Direct coordinate changes
Modeling and control of robot manipulators

Each body i of the mechanism is associated with a direct orthonormal reference frame {X_i , Y_i, Z _i } noted R_i. The particular reference marks are, on the one hand, that of the base {X 0 , Y₀ , Z₀ } noted R₀ and, on the other hand, that, R_n , of the end member {X_n , Y_n , Z_n }. The base reference frame occupies a known position and orientation relative to a fixed reference frame if the robot is at a fixed station in a workshop, or linked to a carrier vehicle to which the base is rigidly attached. The last R_n reference point can be linked to the end effector coupling device as well as to the end effector, which is rigidly attached to it. Its instantaneous situation is called a pose.