Abstract: Methods and systems for measuring multi-turn angular position include a system of N gears meshed with one another, each gear having a unique number of teeth. A first gear is mounted to an input shaft. A set of N angular position sensors are each configured to measure the angular position of a respective gear in the system of N gears within one rotation. A control module is configured to determine an angular position of the input shaft over multiple rotations using the measured angular positions of the N gears.

Abstract: Described herein is a footwear and an article for keeping a foot dry, and a related method. A footwear member may have an exterior surface defining an exterior of the footwear member, an internal surface defining an internal cavity sized to receive the foot and at least portions of the removable membrane, and a footwear size. The removable membrane may be made of a non-rigid, disposable, resilient material that is impermeable to water. The removable membrane may have a membrane exterior surface, a membrane interior surface, and a membrane size corresponding to the footwear size. The removable membrane configured to conform to a shape and a size of the foot. The method may include providing a footwear assembly including a footwear member and a removable membrane, placing the provided membrane over the foot, and positioning the removable membrane with the foot inserted therein within the boot.

Abstract: Methods and systems for measuring multi-turn angular position include a system of N gears meshed with one another, each gear having a unique number of teeth. A first gear is mounted to an input shaft. A set of N angular position sensors are each configured to measure the angular position of a respective gear in the system of N gears within one rotation. A control module is configured to determine an angular position of the input shaft over multiple rotations using the measured angular positions of the N gears.

Abstract: Methods and systems for measuring angular position include measuring an angular position within one rotation of a primary gear and a secondary gear that are meshed together. The primary gear and secondary gear have a first and second number of teeth respectively, where the first number of teeth and the second number of teeth are different. An angular position for the secondary gear is estimated using the measured primary gear angle and a reference value for each of the primary and secondary angle sensors. A number of primary gear rotations is calculated using the estimated angular position for the secondary gear and the measured angular position of the secondary gear. An angular position of the primary gear is calculated over multiple rotations using the calculated number of primary gear rotations, a reference value for the primary angle sensor, and the measured angle value of the primary gear within one rotation.

Abstract: An article for keeping a foot (and potentially a sock) dry, when placed within a boot, the article comprising a non-rigid membrane impermeable to water and disposable material, and conformed to the shape of the foot so that there is little or no excess material when the article is placed over the foot (and potentially the sock, and both are) placed within the boot. The article may comprise a toe section, heel section, lower leg section, top opening, and a means for preventing the lower leg section and the top opening from falling down. Notwithstanding its disposability, the material comprising the article may be sufficiently resilient and durable for withstanding the frequent and substantial forces that the boot and foot may be subjected to during a work day at a wet construction site. The article may also allow continued use of a punctured previously-waterproof boot without the foot becoming wet.

Abstract: Methods and systems for measuring angular position include measuring an angular position within one rotation of a primary gear and a secondary gear that are meshed together. The primary gear and secondary gear have a first and second number of teeth respectively, where the first number of teeth and the second number of teeth are different. An angular position for the secondary gear is estimated using the measured primary gear angle and a reference value for each of the primary and secondary angle sensors. A number of primary gear rotations is calculated using the estimated angular position for the secondary gear and the measured angular position of the secondary gear. An angular position of the primary gear is calculated over multiple rotations using the calculated number of primary gear rotations, a reference value for the primary angle sensor, and the measured angle value of the primary gear within one rotation.

Abstract: An interaction system for facilitating user interaction between users using different virtual environments may generate a user interaction interface for the first user. The user interaction interface may present status information regarding a second user currently participating in a second virtual environment to the first user, while the first user may be participating in a first environment that is different from the second environment. The user interaction interface may facilitate real time or near real time interaction between the first user and the second user.

Abstract: A transaction system for purchasing virtual goods, which are to be expressed within multiple virtual environments, may receive a selection from a user for one or more virtual goods. The transaction system may receive a selection for a plurality of virtual environments within which the selected virtual good(s) are to be expressed upon completion of the purchase transaction.

Abstract: A safety device for a cantilevered beam pivotally mounted adjacent one end thereof to a support surface is adapted to bridge the beam and the support surface and is structured so that when coupled to the beam and support surface, the safety device maintains the beam in a substantially fixed cantilevered condition until a downward force exceeding a threshold is applied to the beam and thereafter controls downward pivoting of the beam.