Manipulators with the mechanisms of a parallel structure are increasingly used in various industries: in mechanical engineering as parts of complex geometry mechanical processing, tool engineering, products packaging, as well as in the technological processes and in the production and processing of the agricultural products. Loading and unloading operations are well-suited for mechanization and automation with the use of a tripod manipulator. Till nowadays due to a limited working area, a relatively small degree of manipulation of a tripod manipulator, and, even less, the technological processes can be subjected to mechanization and automation in processing of the agricultural products: sorting, packaging and canning of fruits and vegetables. In order to increase manipulation of the tripod manipulator (hand) in the joint, where the linear displacement drive units axis geometrically converge at a single point by a spherical five moveable hinge unit, a driven mechanism was designed consisting of three series-connected pairs of the fifth class of links (gripper) with a working body (brush). Since one of the basic requirements, which determine performance of the manipulators, is to ensure an approach of the manipulator's working body to the points of a service object with a given orientation of the working body, we define the tasks of positioning of the manipulator's working body and evaluation of its functional abilities in the service area. The task of a manipulator's positioning is to determine the manipulator's generalized coordinates at a given program position of the working body. In order to handle this problem it is necessary to solve the direct task for the hand of the manipulator, i.e. to determine the Cartesian coordinates of the suspension point in the absolute coordinate system of Oxyz and the inverse task for the gripper. Thus, the proposed scheme of a tripod manipulator with an additional mechanism for the gripper with three degrees of mobility allows us to ensure the necessary manipulation parameters and the optimal configuration of the manipulator in the transition from its initial position to the final one. A method for handling of the direct and inverse problems of the manipulator kinematics was developed. The solution is provided for two design options of the gripper.