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This paper describes the creation of novel transmission mechanisms using algebraic design techniques. The objective is to create novel arrangements comprised of one or more planetary gear sets, a pair of motor-generators and several torque-transmitting mechanisms (clutches and brakes). The algebraic design procedure represents the planetary gear sets, fixed interconnections, clutches/brakes, and motor-generator sets as algebraic constraints. Appropriate subsets of constraint equations are solved to identify viable transmission mechanism designs. We have used the above design approach to create several novel candidate multi-speed transmissions as well as EVT concepts. The main benefit of the algebraic design procedure is that it allows the designer to systematically generate and assess novel designs.