Abstract
Aiming at the problem of judging the degree of freedom (DOF) of the workpiece in the fixture by experience, it is difficult to adapt to the analysis of the DOF of some singular workpieces. The workpiece and the fixture are used as rigid bodies, and the workpiece is allowed to move in the plane or space under the constraints of the fixture positioning point, and a set of geometric theorems for judging the DOF and overconstraint of the workpiece can be derived according to the difference in the position of the instantaneous center of the workpiece speed. The judgment of the DOF and overconstraint of the workpiece is abstracted into rules with universal meaning, which effectively overcomes the limitations of existing methods. The research results show that (1) the DOF and overconstraint of the workpiece in the fixture depend entirely on the number of positioning normal lines of the workpiece and their geometric relationship; (2) the necessary and sufficient condition for limiting the DOF of rotation of the workpiece around a certain axis is that the workpiece has a pair of parallel normal lines in the vertical plane of the axis. Using geometric theorems to judge the DOF of the workpiece is more rigorous, simple, and intuitive, which is convenient for computer‐aided judgment and the reasonable layout of the positioning points of the workpiece, which can effectively avoid the misjudgment of the DOF and unnecessary overpositioning when the complex workpiece is combined and positioned on different surfaces. Several examples are used to verify the accuracy of the method and correct unreasonable positioning schemes.
Highlights
Introduction edegree of freedom (DOF) of the workpiece in the fixture affects the machining accuracy and determines whether the fixture meets the working requirements
Parag et al [6] used the unified manufacturing resource model of the STEP-NC standard to represent the connection with the NC machining center. e main contribution is to allow universal modeling of fixtures and loading equipment, as well as machining workpiece and process modeling, to analyze the DOF of workpieces on the fixture
Based on the positioning constraints of the fixture to the workpiece, this paper proposes the concepts of the constraint positioning normal and the constraint positioning plane and proposes a set of geometric theorems for accurately calculating the DOF of the workpiece. is method can realize the accurate calculation of the DOF of the workpiece and provide a basis for rationally arranging the positioning points of the workpiece
Summary
Oblique axis positioned on the V-block. 1, V-block; 2, workpiece. Figure 2: ree-section positioning of a cylinder. (a) Positioning point on each of the three sections. (b) Add another positioning point to the right section. 1, Workpiece; 2, supporting bolt; 3, pedestal. Based on the positioning constraints of the fixture to the workpiece, this paper proposes the concepts of the constraint positioning normal and the constraint positioning plane and proposes a set of geometric theorems for accurately calculating the DOF of the workpiece. E normal line points to the constraint direction of the workpiece from the position of the constraint point.
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