System and method for locating clamping points for a part to be manufactured through computer numerical control (CNC) machining operations with the aid of a digital computer

A system for locating clamping points for a part to be manufactured through computer numerical control (CNC) machining operations with the aid of a digital computer, comprising:

• a storage of digital information comprising:
• a model of a part to be machined, the model defining the part's surfaces and a constraint volume;
• and
• parameters for a CNC machining tool, the parameters comprising a plurality of orientations at which the tool is able to longitudinally traverse a rotating cutting edge;
• and
• a computer comprising a processor and memory operatively coupled to the storage, comprising:
• an identification module that identifies fixturable regions comprising locations on the part's surfaces that cannot be approached by either the CNC tool in motion or a clamp;
• an evaluation module that evaluates reachable locations comprising collisions with the CNC tool through ray intersections from locations in the fixturable regions and sweeps of the CNC tool in each approach from the locations, wherein the storage denotes a position and unit inward surface normal at the reachable locations;
• a clamp module that specifies that a clamp located at each of the reachable locations exerts a known force along a vector from the unit inward surface normal at the reachable location, wherein the clamp at reachable location i exerts a force fi along ni, where pi and ni comprise vectors that denote the position and unit inward surface normal at the reachable locations indexed by I, such that, in the presence of friction, assuming a Coulomb model and a coefficient of friction μ, a non-slipping tangential force fij along a tangent direction j at location i satisfies the expression:
• ∥fij∥≤∥μfi∥
• and a net non-slipping force acting at any point contact location is:
• ∑
• j
• ⁢
• (
• f
• ij
• +
• f
• i
• )
• wherein limit points of a set of non-slipping tangent forces lie on a circle of radius ∥μfi∥ and a set fij+fi of resultant vectors form a cone that is called the Coulomb friction cone;
• a mapping module that determines a maximum possible non-slipping applied force at each of the reachable locations, and to map the applied force to a wrench at a triangle normal for each of the reachable locations;
• a generator module that generates fixturable locations by finding form closure based on those reachable locations on the part's surface that do not result in a ray intersection;
• and
• a programming module that programs the CNC tool with process plans downloaded by the computer and comprising machining operations by the CNC tool with the part fixtured using the fixturable locations, wherein the CNC tool operates per the machining operations in the downloaded process plans by machining off the removal volumes through longitudinal traversals of the rotating cutting edge over the surfaces of the part.