In this PhD defense talk, an overview of the correspondent thesis is provided and central aspects are discussed. Thereby, the four main areas of thesis – (i) ‘foundations’, (ii) ‘kinematic-dynamic modeling’, (iii) ‘problems, methods, solutions’, (iv) and ‘Euclidean teleoperation’ – are touched within the talk. Taking an application-oriented point of view, the presentation emphasizes the area of ‘teleoperation’ – a central technique and research stream in human-machine interaction. For controlling robots in three-dimensional Euclidean space, a systematic concept has been developed in the scope the thesis. The theoretical concept is presented together with necessary prerequisites and a set of experiments that demonstrate the broad applicability of the approach. With regard to ‘foundations’, the talk introduces a specially developed notation scheme that incorporates four different kinds of attributes: by means of the scheme, various relations within rigid multibody systems are stated systematically. Further, a glimpse is given to a novel, generalized formulation of the Newton–Euler equations. The areas of ‘kinematic-dynamic modeling’ and ‘problems, methods, and solutions’ are reflected in a comprehensive manner: amongst others, the approach of the program CAD-2-SIM is motivated and a refined solution for the redundant inverse kinematics problem of anthropomorphic – SRS-partitioned – mechanical 7R chains is outlined.