In this paper, the inequivalence of the direct-contact mechanisms and their equivalent four-bar linkages in jerk analysis is discussed. Kinematic analyses for three classical types of direct-contact mechanisms consisting of: (a) higher pairs with permanently invariant curvature centers, (b) higher pairs with suddenly changed curvature, and (c) higher pairs with continuously varying curvature are performed, respectively, through their representative case studies. The analyzed results show that the equivalent four-bar linkage cannot give a correct value of jerk for most situations in the three case studies. Subsequently, the concept of “equivalent six-bar linkage” for direct-contact mechanisms is proposed in order to discuss the infeasibility of the equivalent four-bar linkage for jerk analysis. It is found that the suddenly changed or continuously varying curvature of the higher pairs is not considered in sudden or continuous link-length variations of the equivalent four-bar linkage, which further leads to inconsistency between the angular accelerations of the coupler and the contact normal, and finally results in the infeasibility of the equivalent four-bar linkage for jerk analysis of most direct-contact mechanisms. It is also found that the concept of equivalent six-bar linkage could be applied to evaluate more higher-order time derivatives for most direct-contact mechanisms. The presented case studies and discussion can give demonstrations for understanding the inequivalence of the direct-contact mechanisms and their equivalent four-bar linkages in the aspect of jerk analysis.
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