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As one of the most important force production mechanisms of swimming and flying animals, the fluid dynamics of flapping has been intensively studied. However, these efforts have been mainly directed toward animals in forward motion or locomotive appendages undergoing linear translation. Here we seek to complement the existing knowledge of the flapping mechanism by studying angularly reciprocating flat plates without a free stream velocity, under a so-called ‘bollard pull’ condition. We visualize the flow field around the flat plate to find that two independent vortical structures are formed per half-cycle, resulting in the separation of two distinct vortex pairs at sharp edges rather than a single vortex loop which is typical of a starting–stopping vortex paradigm in flows with free streams. Based on our observations, we derive a scaling law to predict the thrust of the flapping plate; this is the first experimentally validated theoretical model for the thrust of angularly reciprocating plates without a prescribed background flow.