Fixturing encompasses the design and assembly of fixtures to locate an
d hold a workpiece during a manufacturing operation such as machining
or assembly. We have implemented an automated design algorithm fora fi
xturing tool kit called the fixture vise: the fixture vise involves tw
o fixture plates mounted on jaws of a vise and modular fixturing eleme
nts (pegs or flatted pegs). Generally, a fixture vise can handle appro
priately sized prismatic workpieces in many different ways. The design
algorithm runs in O(A) time, where A is the number of configurations
achieving simultaneous contact between the modeled object and four fix
ture elements: since simultaneous contact is a necessary but not suffi
cient precondition for force closure, A provides an upper bound on the
number of Force closure fixture configurations.