{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

25gear_geometry

# 25gear_geometry - Gear geometry Consider the curve...

This preview shows pages 1–2. Sign up to view the full content.

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 = E R 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 ⋅π _range_variable θ := tan φ − φ involute φ θ = 8.077deg

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

25gear_geometry - Gear geometry Consider the curve...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online