The paper deals with the problem of kinematic synthesis of dwell linkage mechanisms which are based on the four-bar linkage with a coupler point that traces a curve with a straight-line part. It enables to obtain a dwell of the output link of the mechanism, but the main goal is to find such parameters of the mechanisms that hold the required conditions of the designer: necessary dwell time, to satisfy the necessary cyclogram of the machine with taking into account the number of additional parameters. The main problem is to carry out the kinematic synthesis of the basic straight-line linkage that can be done by the kinematic geometry methods. In this paper it is shown that the fivefold interpolation nodes of the coupler curve with the tangent line can be successfully used to satisfy the necessary criteria. As a result of carried out researches, the regions of existence of such mechanisms’ parameters were determined and that allows to carry out an optimization procedure using different criteria.