| Many of the methods currently available for the design and analysis of fixtures are frequently complicated and costly. This thesis concentrates on the development of methods that provide a rapid and useful approximation to the behavior of the fixture-workpart system from the perspective of the kinematics of rigid body contact. In the first part, we address the problem of the deterministic location of 3-2-1 locator schemes. Using screw theory, we derive new and simple geometric conditions for their deterministic location and good conditioning. Next, we develop combinatorial algorithms for the synthesis of near-optimal 3-2-1 locator schemes. We show that the search can be limited to the boundary of convex regions of valid locator positions specified on each datum face. In the second part, we are concerned with the problem of synthesis of optimal clamping schemes. The goal is to minimize the maximum clamping force, avoiding excessive deformations. Both with and without friction, for the case of planar faces we show a new technique based on a linear program. The model considers several external loads and provides both the optimal positions and forces of the clamps. For cylindrical faces we show a solution based on a nonlinear convex program. Next, we show a new linear algebraic method for computing the dependent and independent regions of form closure of a workpart. The former are regions where the clamp contacts achieve form closure when placed according with certain relationship. The latter, are regions where the clamps achieve form closure and can be placed independent of each other. In the last part, we address the problem of the impact of deterministic errors on the dimensions of the locators of a 3-2-1 scheme on the compliance of geometric tolerances specified on the workpart. First we solve the forward problem, predicting the tolerance deviation as a result of the given errors on the locator dimensions. Then we solve the inverse problem. In it we predict the maximum admissible error on the locators such that a given geometric tolerance is satisfied. We show and implement solutions for the hole position and surface profile geometric tolerances. |
