this invention relates to machines for heating and joining thermoplastic resin sheets and more particularly relates to a portable machine which fuses together the overlapping edges of large stationary sheets as the welding machine travels along the overlapping edges . the machine is moved along the opposed edges of the sheet at a velocity which is changed so that the velocity is substantially proportional to the instantaneous temperature of the heat source . the machine is therefore accelerated or decelerated in accordance with the selected velocity change algorithm which is exponentially in the preferred embodiment .