Adjustable angle gear

A gear, comprising:

• (a) a circular base having a front surface that includes an inner region and an outer region that surrounds the inner region, the circular base being rotatable about a central axis;
• and
• (b) a plurality of gear teeth arranged in a same row and extending outward from the outer region of the front surface and being evenly spaced from each other along a plurality of locations on the outer region of the front surface, each gear tooth having a cross-sectional width that varies with decreasing distance from the central axis of the gear in a manner that, and having an outer shape configured in a manner that together permit any one of the gear teeth in the row of gear teeth to contact and directly mesh with any one of the gear teeth in a corresponding row of gear teeth of a substantially identical gear for any gear angle within a predefined range of gear angles between the central axis of the ear and the central axis of the substantially identical gear;
• wherein
• (c) the outer shape of each gear tooth of the plurality of gear teeth is defined using a common reference plane perpendicular to the axis of gear rotation and a common reference circle disposed in the reference lane and concentric with the axis of ear rotation, and
• (d) for each gear tooth of the plurality of gear teeth,
• (1) a starting profile for that gear tooth is defined in the reference plane and extends outward from the reference circle,
• (2) for each one of a plurality of locations on the starting profile of that gear tooth,
• (A) a corresponding imaginary ray is associated with that location on the starting profile, the corresponding imaginary ray being defined in the reference plane and extending from the axis of gear rotation to that location on the starting profile,
• (B) a corresponding further axis is associated with that location on the starting profile, the corresponding further axis being tangential to the reference circle at the intersection of the corresponding imaginary ray and the reference circle, and
• (C) the location on the starting profile is rotated out of the reference plane about its corresponding further axis while its distance from the further axis remains fixed, the respective path traversed by that location as it is rotated defining a portion of the outer shape of the gear tooth,
• (3) whereby the respective paths traversed by the plurality of locations on the starting profile combine to define the outer shape of that gear tooth.

A gear system, comprising:

• (a) first and second gears, each one of the first and second gears including:
• (1) a circular base having a front surface that includes an inner region and an outer region that surrounds the inner region, the circular base being rotatable about a central axis, and
• (2) a plurality of gear teeth arranged in a same row and extending outward from the outer region of the front surface and being evenly spaced from each other along a plurality of locations on the outer region of the front surface,
• (3) each gear tooth of the plurality of gear teeth having a cross-sectional width that varies with decreasing distance from the central axis of that gear in a manner that, and having an outer shape configured in a manner that together permit any one of the gear teeth in a row of gear teeth of one of the first and second gears to contact and directly mesh with any one of the gear teeth in a corresponding row of gear teeth of another one of the first and second gears for any gear angle within a predefined range of gear angles between the central axis of the first gear and the central axis of the second gear;
• wherein
• (b) using a common reference plane perpendicular to the axis of gear rotation of the first gear, and a common reference circle disposed in the reference plane and concentric with the axis of gear rotation of the first gear,
• (1) a first pivot is coupled to the first gear and located tangential to the reference circle of the first gear at a first distance from the axis of gear rotation of the first gear such that the entire first gear is movable in a same direction at least within a first range of angles about the first pivot;
• and
• (c) using a common reference plane perpendicular to the axis of gear rotation of the second gear, and a common reference circle disposed in the reference plane and concentric with the axis of gear rotation of the second gear,
• (1) a second pivot is parallel to the first pivot, the second pivot being coupled to the second gear and located tangential to the reference circle of the second gear at a second distance from the axis of gear rotation of the second gear such that the entire second gear is movable in a same direction at least within a second range of angles about the second pivot;
• (d) wherein a distance between the first pivot and the second pivot is fixed, and
• (e) a first angle formed between the inner region of the front surface of the first gear and a mid-plane perpendicular to and bisecting an imaginary line extending from the first pivot to the second pivot, and a second angle formed between the inner region of the front surface of the second gear and the mid-plane, each have a same value, so that for any angle within the first range of angles, the gear tooth of the first gear meshes with the gear tooth of the second gear at a corresponding angle within the second range of angles.