## 2 Materials and Methods
### Experimental Set-Up
#### 2.1.1 Vertical Axis Rotor Type Intra-Row Weeding Tool  
A vertical axis rotor (RVA) was used to destroy the weeds by cutting, uprooting and burying in the soil through the rotary action. The RVA was designed following the standard methods and intra-row zone spacings [31; 32]. The diameter of the developed RVA prototype was selected as 120 mm with a thickness of 5 mm. The RVA was moved along the forward direction of travel with rotational motion along the vertical axis as well as side translational motion, perpendicular to the forward travel axis. A trapezoidal-shape tool was selected for weeding operation with a 15\({}^{\circ}\) rake angle after extensive design testing [33]. The shape was selected to ensure maximum weed mortality and efficient soil pulverization. Generally, the depth requirement of the weeding operation varies from 20 to 40 mm within three to five weeks after sowing; however, weeding beyond that period may require down to 60 mm of depth. Keeping a 20 mm clearance from the rotor, a length of 80 mm for the cutting tools was selected. High-carbon steel flats of a length of 80 mm, thickness of 3.5 mm and width of 30 mm were selected for fabrication of the cutting tools. Finally, all these cutting tools were mounted on the periphery of a mild steel (MS) ring as shown in Figure 2. The design parameters of tools were calculated by considering required power, speed of operation, RVA rpm, soil parameters, and the width of coverage.  
The trajectory of the working element of an RVA unit corresponds to a cycloid (Figure 3). A rigid cutting tool of RVA describes the path of a cycloid when the axis of rotation is perpendicular to the direction of the system's travel [31]. The polar coordinates and the length of soil slices are given in Equations (1) and (2) and discussed below.  
Figure 3: Trajectories of working tools and shapes of soil slices for the vertical axis rotary tool.  
Figure 2: Vertical axis rotor for intra-row weeding: (**a**) CAD view of RVA; (**b**) Developed RVA.  
For the tool movement, the general equation for converting polar coordinates to cartesian coordinates was used.  
For tool 1, \(n=1\), the position is given by:  
Xo = 0,  
Yo = r.  
The parametric equation of a cycloid during motion at the time interval \(t\) is given by  
\[\begin{array}{c}x\ =\ v\ \times\ t\ +\ r\ \times\ cos\omega t,\\ y\ =\ r\ \times\ sin\omega t.\end{array} \tag{1}\]  
Contours of the cut soil slices are limited by two cycloids made by two cutting units operating in succession. The length of soil slices (\(L\)) can be calculated as  
\[L=\frac{v}{u}\left(\frac{2\times\pi\times r}{z}\right), \tag{2}\]  
where \(r\) is the outer radius of the working set (mm); \(v\) is the forward speed of travel of the tool (ms\({}^{-1}\)); \(\omega\) is the angular speed of the cutting tool set; \(\omega t\) is the angle of rotation during the measurement time period \(t\); \(u\) is the peripheral speed of the cutting tool (ms\({}^{-1}\)); \(z\) refers to the number of tools operating in one plane of cutting. The length of soil slices depends on speed ratio (\(u/v\)); the higher the ratio, the shorter the cut soil slice. Therefore, the speed ratio (\(u/v\)) was also selected in experimental evaluations of R\({}_{\rm VA}\).