## 1 Introduction  
Conformal array technology is important in the development of antennas [1]. Conformal antenna arrays comprise a collection of antenna units that conform to the shape of the carrier's surface [2]. These array antennas not only increase the receiver's surface area and reduce the aerodynamic drag of the antenna system, but also provide a series of other advantages that planar arrays lack, such as reduction of size as well as physical components required to tether conventional planar array antennas [3, 4]. Conventional antenna structures, which have satisfactory electrical performance, can be fabricated via simple conventional manufacturing approaches. However, fabricating conformal antennas require more complex manufacturing methods [5, 6]. Some researchers [7, 8] have successfully fabricated microstrip antennas on spherical surfaces as well as arbitrary surfaces using photolithography. However, photolithography is expensive. In contrast, microdroplet inkjet [9] printing has become a promising solution [10], with lower cost and high efficiency [11]. This printing technology has been investigated and applied widely [12]. For example, some researchers [13] printed electric circuits on conformal 3D structure using liquid metal. Other researchers [14] were able to print RFID (RadioFrequency Identification) antenna on developable surfaces such as cylindrical surfaces. In other studies, researchers were able to print electric circuits on complex surfaces using the transfer [15] printing technology or flexible electronic [16; 17; 18; 19] printing technology. Researchers at MIT [20] developed a method to print a frequency-selective conformal surface on spherical surfaces. The 3D printing company Neotech AMT GmbH ([[http://www.neotech-amt.com/](http://www.neotech-amt.com/)]([http://www.neotech-amt.com/](http://www.neotech-amt.com/))), Germany, developed an inkjet printer with a single nozzle installed on a five-axis motion system. By controlling the motion of the nozzle and the workpiece with the five-axis linkage technique, their printer was able to print RFID or microstrip antenna on an arbitrary surface. However, all the aforementioned methods for fabricating conformal antennas exhibit several drawbacks [21], including high cost, low efficiency, and stringent printing conditions [22; 23]. When using a single piezoelectric nozzle [24; 25], a complex spatial motion algorithm is required to print antennas on a conformal surface [26]. Arrayed nozzles have already been widely used in planographic printing. The company Nano Dimension ([[https://www.nano-di.com/](https://www.nano-di.com/)]([https://www.nano-di.com/](https://www.nano-di.com/))) has developed a device, DragonFly LDM, to print 3D integrated circuits using arrayed nozzles. However, the printing mode is still based on planographic printing. Currently, there is no efficient and economical conformal surface printing technology based on an array of nozzles. A piezoelectric nozzle array can allow hundreds of integrated nozzles to operate simultaneously. Thus, it only takes a few seconds to print a planar conductive pattern. Compared with the printer using a single piezoelectric nozzle, the proposed method can achieve the same level of accuracy but with \(\sim\)100\(\times\) higher efficiency when performing planographic printing. In ideal conditions, one can ensure the jetting trajectory from a single nozzle to approach normally to the surface plane at the droplet contact point. However, when using the arrayed nozzle, only the contact points of the droplets on the surface will fall on the jet trajectory, while the collision direction of the droplet may not be vertical to the substrate. Therefore, there exists a systematic error when performing planographic printing on a curved surface using an arrayed nozzle. Practically, when the arrayed nozzle is separated from the substrate by a certain distance, the landing point of the droplet will deviate from the preset inkjet coordinate owing to the air medium.