Abstract: A rotary displacement device which can be a spherical internal combustion engine, comprising a housing having a generally spherical cavity therein; a displacement member with generally spherical inner and outer configurations mounted within the cavity in the housing; and a drive mechanism including a drive shaft with a nutating member mounted thereto at a spherically shaped mounting portion positioned within the inner spherical configuration of the displacement member. The drive mechanism, displacemnent member and spherical cavity all share a common, fixed, center point. The displacement member travles in an arc within the cavity such that the axis of the arc passes through the center point. The displacement member drives the nutating member through a defined movement path which path passes through the center point. The nutating member drives the drive shaft in a rotational path the axis of which passes through the common center point.