The paper deals with the problems of direct kinematics related to a 2T6R robot, the direct kinematics of the plane mechanism of the robot. The direct kinematics of this proposed new robot help to study the movement, including the dynamic one, to determine the forces in the mechanism and to model the possible trajectories of the final effector point, thus determining the robot's working space and some of its multiple possible uses. Two totally different methods were used to verify the calculation relations, the results obtained by both methods being practically identical. The first method used is an original trigonometric method, and the second is an original geometrically analytical method.