Open AccessThe paper considers a solution of the relevant tasks related to deriving dynamic equations for the platform manipulators with 6 degrees of freedom. It presents a detailed analysis of the subject area, describes key problems arising in the course of research, and suggests their solution methods. The equations describing dynamics of the mechanical system under discussion were derived using Lagrange equation of the second kind. For this purpose Cartesian coordinates and three Euler angles (angles of precession, nutation and intrinsic rotation) describing the orientation of moving frame of reference connected with the platform towards the base were chosen as generalized coordinates of the model. Such choice allowed us to simplify the derivation of the model considerably, because it was possible to represent a dependence of kinetic energy of the mechanical system on the generalized coordinates in an explicit form. In addition, formulation of kinetic energy was supplemented with correlations describing kinetic energy of the mechanism legs. During the derivation of equations for the legs velocities the part of the component defining a rotation movement of the leg against the joint of the base was ignored because of it was small in comparison with the component of linear separation. Besides, during the derivation of equations for kinetic energy of the legs, modified correlations for kinematics of platform manipulators with 6 degrees of freedom suggested in the previous papers of the authors were used.
he paper examines a numerical example to solve a reverse dynamic problem in the case of equal harmonic changes of controlling forces. It was found out that under controlling forces described above the platform carries out harmonic advancing movements along the vertical axis.
Further planning research concerns the extended capabilities of the model to consider the influence of the working load and to create algorithms for deriving dynamic models of a multisectional manipulator with a parallel structure.