Electrical socket with contoured contact beams

An electrical socket, comprising:

• a cylindrical body defining a longitudinal axis and having opposite first and second end rings, a plurality of spaced contact beams extending between the first and second end rings, and an inner receiving area for accepting a mating pin, the first and second end rings being rotatably offset from one another with respect to the longitudinal axis, thereby twisting the contact beams into a hyperbolic geometry, and each of the contact beams comprising a middle section between first and second end sections, the first and second end sections being attached to the first and second end rings, respectively, and
• wherein the middle section of each contact beam has a contour that defines an inner contact area such that the middle section extends further into the inner receiving area than the first and second end sections and such that the inner contact areas are positioned for contact with the mating pin when inserted into the inner receiving area, the contour of each of the middle sections of each contact beam comprising angled radii forms extending across the middle section substantially parallel to the longitudinal axis of the cylindrical body, and
• wherein the angled radii forms are configured to match to the radius of a mating pin, such that the angled radii forms defined tangent points with the inner contact area being between the tangent points, such that the inner contact areas are positioned for smooth contact with the mating pin when inserted into the inner receiving area of the cylindrical body.