Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.
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