Singularity Analysis and Representation of 6DOF Parallel Robot Using Natural Coordinates

Singularity research is carried out. The problem, which is about six-dimensional parameters of position and orientation can not realize three-dimensional visualization for 6DOF parallel robot, has been solved. Firstly, according to the structural characteristics of the 6DOF parallel robot with the planar platform, the position and orientation of the mobile platform are described, respectively, and the six equations of forward kinematics are established by choosing the natural coordinates of three representative points as parameters. Then, the singularities of the 6DOF parallel robot with a planar platform are divided into input singularity and output singularity. Aiming at the output singularity, in combination with six constraint equations among the position vectors of three representative points, an analytical algorithm is proposed to express the coupling singularity of position and orientation and the analytical expression is derived. In further research, three kinds of output singularities are found, the spatial distribution of the output singular trajectory is determined, and a unified three-dimensional fully visualized description of six-dimensional coupling variables is realized for the first time. The problems of finding the singular orientation at a given position or the singular position at a given orientation are solved. The analysis of the singularity lays a solid foundation for the description of the three-dimensional complete visualization of a six-dimensional singularity-free workspace based on forward kinematics. What is more, it has great significance for both trajectory planning and control design of the parallel robot.

Another Multibody Dynamics in Natural Coordinates through Automatic Differentiation and High-Index DAE Solving

The Natural Coordinates (NCs) method for Lagrangian modelling and simulation of multi-body systems is valued for giving simple, sparse models. We describe our version of it (NPNCs) and compare with the classical ap- proach of Jalón and Bayo (JBNCs). NPNCs use the high-index differential- algebraic equation solver DAETS. Algorithmic differentiation, not symbolic algebra, forms the equations of motion from the Lagrangian. NPNCs give significantly smaller equation systems than JBNCs, at the cost of a non- constant mass matrix for fully 3D models—a minor downside in the DAETS context. A 2D and a 3D example are presented, with numerical results.

Multiscale modeling of reaction rates: application to archetypal SN2 nucleophilic substitutions

This work outlines the development and application of a multiscale computational protocol to evaluate reaction rates of elementary reactions in internal natural coordinates.