On Weierstrass points of Hurwitz curves

A transmission includes a first simple planetary gear set having first, second, and third elements, the first element of the first gear set receiving rotational motion input to the transmission, and a second simple planetary gear set having first, second, and third elements, the first element of the second gear set outputting rotational motion from the transmission and the third element of the second gear set being connected to the third element of the first gear set. The elements of the first gear set include a sun gear, a first carrier, and a first ring gear, and the elements of the second gear set include a second sun gear, a second carrier, and a second ring gear. A first clutch selectively couples the second element of the first gear set to the first element of the second gear set. A second clutch selectively couples the first element of the first gear set to the second element of the second gear set. A third clutch selectively couples two elements selected from the group consisting of the first, second, and third elements of the first gear set and the third element of the second gear set. A first brake selectively brakes the second element of the second gear set, and a second brake selectively brakes the third element of the second gear set.