Abstract:Screw theory has some advantages, such as legible geometry concept, explicit physical meaning and simple expression form and so on. With these advantages, it is often be used to analyze the DOF (Degree of Freedom) of mechanisms. According to the conventional GK formula, it is easy to compute the DOF of serial mechanisms, but for some special mechanisms, in particular the complicated parallel mechanisms with closedloop sub chains, it is difficult to get a reasonable DOF. A Delta robot was studied which was owning 〖BF〗3R(4S)&1RUPU]+R〖BFQ〗 topology. To solve the problem which was mentioned above, the equivalent kinematic pair screw system was solved to the 4S closedloop sub chain, and second, the idle DOF and common constraint were discriminated. Using the modified GK formula, the DOF of the original mechanism and the equivalent one were examined. The results show that the number of the DOF is four in both case, and the character of DOF includes three translation and one rotation, which matches the practical case.