1. Field of the Invention
This invention relates to a method for generating tool paths in CAD (Computer Aided Design)/CAM (Computer Aided Manufacturing) systems, and more particularly to a method for generating tool paths which can easily check the collision with a tool and can enhance efficiency in manufacture by offset-processing environmental model including a workpiece which is expressed in solid models.
2. Description of the Prior Art
The issue of tool path generation has so far been approached from points of automatic programming system and so on typified by APT (Automatically Programmed Tools. In the automatic programming system, however, patterns of workpieces should be recognized by operators, and if the workpieces are of complicated shapes, it should require much skill and time.
What is most principal in the issue of tool path generation are the problems related to the collision between the environmental model and the tools such as:
1. The problem to recognize the area where cutting is impossible in a designated tool approach direction; PA0 2. The problem of the collision between the environmental model including the workpiece and the portion the tool does not cut; and PA0 3. The problem of how to recognize an intersurface relation between an area to be cut which may comprise plural surfaces and the cutting edge of the tool.
In order to solve the above problem, in the APT system, as shown in FIG. 1, an operator should set three surfaces where a tool TL can move: i.e. a part surface PS, a drive surface DS and a check surface CS. The intersurface relation or the collision check between an envionmental model (3D-solid model) and a tool (3D-solid model) cannot be solved analytically, and even if solved by the search, it would consume much time and energy. In offset-processing, the conventional method needs a large amount of data as new points should be obtained by the following equation (1) for each point on the surface and an offset surface should be formed by interpolating those new points. FIG. 2 shows the relation between the original surfaces RS and an offset surface OFS wherein the points X.sub.1, X.sub.2, . . . , X.sub.n are respectively offset value OF to become the points X.sub.1 .degree., X.sub.2 .degree., . . . , X.sub.n .degree. on the offset surface OFS. The relation can be expressed mathmatically by the equation (1) below: EQU X.degree.=X.+-.OF.multidot.N(X) (1)
wherein OF denotes the offset value, and N (X) denotes a unit normal vector at a point X. The offset surface OFS thus obtained is an approximated surface, and therefore the collision check with tools cannot be solved analytically therein.
Studies have been conducted in recent years to generate tool paths by building up in advance 3D-solid models in a computer, and modifying the models for a particular problem everytime it needs to be solved. Two types of the solid models exist; i.e. CSG (Constructive Solid Geometry) and B-Reps (Boundary Representation). As shown in FIG. 3, CSG is advantageous in that the data structure is simple and processing at high speed is possible, since a shape can be expressed by a set operation of primitives such as a cylinder, a rectangular parallelepiped, etc. On the other hand, B-Reps is not expected to operate at higher speed as the amount of data is large and the structure complicated as shown in FIG. 4. It creates a closed two-dimensional manifold in a three-dimensional space for modeling by supplying the basic topological data of a model and the geometric data on elements of the topological relation such as a vertex, an edge and a curved surface.