Origami processes can generate both rigid and compliant structures from the same homogeneous sheet material. In this article, we advance the origami robotics literature by showing that it is possible to construct an arbitrary rigid kinematic chain with prescribed joint compliance from a single tubular sheet. Our “Kinegami” algorithm converts a Denavit–Hartenberg specification into a single-sheet crease pattern for an equivalent serial robot mechanism by composing origami modules from a catalogue. The algorithm arises from the key observation that tubular origami linkage design reduces to a Dubins path planning problem. The automatically generated structural connections and movable joints that realize the specified design can also be endowed with independent user-specified compliance. We apply the Kinegami algorithm to a number of common robot mechanisms and hand-fold their algorithmically generated single-sheet crease patterns into functioning kinematic chains. We believe this is the first completely automated end-to-end system for converting an abstract manipulator specification into a physically realizable origami design that requires no additional human input.