A Unified Approach to Kinematic and Tolerance Analysis of Locating Fixtures

A workholding fixture should ensure a stable and precise positioning of the workpiece with respect to the machine tool. This requirement is even more important when modular fixtures are used for the sake of efficiency and reconfigurability. They include standard locating elements, which set the part in a predefined spatial orientation by contacting its datum surfaces. In the computer-based design of a fixture, the layout of locators must be tested against two main sources of problems. Kinematic analysis verifies that any relative motion between the part and the worktable is constrained. Tolerance analysis evaluates the robustness of part orientation with respect to manufacturing errors on datum surfaces. We propose a method to carry out both tests through a common set of geometric parameters of the fixture configuration. These derive from the singular value decomposition of the matrix that represents positioning constraints in screw coordinates. For a poorly designed fixture, the decomposition allows us to find out either unconstrained degrees of freedom of the part or a possible violation of tolerance specifications on machined features due to geometric errors on datum surfaces. In such cases, the analysis provides suggestions to plan the needed corrections to the locating scheme. This paper describes the procedure for kinematic and tolerance analysis and demonstrates its significance on a sample case of fixture design.