This paper deals with teaching kinematic and dynamic analysis of 3-D multibody systems in a context of courses with severe time constraints and the objective of attaining practical abilities. This high course efficiency is intended by the use of a simple theoretical approach (the natural or fully Cartesian coordinates) and a high level programming language (the function rich and easy to learn development tool Matlab. The theoretical prerequisites for such a course can be kept to a minimum. This approach would allow the introduction of some lessons on multibody systems inside more general courses on machine dynamics. It can also be useful for short courses addressed to engineers in industry and for numerical analysis courses addressed to mechanical engineering students that are interested in practical applications of these numerical methods. In this paper the achievable theory level will be presented in detail by means of a practical but non trivial example: a closed-chain 3-D robot. Natural coordinates and Matlab are also a good starting point to present more advanced techniques such as numerical integration methods for ODEs and DAEs, or the not very well known automatic differentiation techniques. The latter is considered as a more advanced example in this paper.

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