Gear form constructions

A gearing system comprising:

• a first gear having a first plurality of teeth each having a first tooth profile lying entirely within the pitch circle of said first gear;
• and
• a mating gear having a second plurality of teeth each having a second tooth profile, conjugate to said first tooth profile through all transverse sections of the first and second profiles, and lying entirely outside the pitch circle of said mating gear, said first and second tooth profiles having a common normal at a contact point which always passes through a pitch point of said first and second tooth profiles, said first and second tooth profiles further satisfying the equation:
• 1 ρ 1 - S + 1 ρ 2 + S = 1 sin ⁢ ⁢ φ ⁢ ⁢ ( 1 R p1 + 1 R p2 )
• wherein Rρ1 and Rρ2 are pitch circle radii, φ is the gear pair pressure angle, S is the distance from the pitch point to the contact point, wherein S is positive when the contact point lies on one side of a line of centers, and is a negative when the contact point lies on another side of the line of centers, and wherein ρ1 and ρ2 represent radii of curvature, wherein the radii of curvature are positive for convex profiles and negative for concave profiles,
• wherein a relative curvature of said first tooth profile of said first gear and said second tooth profile of said mating gear is substantially a constant.

A gearing system comprising:

• a first gear having a first plurality of teeth each having a first tooth profile lying entirely within the pitch circle of said first gear, said first tooth profile having a radius of curvature p1;
• and
• a mating gear having a second plurality of teeth each having a second tooth profile, conjugate to said first tooth profile through all transverse sections of the first and second profiles, and lying entirely outside the pitch circle of said mating gear, said second tooth profile having a radius of curvature ρ2, said first gear and said mating gear having a gear pressure angle φ,
• wherein the function 1 cos ⁢ ⁢ φ ⁢ ( 1 ρ 1 + 1 ρ 2 ) = C
• wherein C is a constant, said first and second tooth profiles having a common normal at a contact point which always passes through a pitch point of said first and second tooth profiles, said first and second tooth profiles further satisfying the equation:
• 1 ρ 1 - S + 1 ρ 2 + S = 1 sin ⁢ ⁢ φ ⁢ ⁢ ( 1 R p1 + 1 R p2 )
• wherein Rρ1 and Rρ2 are pitch circle radii, φ is the gear pair pressure angle, S is the distance from the pitch point to the contact point, wherein S is positive when the contact point lies on one side of a line of centers, and is a negative when the contact point lies on another side of the line of centers, and wherein ρ1 and ρ2 represent radii of curvature, wherein the radii of curvature are positive for convex profiles and negative for concave profiles.

A gearing system comprising:

• first gear having a first plurality of teeth each having a first tooth profile lying entirely within the pitch circle of said first gear, said first tooth profile having a radius of curvature ρ1;
• and
• a mating gear having a second plurality of teeth each having a second tooth profile, conjugate to said first tooth profile through all transverse sections of the first and second profiles, and lying entirely outside the pitch circle of said mating gear, said second tooth profile having a radius of curvature ρ2 said first gear and said mating gear having a gear pressure angle φ,
• wherein the function 1 cos ⁢ ⁢ φ ⁢ ( 1 ρ 1 + 1 ρ 2 ) = C
• wherein C is substantially a constant, said first and second tooth profiles having a common normal at a contact point which always passes through a pitch point of said first and second tooth profiles, said first and second tooth profiles further satisfying the equation:
• 1 ρ 1 - S + 1 ρ 2 + S = 1 sin ⁢ ⁢ φ ⁢ ⁢ ( 1 R p1 + 1 R p2 )
• wherein Rρ1 and Rρ2 are pitch circle radii. 0 is the gear pair pressure angle, S is the distance from the pitch point to the contact point, wherein S is positive when the contact point lies on one side of a line of centers, and is a negative when the contact point lies on another side of the line of centers, and wherein ρ1 and ρ2 represent radii of curvature, wherein the radii of curvature are positive for convex profiles and negative for concave profiles.