A bushing for use in a tracked undercarriage of a track-type machine includes a first end and a second end disposed opposite the first end. An outer surface extends between the first end and the second end and is shaped to engage a sprocket of the tracked undercarriage. The bushing also includes an annular inner surface disposed between the first end and the second end defining an internal cavity shaped to receive a track pin. An innermost portion of the inner surface forms a crown having a radius less than or equal to (PL2)/[(24E pDRBush 4)(l-cos[(PL)/(16EpDRBush 4))] where L is the length of the bushing, P is the weight of the track-type machine, E is the Modulus of Elasticity of the bushing, and RBush is a radius of the innermost portion of the annular internal cavity.