Force-assemblability: insertion of a workpiece into a fixture guided by contact forces alone

The authors describe the concept of force-assemblability, which may be applied to fixture insertion as well as other assembly tasks. They define a linear force assemblable fixture to be one for which there exists a linear motion control law (examples of which include compliance and accommodation) which necessarily results in workpiece contact with all fixture elements (fixels) despite initial positional error. For reliable insertion, the fixture should have the property that contact with all fixels insures a unique workpiece position (i.e. the fixture should be deterministic) and the property that, after the inserting motion terminates, contact with all fixels is insured. It is shown that all deterministic fixtures are force-assemblable when friction is less than some value dictated by the workpiece/fixture geometry. It is also shown how to generate a motion control law that satisfies force-assemblability at this value of friction