Subject for inquiry: functions of positions of mechanisms, connections equations of these mechanisms, singular positions of mechanisms and their algorithm of computation, Newton’s polyhedron.
Aim of the inquiry: description of connections equations of mechanisms with the help of a system of nonlinear algebraic equations. Classification singular points of the position function of mechanisms. Construction of algorthm for computation of singularities of the position function of mechanisms. Investigation of singularities fiflink mcchnisms, plane mechanism with three degrees of freedom and plane fourlink with hydrosilindrs.
Methods of inquiry: in the work methods of computational mathematics, linear algebra and exponential geometry, and algorithms of finding of singularities of curves arc applied.
The results achieved and their novelty: classification of singularities of position function of mechanisms which arc expressed by algebraic curves is obtained. The algorithm for computation of singular positions of position functions of mechanisms is constructed. Local presentations of position function of plane mechanisms with two and three degrees of freedom arc found.
Practical value: the results of the dissertation have scientific-applied character.
Sphere of usage: the results of the present dissertation work may be used in the further development of the theory of singularities of algebraic curves, in problems which appear in investigations and design of mechanisms, in creation automatic and semiautomatic robots and in other theoretical and practical problems.
