  In this work, we present a theoretical investigation into an
antiferromagnetically coupled spin system, specifically
$\text{Cu}_{3}-\text{X}(\text{X=As, Sb})$, which exhibits a configuration of a
slightly distorted equilateral triangle, as identified in previous literature.
This system is modeled using the Heisenberg model within a triangular
structure, incorporating exchange interaction, Dzyaloshinskii-Moriya
interaction, g-factors, and an external magnetic field. We explore three
quantum machines based on the $\text{Cu}_{3}$-like antiferromagnetically
coupled spin system. The magnetocaloric effect (MCE), which is notably more
significant at low temperatures, around $T\sim1$K, for a perpendicular magnetic
field at approximately $\sim5$T, has been analyzed. We examine the Carnot
machine, observing the influence of the external magnetic field on its
operation as both a heat engine and refrigerator, and discuss the thermal
efficiencies under these conditions. Our findings suggest that enhanced MCE
allows for broader operation regions as a heat engine. Additionally, we explore
the quantum Otto machine, showing its versatility in functioning as a heat
engine, refrigerator, heater, and thermal accelerator. However, it mainly
operates as a refrigerator and accelerator. We also explore their corresponding
thermal efficiencies. Similarly, we have analyzed the quantum Stirling machine,
which is capable of functioning as a heat engine, refrigerator, heater, and
thermal accelerator, but it mainly operates as a refrigerator and thermal
accelerator. We also examined the corresponding thermal efficiencies. It is
worth mentioning that the Otto machine performance as a heat engine is notably
influenced by the MCE, while the operational mode of the Stirling machine
switches between a heat engine and accelerator around MCE is more prominent.
