Maintaining clearance, or distance from obstacles, is a vital component of successful motion planning algorithms. Maintaining high clearance often creates safer paths for robots. Contemporary sampling-based planning algorithms That utilize The medial axis, or The set of all points equidistant To Two or more obstacles, produce higher clearance paths. However, They are biased heavily Toward certain portions of The medial axis, sometimes ignoring parts critical To planning, e.g., specific Types of narrow passages. We introduce Uniform Medial Axis Probabilistic RoadMap (UMAPRM), a novel planning variant That generates samples uniformly on The medial axis of The free portion of Cspace. We Theoretically analyze The distribution generated by UMAPRM and show its uniformity. Our results show That UMAPRM's distribution of samples along The medial axis is not only uniform but also preferable To other medial axis samplers in certain planning problems. We demonstrate That UMAPRM has negligible computational overhead over other sampling Techniques and can solve problems The others could not, e.g., a bug Trap. Finally, we demonstrate UMAPRM successfully generates higher clearance paths in The examples.