## 1 Introduction  
The applications of advanced ceramics such as alumina and zirconia are increasing gradually in the medical and engineering fields due to the significant advancements in the fabrication techniques [1]. Moreover, advanced ceramics offer excellent properties such as high-temperature resistance, high strength to weight ratio and anti-corrosive properties comparing to their competitor materials such as titanium and Inconel alloys. Recently, advanced ceramics were used in the manufacturing of microcomponents such as micro-molds, micro-dies, micro-fluidics and micro-nozzles [1]. Micro-features such as microchannels and micro-pockets with sound surface integrity and high dimensional accuracy are often required in the miniaturized/micro-components for their functioning with ever-increasing stringent specifications [2]. Alumina (Al2O3) is mostly employed material in biomedical applications due to its high conformance to biocompatibility standards [3]. Like other advanced ceramics, Al2O3 is classified as difficult to fabricate material due to its poor thermal and electrical conductivities and high hardness [4]. The traditional machining processes such as turning, milling and drilling are not desirable for the economical machining of the Al2O3 due to excessive tool wear, poor surface integrity and high edge chipping of the machined parts [5]. Non-traditional processes such as chemical machining and electric discharge machining have their own limitation in the machining of ceramic materials as these processes depend on the chemical and electrical properties of the processedmaterials. On the other hand, advanced machining processes such as ultrasonic machining (USM), laser machining and waterjet machining have the potential to machine the Al\({}_{2}\)O\({}_{3}\) ceramic components. Several attempts have been reported on machining micro/macro features in Al\({}_{2}\)O\({}_{3}\) by using laser machining. For example, the fabricating of pockets in Al\({}_{2}\)O\({}_{3}\) by using laser ablation was performed by [PERSON] et al. [6]. The authors applied the multi-objective optimization tool in order to optimize the MRR and the surface roughness (Ra) of the fabricated pockets. Results showed that the optimal values of Ra and MRR of the produced pockets were 4.1 \(\upmu\)m and 0.7 mm\({}^{3}\)/min respectively. Laser milling was also applied by [PERSON] et al. [7] for fabricating square pockets (5 \(\times\) 5 mm\({}^{2}\)) in Al\({}_{2}\)O\({}_{3}\). The effects of fiber laser process parameters and scanning strategy on surface roughness (Ra) and MRR were analyzed. Results indicated that the best value of Ra = 3 \(\upmu\)m was achieved under a certain range of the selected parameters. Many limitations such as high heat-affected zones, poor surfaces, a lack of geometrical accuracy, etc., that can be associated with laser ablation [5; 8; 9; 10]. Therefore, the machining of microchannel on advanced ceramics, like Al\({}_{2}\)O\({}_{3}\), ZrO\({}_{2}\), etc., is a difficult task as documented in earlier the studies. As a result, there is an essential need for a new machining technique, which can efficiently fabricate the ceramic components. Rotary ultrasonic machining (RUM) is a non-traditional hybrid process, which combines the mechanisms of diamond grinding and USM [11]. It can machine brittle and hard materials regardless of their mechanical, electrical and thermal properties. Moreover, RUM can be used to produce components with high surface quality and high dimensional accuracy without altering their physical properties [11; 12; 13]. It can be used for micro/macro machining both brittle materials such as glass and hard to machine materials [14; 15; 16]. For example, [PERSON] and [PERSON] [14] applied RUM for drilling micro-holes (300 \(\upmu\)m dia.) in borosilicate glass.