Compact　and　lightweight　rotary　series　elastic　actuator　(SEA)　is　a　new　scheme　to　realize　safe　and　friendly　human-robot　interaction　of　exoskeletons　and　other　human-robot　interaction　applications.　The　custom　monolithic　torsional　elastic　element　is　a　good　choice　for　the　compact　design　of　rotary　SEA,　but　there　is　a　lack　of　guidance　on　selecting　the　topology　of　elastic　elements　in　a　lightweight　SEA　design.　In　this　paper,　with　the　help　of　the　concept　of　specific　energy,　a　method　based　on　finite　element　simulation　environment　and　parametric　3D　CAD　environment　is　proposed　to　determine　the　topology　of　the　elastic　element　suitable　for　lightweight　SEA　by　maximizing　the　specific　energy.　By　adopting　this　method,　we　come　to　this　conclusion:　The　topology,　Archimedes-spiral-based　double　spiral　structure　without　the　outer　ring,　can　be　determined　as　a　suitable　topology　of　elastic　element　for　a　lightweight　rotary　SEA.　©　Published　under　licence　by　IOP　Publishing　Ltd.