The method of classification of mechanisms according to kinematic structure and function is used to systematically enumerate gearless differential mechanisms. The method adopted here is to first enumerate 1:-1 constant-velocity shaft couplings which are later transformed into gearless differential. Preliminary screening of the enumerated mechanisms resulted in four potential 1:-1 constant-velocity shaft couplings that are free from singular conditions. With a little modification, these mechanisms are then converted to gearless differentials. A promising candidate mechanism is chosen and kinematic and dynamic analyses are performed. The dynamic analysis is done using the software package DADS. It is shown that the proposed mechanism does have the potential for use as a gearless differential. Finally design rules are laid out which can be used for the design of an optimal gearless differential.