A self-organizing mechanical system is currently developed at the Mechanical Engineering Laboratory. The system is composed of many mechanical units and in order to generate cooperative motion, it is required to establish common clock timing. In this paper, two algorithms are proposed to establish the common clock without being trapped in a deadlock condition. The algorithms work in the situation that all units follow the same procedure and neighbor-neighbor communication is possible. The operation of the units is analyzed with a physical spring damper model and it is concluded that with these algorithms the common clock timing can be established if parameters are chosen correctly in each unit.