This study presents a simplified analytical model for synchronous reluctance machines (SynRMs) with and without permanent magnets (PMs) to rapidly investigate the influences of flux-barrier-end angles or salient poles angles on the torque ripple. With the proposed method, the optimal flux-barrier-end angles or salient poles angles can be computed directly to eliminate a specific torque harmonic. To further minimise two main low-order torque harmonics, a compensation strategy is adopted by choosing different optimised flux-barrier-end angles or salient poles angles in rotor adjacent poles. Moreover, two types of optimal combinations are evaluated and compared with transient finite element analysis. The results show the torque ripple can be significantly reduced in the optimised SynRMs with and without PMs and the average torque loss is acceptable. Finally, the prototype motor of five-phase SynRMs without PM is built and tested to validate the analyses.