Transmission device

A transmission mechanism for transmitting motion between a rotating shaft and a linearly translating member having nonparallel axes, comprising a set of cams disposed at axially spaced-apart locations on said rotating shaft for rotation therewith about said axis of said rotating shaft, and corresponding arrays of spaced-apart rollers connected to said linearly translating member for movement therewith, each said cam being in a common plane with one of said corresponding arrays of spaced-apart rollers placed in axially extending rows on said linearly translating member, said axially extending rows being parallel to a direction of motion of said linearly translating member, and wherein each said cams has a fully convex contoured cam surface generated by a vector rc which is defined as follows:

• a 3 ⁢ < ⁢ a 1 1 ⁢ + ⁢ 1 / N k 1 ⁢ = ⁢ - 2 ⁢ ⁢ π ⁢ ⁢ a 3 N ⁢ ⁢ sin ⁢ ⁢ α 1 k 2 = ( 2 ⁢ ⁢ π ⁢ ⁢ a 3 ⁢ ⁢ ψ ⁢ ⁢ sin ⁢ ⁢ α 1 N ) 2 ⁢ + ⁢ ( a 1 ⁢ + ⁢ a 3 ⁢ + ⁢ 2 ⁢ ⁢ π ⁢ ⁢ a 3 ⁢ ⁢ sin ⁢ ⁢ α 1 N ) 2 k 3 = arctan ⁢ ⁢ ( - 2 ⁢ ⁢ π ⁢ ⁢ a 3 ⁢ ⁢ ψsin ⁢ ⁢ α 1 ( a 1 ⁢ + ⁢ a 3 ) ⁢ ⁢ N ⁢ + ⁢ 2 ⁢ ⁢ π ⁢ ⁢ a 3 ⁢ ⁢ sin ⁢ ⁢ α 1 ) r c = [ k 1 ⁢ ⁢ cos ⁢ ⁢ ψ ⁢ + ⁢ ( k 2 ⁢ - ⁢ a 4 ) ⁢ ⁢ cos ⁢ ⁢ ( k 3 - ψ ) - k 1 ⁢ ⁢ sin ⁢ ⁢ ψ ⁢ + ⁢ ( k 2 ⁢ - ⁢ a 4 ) ⁢ ⁢ sin ⁢ ⁢ ( k 3 - ψ ) λ ]
• wherein:
• ψ:
• is an angle of rotation of the rotating shaft;
• α1:
• is the angle between the rotating shaft and the linearly translating member;
• a1:
• is a distance between the axis of the rotating shaft and a reference line parallel to the direction of motion of said linearly translating member;
• a3:
• is a distance between the reference line and an axis passing through the center of the rollers;
• a4:
• is a radius of the rollers;
• ki:
• are temporary variables, where i=1,2,3 . . .
• λ:
• is a real number defining one specific point along the contoured cam surface
• 1/N:
• where N is an integer denoting the number of rollers on each side of the linearly translating member that enter in contact with corresponding cams upon a 360 degrees rotation of cam shaft;
• and in which a3 satisfies the following condition:
• a3<a1/(2/N+1).