Hello,
My name is Renato Maia Matarazzo Orsino, a PhD student from University of São Paulo, Brazil, and I am currently working as a guest in the Bicycle Lab of TU Delft (The Netherlands) under the supervision of Professor PhD Arend Schwab.
I am working on a new modular approach for modelling multibody systems (which can be used both on symbolic modelling and numerical simulations). In this approach you consider a complex multibody system as consisting of a set of constrained subsystems. Each subsystem can be either a single body or another "simpler" multibody system.
Consider that you already know the mathematical model of these subsystems (no matter which variables have been used for the modelling, not the formalism which has been used on its derivation, eg. Lagrange, Kane, etc.., of any of them).
Consider also that you are able to describe the constraints among these subsystems (which can be referred as "external constraints") using the modelling variables from the subsystems involved, then, by an algorithm based on finding the orthogonal complements of matrices which are associated with the jacobians of these external constraints, it is possible to obtain directly from the already known motion equations of the subsystems, the system of motion equations for the whole system (with as much equations as the number of degrees of freedom of the system) without the need of including or eliminating any constraint force.
I have already developed all the theoretical derivations of this methodology as well as some modelling and simulation examples using Mathematica and Octave. Now I want to have implemented on SymPy so that it can be shared with Multibody Systems community.
My fellow André Garnier Coutinho will also be applying once he has developed some specialized versions of this methodology to the modelling of serial and parallel robots.
Thank you for your attention.
Renato Maia Matarazzo Orsino