A vertical stepping machine includes a frame, a crank wheel connected to the frame, a crank arm extending away from a rotational axis of the crank wheel, and a pedal beam connected to the crank arm. A linkage assembly is connected to the frame at a fixed frame location and to the pedal beam at a fixed pedal beam location. A first linkage member of the linkage assembly has a length that forces the pedal beam to travel along an elliptical path as the crank wheel rotates.