We have previously developed a hollow cylindrical bolt-clamped Langevin-type transducer with a high mechanical quality factor (Q) for excitation of high-amplitude torsional vibrations. In this paper, we propose a construction of vibrating systems that comprise a `stepped horn' (a mechanical transformer of torsional vibration) and the stumpy `twisting' transducer developed by us. The distinctive feature of the construction is that it achieves compactness without sacrificing the volume of piezoelectric ceramics that is important for high-power ultrasonic applications. Through experiments, we have found some crucial points in the procedure for constructing torsional-vibration systems that can be operated at a relatively high frequency. In addition, we have conducted some experiments of ultrasonic plastic welding using one of the vibrating systems for evaluation of the feasibility of the construction in this manufacturing technique