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

• Published in: Computer aided geometric design Vol. 31; no. 1; pp. 13 - 26
• Main Authors: Farouki, Rida T., Han, Chang Yong, Li, Shiqiao
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2014
• Subjects: 5-axis CNC machining; Ball-end tool; Computer numerical control; Cutting speed; Inverse kinematics; Machining; Mathematical analysis; Mathematical models; Orientable-spindle machine; Orientable-table machine; Orientation; Sampling; Tool orientation; Tool orientation; Ball-end tool; Orientable-table machine; 5-axis CNC machining; Orientable-spindle machine; Inverse kinematics
• ISSN: 0167-8396; 1879-2332
• DOI: 10.1016/j.cagd.2013.11.002

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.