A linear rotary mechanism includes: a pair of elongated guide rails in parallel to each other: a linear motor having a tubular primary side slidably disposed on the guide rails and a shaft-shaped secondary side coaxially extending into an internal hole of the tubular primary side, the shaft-shaped secondary side being axially linearly reciprocally movable along the tubular primary side; and a rotary motor fixedly disposed on the guide rails and connected with one end of the shaft-shaped secondary side. Accordingly, the rotary motor is linearly reciprocally movable along the tubular primary side in synchronism with the shaft-shaped secondary side and the guide rails.

Disclosed herein are methods, systems, and components for the design of a flat belt based block and tackle design that is theoretically free of fleet angles. A mapping technique forms a set of planar positions for the centerlines of the free spans that provides a plurality of sheave geometries, which reside on a common axis and spans that are free of fleet angles at the sheave engagement interfaces. This permits the use of high-performing flat belts in high-reduction block and tackle topologies, with the principal benefits of an extended service life, high power transmission efficiency, more effective traction power transfer, and a compact machine design.