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After three decades of computational multibody system (MBS) dynamics, currentresearch is centered at the development of compact and user friendly yetcomputationally efficient formulations for the analysis of complex MBS. The keyto this is a holistic geometric approach to the kinematics modeling observingthat the general motion of rigid bodies as well as the relative motion due totechnical joints are screw motions. Moreover, screw theory provides thegeometric setting and Lie group theory the analytic foundation for an intuitiveand compact MBS modeling. The inherent frame invariance of this modelingapproach gives rise to very efficient recursive $O\left( n\right) $ algorithms,for which the so-called 'spatial operator algebra' is one example, and allowsfor use of readily available geometric data. In this paper three variants fordescribing the configuration of tree-topology MBS in terms of relativecoordinates, i.e. joint variables, are presented: the standard formulationusing body-fixed joint frames, a formulation without joint frames, and aformulation without either joint or body-fixed reference frames. This allowsfor describing the MBS kinematics without introducing joint reference framesand therewith rendering the use of restrictive modeling convention, such asDenavit-Hartenberg parameters, redundant. Four different definitions of twistsare recalled and the corresponding recursive expressions are derived. Thecorresponding Jacobians and their factorization are derived. The aim of thispaper is to motivate the use of Lie group modeling and to provide a review ofthe different formulations for the kinematics of tree-topology MBS in terms ofrelative (joint) coordinates from the unifying perspective of screw and Liegroup theory.

Screw and Lie Group Theory in Multibody Kinematics -- Motion Representation and Recursive Kinematics of Tree-Topology Systems