System and method for fixture configuration determination for part manufacturing with the aid of a digital computer

A system for fixture configuration determination for part manufacturing with the aid of a digital computer, comprising:

• a storage of digital information comprising:
• a model of a part to be manufactured and a constraint volume;
• and
• a catalog of multiplicity of fixture elements specific to a manufacturing facility and configurable to fixture the part;
• 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 a tool in motion used during manufacturing of the part or a clamp;
• a clamp module that specifies that a clamp located at each of a plurality of reachable locations exerts a known force along a vector from a unit inward surface normal at the reachable locations, wherein the clamp at reachable location i exerts a force fi along ni,
• where pi and ni comprise vectors that denote a position and the 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;
• an immobilization module that identifies fixturing points for immobilization of the part by computing form closure over the fixturable regions;
• a selection module that uses the fixturing points and the constraint volume to select a plurality of the fixture elements for a fixture configuration that ensures stability of the part;
• and
• the tool manufactures the part following a determination of the fixture configuration that ensures the stability of the part.