Abstract: In order to guarantee the successful machining of a workpiece, a multiple fixturing is usually used to assure proper clamping forces. A fixturing model and its analysis method of existence of solutions are formulized to judge the fixturing performance of multiple fixturing layout. A clamping surface is meshed as candidate clamping points, and then two adjacent clamping forces are selected with a given step from the beginning of the first candidate clamping point with force-closure. The decreasing coefficient of the current step can be determined according to the the similarities and differences of selected clamping forces. The clamping force at current clamping point can be obtained until the current step is less than the threshold. The planning of “1-clamping force” is completed after the last clamping point with force-closure is found. Each polar angle can be discretized into minimum angles by describing n-clamping forces as a function of one polar radius and n-1 polar angles. “1-clamping force” planning algorithm is called to calculate the magnitudes and placements of “n-clamping forces” at each minimum angle with force-closure. Finally, “n-clamping forces” planning algorithm and analytical method are used to calculate the clamping forces for typical double fixturing layout. Results show that the maximum relative errors of “n-clamping forces” planning algorithm is only 0.979%. The proposed method can be used to transform the continuous design issue of multiple clamping forces into the discrete analysis issue of fixturing performance. Therefore, it can not only apply to the complex workpiece, but also benefit the implementation of automated fixture design. Key

Key words: clampingforce, clampingpoint, forceclosure, forcefeasibility, stepdecreasement, polarangle, polarradius, minimumangle