Due to the potential advantages of heavy load, high speed, and high precision, hundreds of parallel kinematic machines have been proposed. However, only a few of them have been practically applied, and one of the recently-developed parallel kinematic machines is the Exechon machine tool. It is based on the success of the Tricept, and its inventor has made tremendous efforts to promote its machining applications in aerospace and automotive manufacturing. The current control system of the Exechon machine tool has been developed by Siemens. However, quantifiable theoretical studies have not yet conducted to prove its super performance, and its kinematic model has been publically available. In this paper, the kinematic characteristics of this new machine tool is investigated, the concise models of forward and inverse kinematics have been developed. These models can be used as a tool or references for the evaluation of the performances of the Exechon machine tool or other over-constrained parallel kinematic machines.