Filling Insertion by Rapier: A Kinematic Model

A model of rapier filling insertion, using two half-width rapiers and end transfer, is proposed and its implications analyzed. Normalized forms of the critical characteristics that impose constraints on the system are evaluated. In particular, filling pickup velocity and the maximum velocity and maximum acceleration of the rapier are considered. The effects are examined of the parameters of the model, and of the form of generating function used to specify the rapier motion, on these normalized characteristics. The influence of the critical characteristics on the relation between working width and loom speed is then considered. The forms of width-speed relation implied by the limiting values of the critical characteristics are determined and compared with the form of this relation in practice.