A method for determining the degree of freedom of workpiece based on developed geometry theorem

Abstract

The traditional 6-point positioning principle could not indicate the specific features of the workpiece constrained at the six locating points and could not provide the influence law of geometric relationship between each constraint and the DOF of the workpiece, which makes it difficult to adapt to various complex positioning and often mistakes DOF of workpiece to lead to fail in jig design. The normal line of the workpiece at the jig anchor point is defined as the positioning normal line in this paper. According to the number of the positioning normal lines and the geometrical relationships between them, a set of geometrical theorems on determining the DOF of the workpiece are deduced. The judgement criterion for the distribution of the normal line in over-positioning condition is also provided. The DOF of the workpiece and the solutions to the unreasonable positioning are provided by using the geometric theorems in several examples, which proves that the geometric theorems can quickly and accurately determine the DOF of the workpiece in the complex positioning. The geometrical theorems of the workpiece positioning develop and perfect the positioning theory of the workpiece and can make the method of determining DOF more precise, simple and intuitive; furthermore, the geometrical theorems are beneficial to accurately determine the DOF of the workpiece in computer-aided fixture design.