Generators are presented herein for generating power outputs using a plurality of linear electromagnetic machines (LEMs) affixed to a frame such that adjacent LEMs interact with a single power cylinder. The power cylinder includes a reaction volume, a first bore coaxial with a first axis, and a second bore coaxial with a second axis, different from the first axis, wherein the first axis and the second axis intersect in the reaction volume. The frame includes a plurality of members arranged in a polygon and a plurality of intermediate structures each comprising respective rigid extension, wherein each respective rigid extension is fixedly attached to respective axial ends of adjacent members of the plurality of members. Adjacent LEMs of a plurality of LEMs are coupled at each respective axial end of each respective LEM to the power cylinder using an intermediate structure of the plurality of intermediate structures.