Inverse kinematics for optimal tool orientation control in 5-axis CNC machining

The problem of determining the inputs to the rotary axes of a 5–axis CNC machine is addressed, such that relative variations of orientation between the tool axis and surface normal are minimized subject to the constraint of maintaining a constant cutting speed with a ball-end tool. In the context of an orientable–spindle machine, the results of a prior study are directly applicable to the solution of this inverse–kinematics problem. However, since they are expressed in terms of the integral of the geodesic curvature, a discrete time–step solution is proposed that yields accurate rotary–axis increments at high sampling frequencies. For an orientable–table machine, a closed–form solution that specifies the rotary–axis positions as functions of the surface normal variation along the toolpath is possible. In this context, however, the feasibility of a solution is dependent upon the surface normal along the toolpath satisfying certain orientational constraints. These inverse–kinematics solutions facilitate accurate and efficient 5–axis machining of free–form surfaces without “unnecessary” actuation of the machine rotary axes. keywords: 5–axis CNC machining; tool orientation; inverse kinematics; ball–end tool; orientable–spindle machine; orientable–table machine. e–mail: [email protected], [email protected], [email protected]