A radial cam engine with an optimized cam configuration can provide improve performance over crankshaft internal combustion engines. The cam configuration can include a flat-top or flat bottom piston motion, multiple lobe cam configurations, matching piston force with torque/force ratio in combustion phase, asymmetry piston motions for improved power transfer during combustion phase, and/or offset piston and cam configurations. The radial cam engine can be used in vehicles, such as hybrid vehicles.