Dimensional errors of the parts from a part family cause the initial misplacement of the
workpiece on the fixture affecting the final product quality. Even if the part is
positioned correctly, the external machining forces and clamping load cause the part to
deviate from its position. This deviation depends on the external load and the fixture
stiffness. In this article, a comprehensive analytical model of a 3-2-1 fixturing system
is proposed, consisting of a kinematic and a mechanical part. The kinematic model
relocates the initially misplaced workpiece in the machine reference through the axial
advancements of six locators taking all the fixturing elements to be rigid. The
repositioned part then shifts again from the corrected position due to the deformation of
fixturing elements under clamping and machining forces. The mechanical model calculates
this displacement of the part considering the locators and clamps to be elastic. The rigid
cuboid baseplate, used to precisely relocate the workpiece, is also considered elastic at
the interface with the locators. Using small displacement hypothesis with zero friction at
the contact points, Lagrangian formulation enables us to calculate the rigid body
displacement of the workpiece, deformation of each locator, as well as the stiffness
matrix and mechanical behavior of the fixturing system. This displacement of the workpiece
is then finally compensated by the advancement of the six axial locators calculated
through the kinematic model.