Determination of Local Mobility in Parallel Manipulators with Higher and Lower Order Constraints with Singular Configurations

This paper deals with the development of methods and algorithms for automatic determination and avoidance of singularity regions when solving forward and inverse control problems of manipulators of a given (arbitrary and singular) configuration. The results of realization of this research are the modeling of the workspace of mechanisms under the given constraints of several types of kinematic structures and the testing of the proposed methods and algorithms on the basis of the developed experimental stand. The following problems are identified as promising solution paths in this paper: a mathematical model of a five-link parallel manipulator and a 3-RRR type manipulator using a differential geometric approach without using the coordinate method, and its implementation on a computer; a numerical method based on Gröbner bases to investigate kinematic schemes and discretization of multidimensional space in order to estimate the locus of singularities in models. Higher-order constraints are defined recursively in terms of instantaneous kinematics by the product of the angular velocity in the rotation of kinematic pairs. Explain higher-order mobility and the necessary restrictions for mechanisms with higher kinematic pairs. In addition to studying the Singularity of different mechanism types, the analysis of C-space enables the determination of finite local mobility and the examination of singularities. Our understanding of motion enables us to explore mobility, detect singularities in motion, identify bifurcations and reconfigurations of motion, and assess the instability of this mechanism.