Contrary to the conventional serial kinematics machine tools, the parallel kinematics machine tools exhibit nonlinear behavior which is a major source of the machining error. This causes even a linearly programmed path to be traversed along a nonlinear path. The resulting error, known here as the kinematic error, should be critically considered during the toolpath planning. The estimation of the maximum kinematic error using the concept of median osculating circle is introduced in this article. The proposed formulation demonstrates that the maximum kinematic error depends on the curvature of the actual trajectory. In order to estimate the curvature, constant curvature contour maps are introduced. These maps depend on the structural parameters of the machine and are recommended to be provided by the machine’s manufacturer. The constant curvature contour maps are illustrated to be an effective graphical tool for kinematic error estimation and thus successfully conducting the optimal planning of the toolpath and the workpiece setup. Consequently, it is recommended in this article that the constant curvature contour maps be employed in the format of a database by computer-aided manufacturing systems during toolpath planning and by interpolators during command generation or by a part programmer to optimally setup the workpiece or conduct the toolpath planning such that the least kinematic error occurs during the machining.