The article describes a new class of manipulators, built on the basis of solid elements with a spherical surface. Their bending link is implemented by changing the lengths of the cables passing through 4 holes on the edges of the elements. The authors propose a method for a synthesis of a complete kinematic model of such manipulator's link. The main problems were with finding solutions to the fact that when a link is bent, there was a complex movement of the components' link: a turn of the coordinate system of the elements and their movement via the complicated path - epitrihoide. In the received kinematic model the movement of the manipulator was simulated (a direct problem of kinematics) and constructed on the basis of 1, 2, 3 and 4 links. A solution to the inverse kinematic task for a link manipulator based on a geometric approach was also obtained. The problems, which have to be taken into account when solving the direct and inverse dynamic tasks: 1) stretching of ropes of the flexural link and load changes; 2) non-linearity: transition from a static friction to the rolling friction at the points of contact of the elements at the beginning of the movement of elements. One possible solution is installation of 3-axis accelerometers and gyroscopes to link the elements for the study of the above-mentioned phenomena. A large number of matrix transformation multiplications require development of algorithms for fast calculation and relevant hardware architecture.