Many fields of active research such as biomedical engineering, electronics, and optics have need of small metallic parts less than 1mm in size, with features measured in hundreds or tens of microns, with tolerances as small as 0.1 micron. Such parts include devices for studying the processes in the human body, devices that can be implanted in the human body, small lenses, and other small components. Micromilling is a microscale manufacturing process that can be used to produce a wide range of small parts, including those that have complex 3- dimensional contours. Micromilling is a process that is, on the surface, similar to conventional-scale milling, except for the use of tools that are around two orders of magnitude smaller than conventional endmills, and spindle speeds that are one or two orders of magnitude faster than conventional milling spindles. However, the underlying physical processes which occur in micromilling are unique due to scale effects, which occur due to the unequal scaling of physical properties between the conventional and the micro scale. One of the more recently-uncovered scale effects in micromilling is the increased ratio of tool size to feature size . This scale effect causes an exacerbation of a kind of geometric error known as chord error and places a fundamental limitation on achievable feedrates within allowable machining error constraints. In this research, we hypothesize that the increase of chord error in microscale milling can be alleviated by intelligent modification of the kinematic arrangement of the micromilling machine. Currently, all 3-Axis micromilling machines are constructed with a Cartesian kinematic arrangement, in which three linear axes are mounted perpendicularly. In this paper, we propose an alternate kinematic arrangement consisting of two linear axes and one rotary axis, creating a Polar kinematic arrangement. Through numerical simulation, we show that there are distinct classes of curvilinear geometries in which the Polar kinematic arrangement is preferable, and allows significant gains in allowable feedrates and reduction in chord error, while other curvilinear geometries show reduced chord error with the Cartesian arrangement.