Abstract: According to the direction constraints of contact forces between the workpiece and fixturing elements, the static equilibrium condition of the workpiece is considered to establish the fixturing model. In connection with the linear programming technology, the existence model of the force and its solution trick are further formulated to judge whether the existence model has solutions for the independent variable of the clamping force. Under the condition that the clamping force has solutions, the feasibility model of the force feasibility and its judgement criterion are derived form the fixturing model and the linear programming technology. The feasibility model can be used to validate whether the given clamping force is acceptable. With consideration of the value range, the clamping force can be selected as the minimum value with a certain step along the positive direction. According to the feasibility difference of the current selected clamping force with the last one, the step and its direction can be determined for the next selection. If the feasibilities are same, the next clamping force is selected with the same step along the same direction. Or else, it is chosen with the half step along the negative direction. The feasibility of the selected clamping force is iteratively validated until the absolute value of the step is not more than the given threshold value. Thus, the half step with the reverse direction planning method of the clamping force can be suggested to approximate the true clamping force. The proposed method can transform the continuous design problem of clamping forces into the discrete one. Therefore, it can not only benefit the development of computer aided clamping force design, but also apply to the complex workpiece.

Key words: clamping force, existence of force, feasibility of force, half step with the reverse direction, threshold value