DESIGN OF RATIONAL CAM PROFILES WITH PYTHAGOREAN-HODOGRAPH CURVES

Current cam design practice, based on acceleration curves defined by t rigonometric, polynomial, or spline functions of the rotation angle, y ields profiles that require approximation before they can be imported to CAD systems or downloaded to CNC machines. A novel approach, employ ing Pythagorean-hodograph (PH) curves to define transitional segments of the pitch curve, is described: the polynomial rectification and rat ional offset properties of these curves eliminate computational limita tions to the accuracy of cam manufacture. The pitch curve and cam shap e both admit exact representation in CAD systems, and for a roller fol lower their coefficients can be passed directly to a CNC mill incorpor ating a real-time PK-curve interpolator to cut the cam using a tool wi th the same radius as the roller. In particular, algorithms for degree -9 PH pitch curves are presented that require only the solution of a c omplex quadratic equation, and provide four free parameters for adjust ing the output displacement, velocity, and acceleration curves. (C) 19 98 Elsevier Science Ltd. All rights reserved.