To meet the quality and flexibility requirements of a hole-making process and to overcome the limitations of traditional manual grinding and cam-type automatic grinding in new drill point geometry development, a three degrees of freedom (3-DOF) parallel-mechanism-based drill point grinder is proposed in this paper. With the consideration of different inclination angle configurations of the grinder guideway, the inverse kinematics and the workspace analysis of the parallel grinder are developed; the relationship between the workspace and the structural parameters of the grinder, such as installation pattern, radius of joint distribution circle, length of the links etc. is discussed in detail. A numerical–symbolic method and a net search method are employed in the singularity analysis. The analysis of the kinematics, workspace and singularity provides the basis for understanding the characteristics of the new parallel grinder and also helps in the structural design of the proposed grinder.