Abstract The present study aims at the development of a new methodology for designing a curve-edged twist drill with an arbitrarily given distribution of the cutting angles along the tool cutting edge. The new methodology consists of 81 major mathematical equations and is developed using a method of mapping relevant planes and straight lines of a cutting tool (such as the cutting plane and the cutting edge) as corresponding image points and image lines on a projection plane. The developed methodology is used to intuitively and graphically analyze and determine the relationship between the orientation of the cutting edge and the cutting angles at each point on the cutting edge. A set of image points and image lines is established to calculate the cutting angles on the cutting edge of a twist drill, including the working tool rake angle, the working tool inclination angle, the working cutting edge angle, and the working normal rake angle. Three computer case studies are provided to show curved cutting edges that correspond, respectively, to a linear distribution of the working tool rake angle, a combined linear and uniform distribution of the working tool rake angle, and a linear distribution of the working tool inclination angle along the tool cutting edge. Finally, a set of metal drilling experiments is performed to compare the drilling torque and the thrust force between a conventional straight-edged twist drill and a new curve-edged twist drill that has a combined linear and uniform distribution of the working tool rake angle along the tool cutting edge. The experimental results show that the new curve-edged drill reduces the drilling torque by 28.5% and the thrust force by 24.6% on average.