A unified point-by-point planning algorithm of machining fixture layout for complex workpiece

Workpiece-fixturing is necessary to achieve the correct position of the workpiece with respect to the cutting tool. Therefore, a unified point-by-point planning algorithm of fixture layout is systematically created for a complex workpiece based on the discretization thought. Firstly, based on the inclusion of the theoretical Degrees of Freedom (DOFs) within the practical DOFs and the relationship between the locator number and the rank of Jacobian matrix, two necessary and sufficient conditions are suggested for the judgment criterion of locating determination. According to the variation of locating reference and locator number, a planning algorithm of locating layout is further established by iteratively analysing the locating determination. Secondly, the combination of the virtual work principle with the linear programming technology is employed to formulate a judgment criterion for fixturing stability. Consequently, with the discretization of clamping surfaces, a deterministic algorithm of clamping force is suggested by evaluating the fixturing stability at every node. Three typical examples are finally used to demonstrate the design procedure of fixture layout.