Fixture kinematic analysis based on the full contact model of rigid bodies

The conventional point-kinematic model of fixtures has only treated point geometry of the contacts between locators and workpiece. However, this model, which ignores the underlying surface properties of the locators-plus-workpiece system, is inherently incapable of capturing the effects of the geometric properties important to accurate positioning of the workpiece. In this paper, we present a fixture kinematic analysis based on the full kinematics of locator-workpiece contact. This model incorporates a "virtual" kinematic chain with meshing parameters of contact kinematics in a velocity formulation. Conditions of a deterministic fixture are derived. It is shown that the workpiece position and orientation are completely characterized by the kinematic properties of the locator contacts with the workpiece, including not only the arbitrary locator location errors but also the surface properties at nonprismatic locator-workpiece contacts. This is illustrated with numerical examples. The fixture kinematic analysis developed here has a strong implication for designing fixtures with high locating precision requirements.