MTM 2 Notes
Unit 69
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Unit 69: Machining Compound-Angular Surfaces
Big Idea: A compound angle surface can be machined by placing the piece on an angle plate, rotating it with
respect to the tilt axis, then tilting the plate up until the surface to be machined is perpendicular to the axis of the
cutting tool. When the compound angle surface is specified by angles on the orthographic drawings, then
calculating the angles of rotation and tilt are done using these formulas:
Type of Given
Dimensions
Angles
Angle of Rotation
tan  R  
tan  B 
tan  A 
Angle of Tilt
tan  T  
 tan  A   tan  B 
2
2
Big Skill: You should be able to calculate the angles of rotation and tilt for a compound angle surface given
angle dimensions on the faces of the piece to be drilled.
Let’s say you have to machine a compound angle surface on a block of material as specified in the orthographic
views below. Note that angle A will always be on the front face, and angle B will always be on the end
face, and that they are measured from the horizontal (and not the vertical like for compound angle holes).
MTM 2 Notes
Unit 69
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The way to figure out the angles of rotation and tilt is to think of the surface as cutting across all three faces of a
rectangular solid defined by the angles on the orthographic drawing. The trick is to assume that the height of
the solid is H = 1”.
1. What is the angle of rotation R for the compound angle surface above?
2. What is a formula for the angle of rotation R in terms of A and B?
MTM 2 Notes
Unit 69
3. What is the angle of tilt T for the compound angle hole above?
4. What is a formula for the angle of tilt T in terms of A and B?
5. Calculate R and T when A = 25 15 and B = 22 37.
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MTM 2 Notes
Unit 69
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