Reluctance machines such as the switched reluctance machines (SRMs) and the synchronous reluctance machines (SynRMs) are recently investigated for propulsion motors of the electrified vehicles owing to their robust mechanical construction, high thermal tolerance, and cost-competitiveness. However, practical application of the reluctance machines to the vehicle propulsion has been hindered by the fact that the conventional SRMs and SynRMs are difficult to meet all the three preferable features for the vehicular application: 1. High power density, 2. Low torque and input-current ripples, 3. Being drivable by the normal three-phase inverter. This paper addresses this issue by proposing a novel reluctance machine. The prominent features of the proposed reluctance machine are the sinusoidal reluctance profile and the delta-connected phase windings, both of which differ from conventional reluctance machines. Along with the theoretical discussion of the basic operating principles of the proposed reluctance machines, this paper presents a simple performance estimation of the proposed machine, the SRM, and the SynRM, which supported that the proposed machine can meet the three preferable features. Furthermore, the experiment successfully supported the operating principles of the proposed machine, suggesting the feasibility of the proposed machine for vehicle applications.