Abstract: Analyses and experiments demonstrate the potential benefits of optimizing piston and displacer motion in a free-piston Stirling Engine. Isothermal analysis shows the theoretical limits of power density improvement due to ideal motion in ideal Stirling engines. More realistic models based on nodal analysis show that ideal piston and displacer waveforms are not optimal, often producing less power than engines that use sinusoidal piston and displacer motion. Constrained optimization using nodal …