The traditional algorithm of arccam contour surface is the profile surface of roller coordinate transformation

then export the contact angle of the formula with the help of engagement theory

simultaneous two equations at last. Its biggest drawback is when the profile surface of the roller is not a straight line

the profile equat ion can not explicit expression

which for solving nonlinear equat ions and the computation is huge and not easy to focus on similar problems. With the differential geometry of surfaces theory

the arc cam profile can be calculated directly with any roller profile shape. The method is simple and easy to spread.