Incremental sheet forming is a state-of-the-art manufacturing process for the rapid manufacture of sheet metal components without the use of geometry-specific dies. In this paper, a novel ISF machine, based on a unique overconstrained parallel robot called the Tri-pyramid robot, is introduced. The inverse and forward kinematics of the machine are first analyzed and calibrated based on experimental measurements. In turn, to compensate the kinematic and compliance errors of the machine, a linear encoder system, developed to directly measure the end-effector positions, in conjunction with a neural network, trained to map encoder readings and spatial end-effector positions, is used. A feedback control law is then implemented to compensate the errors in real-time. Experimental results demonstrate that after calibration and error compensation the accuracy of the machine is improved tenfold, making it adequate for incremental forming applications.