Precise pipe-bending by 3-RPSR parallel mechanism considering springback and clearances at dies

The authors have been developing a pipe bender based on the penetration bending method using a 3-RPSR parallel mechanism as the movable-die drive mechanism and a fixed die on the ground. In this paper, a theoretical model to estimate the curvature of bent pipe in the penetration bending process has been developed by constructing an algorithm to calculate the center line of the bent pipe from the pose of the movable die taking into consideration the springback effect of the pipe and clearances at the dies. Based on this model, maps of estimated curvature radius of bent pipe and bending force have been obtained, and a bending strategy to perform precise bending, in which the pose of the movable die is determined so that the tilt of the movable die is maximized, has been proposed. Improvement of accuracy in radius of curvature of bent pipe based on the proposed model and bending strategy has been shown by experimental results obtained by our prototype pipe bender. In experiments, error of 2% and 4% in bent pipes with shapes of uniform curvature and clothoid curve was achieved while error without the proposed method was around 10-20%.