Mathematical description of concrete laying robots

The object of the research is robots with a manipulation system for concrete-laying operations. The kinematic scheme of a robot with an articulated distributive arm, providing delivery of concrete to any point of the erected object and allowing to bypass various kinds of encountered obstacles, is presented. The closed loops in the form of three- and four-links, which make up the manipulation system, are considered and mathematically described, which is conditioned by the use of a hydraulic drive. On the basis of geometrical approach connections between them are defined, as well as dependences of their velocities and accelerations are established. The description of the dynamics of the manipulating system is made on the basis of the Lagrange method, formulated through the D'Alamber principle, which allowed to obtain the resulting equations in a convenient vector-matrix form. The problem of planning the trajectories of a robotized concrete-laying arm nozzle on the examples of monolithic buildings and structures erection by means of sliding, repositionable and volumetric formwork has been solved. Approximation methods are used to form the time laws of changes in the generalized coordinates of the manipulation system.