Tool positioning for 3½½-axis and 5-axis surface machining

The work in this thesis presents two new tool positioning strategies that are simple to implement and compute. The first is called the Rolling Ball Method (RBM), which makes use of a new concept developed in this thesis called 'regional curvature'. In the RBM, a variable radius ball is rolled along the tool path. At each tool position, a small region of the ball's surface is used to approximate a small region of the surface being machined. The radius of each ball is computed by checking a grid of points in the area of the surface that the tool casts a shadow over for each tool position. A Pseudo-Radius is computed for each grid point and the most appropriate radius is selected to be the rolling ball's radius. The selection process follows a hierarchy of surface profiles ranging from convex to concave. Convex, concave, and saddle (mixed) surface regions are all computed in a similar fashion and there are no special cases for which the positioning strategy must be altered to compute a tool position. Local gouge checking is automatically incorporated into the position computations, eliminating the need to perform the typical iterative strategy of checking for gouging and incrementally tilting the tool until no gouges are detected. The method is shown to be robust and simple to implement since only surface coordinates and surface normals are required in the algorithm. This computational method allowed for the development of a graphics-assisted implementation that uses the computer's graphics hardware to position the tool to triangulated surface data.; The second method presented in this thesis is called the Arc-Intersect Method (AIM), which improves upon the RBM by eliminating the use of an overly conservative area and directly positioning the tool to touch the surface region. As with the RBM, the AIM is applied to triangulated surfaces and uses the computer's graphics hardware to assist in the tool position calculations. This means the strategies can be applied to any surface representation, since they only use surface coordinates and surface normals for computation.; An inherent problem with 5-axis machining is that it can suffer from dramatic reductions in the feed rate when the tool axis is in the vicinity of the singularity point of the machine and during large orientation changes. 3½½-axis machining offers an alternative strategy that can be used to overcome this problem and still maintain some of the salient features of 5-axis to improve machining times over conventional 3-axis ballnose machining. In 3½½-axis machining, the tool orientation is locked during cutting so the motion of the machine is only in its three linear axes and the two rotary axes are locked, which generates more consistent feed rates than simultaneous 5-axis machining. A new tool positioning strategy, based on the 5-axis AIM positioning strategy, is presented here for 3½½-axis machining on continuously variable 5-axis machines. (Abstract shortened by UMI.)...