In the design of a planar conveying machine, individual links must be arranged separately on parallel planes, which are called layers in this paper, to avoid mutual interference among moving links during a cycle of motion. In the present study regarding a planar 6-link conveying machine, conditions which determine the minimum number of layers required for constructing the conveying machine are formulated. Moreover, in order to determine the optimum profiles of links which satisfy the minimum number of layers to avoid mutual interference among moving links, relative loci of pairing points and positions of links on the same layer during a cycle of motion are analyzed. Based on the results of analysis the planar 6-link conveying machine satisfying minimum number of layers is synthesized.