Analytic Approaches for Design and Operation of Haptic Human-Machine Interfaces
2015. Universität Bremen.
The present dissertation provides answers to different questions arising in the areas of interaction with robotic systems, kinematics and dynamics of mechanisms, and the representation of finite and instantaneous states of rigid body systems. The application-oriented starting point for the thesis is to ask in which ways two mechanisms of different geometry may move coherently. For answering this question, an approach is developed that permits the realization of various kinds of coherent motion in Euclidean space. A characteristic feature of the approach is the embedding of the respective kinematics and dynamics computations into the mapping between the two interacting systems.
For this reason, methods for modeling and solving kinematic and dynamic problems of mechanisms are developed further and newly in the context of this work. This includes a program for semiautomatic generation of mechanism specifications in several description formats of common simulation environments. Further, novel solutions for specific kinematic problems are developed: this contains an entire characterization of the workspace of general spherical 3R chains and an improved solution to the redundant inverse kinematics problem of anthropomorphic 7R chains.
The first part of the dissertation comprises a review and advancement of the geometric, algebraic, and physical fundamentals for answering the mentioned use-oriented questions. Amongst others, this concerns the algebraic representations of vectors, lines, finite screws, and coordinate systems in three-dimensional space and their geometric interrelations. In addition, the description of velocities and forces of rigid bodies by means of instantanenous screws is covered. For both cases, a specially developed notation system is applied that allows novel connections to be worked out. In particular, the two classic formulations of the basic motion laws by Newton and Euler for spatial rigid bodies are unified by means of this newly introduced notation scheme.