Two special coupled spins, one is an arbitrary spin-s and the other is a fixed spin-1/2, are proposed as the working substance of the quantum Otto and Carnot cycles. The quantum adiabatic stages of the cycles are considered the simultaneous changes of the frequencies of the spins and the interaction strength in which all the energy gaps of the working substance are changed by the same ratios in the two quantum adiabatic stages. The role of quantum interactions and the spin-s on the performance of the quantum cycles is investigated in detail. It is found that the thermal efficiencies of the cycles are independent of the spin-s and the interaction strength and are also equivalent to their classical counterparts. The work output of the cycles is found to be significantly enhanced by the quantum interactions. Compared to the uncoupled case, the coupled working substance with a smaller spin-s is found to produce more useful work in the weak coupling regime, while the harvested work with a smaller spin-s is less in the strong coupling regime. The concept of local thermodynamics and the role of inner friction are also addressed for the proposed quantum Otto and Carnot cycles.