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<p>Mechanisms are prone to stuttering or even jamming due to the deformation of components, especially for overconstrained linkages for which geometric conditions must be strictly satisfied. In this paper, joint clearance is actively introduced to release the local constraint so that the linkages can still achieve general movement under the deformation of components. And a joint clearance model with a revolute joint (<span class="inline-formula"><i>R</i></span>-joint) is built. Based on the model, the minimum joint clearance introduced, which keeps mechanisms moving smoothly, is found when the components of the linkages have a certain deformation. The correctness of the proposed method is verified with a numerical case, and the optimal position for clearance introducing is analyzed. It opens up an important way to solve the phenomenon of stuttering or jamming in overconstrained linkages.</p>