This Linnaeus’s Two-Toed Sloth (Choloepus didactylus) is kindly demonstrating the suspensory locomotion that extant sloths (Choloepus, Bradypus) typically engage in. Two- and Three-Toed Sloths are distant relatives and since no known fossil sloths were suspensory, this suggests the unusual method of locomotion evolved convergently (Pujos et al. 2012). As for how the 400+ extinct sloths got around, it was much more variable than the “ground sloth” label implies; some burrowed (Scelidotherium, Glossotherium), had some bipedal capability (Megatherium), were tree climbers (some Antillean species), rock climbers (Diabolotherium), and even aquatic and semi-aquatic (Thalassocnus) (Pujos et al. 2012).
Pujos, F., et al. (2012) Recent Advances on Variability, Morpho-Functional Adaptations, Dental Terminology, and Evolution of Sloths. Journal of Mammalian Evolution DOI: 10.1007/s10914-012-9189-y