With the recent increase in the availability and widespread use of inverters, exotic rare earth permanent-magnet materials, and low-cost, precision manufacturing, new design tools are needed to aid engineers in designing state-of-the-art electromechanical systems. For this purpose, recent software advances allow a reexamination of previously intractable analytical solutions to the boundary value problems governing these systems. This paper presents an analytical field analysis method for electric machines utilizing the Schwarz-Christoffel transformation and implemented with the SIC Toolbox software package. With the method, general 2-D electric machine cross sections with linear magnetic materials are analyzed. The method is then extended using superposition to analyze wound-rotor induction machines in the time domain. With this extension, numerous machine geometries, stator excitations, winding and slot harmonics, and torque ripple can be examined.