In this paper, we introduce a strategy for the design and computational analysis of compliant DNA origami mechanisms (CDOMs), which are compliant nanomechanisms fabricated via DNA origami self-assembly. The rigid, compliant, and flexible parts are constructed by bundles of many double-stranded DNA (dsDNA) helices, bundles of a few dsDNA helices or a single dsDNA helix, and single-stranded DNA (ssDNA) strands, respectively. Similar to its macroscopic counterparts, a CDOM generates its motion via deformation of at least one structural member. During the motion, strain energy is stored and released in the compliant components. Therefore, these CDOMs have the advantage of suppressing thermal fluctuations due to the internal mechanical energy barrier for motion. Here, we show that classic pseudorigid-body (PRB) models for compliant mechanism are successfully employed to the analysis of these DNA origami nanomechanisms and can serve to guide the design and analysis method. An example of compliant joint and a bistable four-bar CDOM fabricated with DNA origami are presented.