25gear_geometry - Gear geometry Consider the curve...

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Gear geometry Consider the curve generated by unwrapping a string from around a disk of radius R B . The end of the string will trace an involute curve. To mathematically define an involute consider the following: R c = length_of_string_unwrapped R C involute curve Rc RB R θ φ E (not exact) () tan φ = tangent with disk at one end R B R B = radius_of_generating_cylinder φ = pressure_angle direction of loading perpendicular along involute curve θ = position_paramter_associate_with_involute E = θ + φ point at loose end of curve is at polar coordinates R, θ E = interim_variable_sum_of_angles length of arc = radius * angle R C = ER B substitute above . .. tan φ + φ R B R B => R C = E = θ + φ = R C = E = θ + φ tan φ = θ basic definition for angular coordinate of involute curve for any φ . Curve is generated by setting φ to range from 0 to max θ = tan φ − φ from geometry . .. cos R B => = R B φ = R the other coordinate, R=pitch_radius R cos φ when φ = pressure angle for design involute curve φ:= 40deg pressure_angle θ 1 := , .. 0 0.01 2 ⋅π 2 _range_variable θ := tan φ − φ involute φ θ = 8.077deg
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25gear_geometry - Gear geometry Consider the curve...

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