Closed form equations for kinematic variables that control motions in a LLLRR five-axis machine were developed using a kinematic closed loop link mechanism model based on the principles of Denavit-Hartenberg 4×4 transformation techniques. These equations developed here can be used to grinding the ball nose mill on the five-axis machine. Details of the equations for grinding the rake face and flank face of the ball nose mill were presented. Conical grinding wheel produces rake face and cylinder face grinding wheel forms flank face. The equations are simply enough to be solved on line with a computer.