Rigid Body Dynamics: Links and Joints

Physics-based multibody simulations have a wide range of applications. In order to be capable of analyzing complex problem formulations, e.g. the motion of the human skeleton, joints are a necessary requirement for multibody simulation frameworks. The major focus of this thesis lies on the development and implementation of a general scheme to integrate joint motion constraints into the pe framework, which is developed at the Chair for System Simulation at the Friedrich-Alexander University Erlangen-Nuremberg. The mathematical background based on complementarity constraints is elucidated profoundly. Full-Coordinate methods are used to preserve the motion constraints. The complex mechanical background is elaborated. An abstract formulation, which incorporates joint, contact and limit constraints, and which is based on analytical mechanics is deduced. The Jacobian matrix notation is introduced to achieve a unified complementarity formulation. Several example joints are modeled and explained in detail. Error correction parameters for drifting problems due to the Full-Coordinate method are introduced in order to keep the errors to a minimum. Special emphasis lies on the modular class design, which enables the easy addition of other joint types in the future. In order to demonstrate the suitability of the extension selected joints are implemented. The correctness is substantiated with the help of several test scenarios, which test the specific characteristics of each implemented joint type. The results of these validation tests are analyzed and further interesting joint types and augmentations to the implementation are suggested.