Media Dordrecht
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Kecskeméthy, A. (1993). On Closed Form Solutions of Multiple-Loop Mechanisms. In: Angeles, J., Hommel, G., Kovács, P. (eds) Computational Kinematics. Solid Mechanics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8192-9_24
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DOI: https://doi.org/10.1007/978-94-015-8192-9_24
Publisher Name: Springer, Dordrecht
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