# Design and Comparative Analysis of a Ground-Level Trellising Tool for Greenhouse Tomato Cultivation
## 2 Materials and Methods
### Description of the Machine's Design and Operation  
The operating principle of the tool is based on the magnetic forces generated by electromagnets (F), which enable the gripping of the hangers supporting the plants. The rotary motion transmitted by a direct-current motor (Tmotor) allows for the roll or unroll of the thread to which the plant is attached. The main forces involved are shown in Figure 5 and described below. During the trellising process (Figure 6), the plant is initially supported by a hanger on the main trellising line (Step 1). The first action performed by the tool is to grasp the hanger holding the plant (Step 2). This is achieved by activating electromagnets, which secure the iron hanger. Next, the rotation motor is activated in the desired direction, depending on whether the intention is to release or roll the raffia (Step 3). Finally, the hanger is placed back on the main trellising line, and the electromagnets are deactivated, leaving the hanger suspended in a new location (Step 4). Figure 5: Trellising tool: (**a**) tool with forces and torques present; (**b**) tool prototype. Figure 6: Plant trellising process: (**Step 1**) tomato plant; (**Step 2**) lowering plant with tool; (**Step 3**) rotation of the hanger to release thread and lateral movement of the plant; (**Step 4**) with the help of the tool, the plant is placed in the new location. The force \(F\) generated by the intensity of the magnetic field of the electro-magnet depends on the magnitude of the electric current flowing through the conductor, the number of turns of the wire around the core, and the properties of the ferromagnetic material used. The magnetic attraction force between an electromagnet and an object made of ferromagnetic material is described by the following magnetic attraction force equation:  
\[F=\frac{0\cdot N^{2}\cdot I^{2}\cdot A}{2\cdot g^{2}} \tag{1}\]  
This equation is an expression derived from Ampere's law, which describes the force of attraction or repulsion between two coils carrying an electric current. In this equation, \(F\) represents the force (in newtons, N) between the coils. The term \(\mu_{0}\) is the vacuum permeability (measured in henries per meter, H/m), a constant value that quantifies the capacity of the empty space to transmit magnetic fields. \(N\) is the number of turns or coils in the coil (unitless), while I is the electric current flowing through the coil, measured in amperes (A). The area \(A\) is the cross-section of the coil, expressed in square meters (m\({}^{2}\)), and g is the distance between the coils, measured in meters (m). This equation reflects how the force is directly proportional to the square of the current and the number of turns, and it is inversely proportional to the square of the distance between the coils. This equation shows that the force of attraction increases with the number of turns, the intensity of the current, and the area of the core, and it decreases with the distance between the objects. Therefore, electromagnets are used as magnetic levitation devices to grasp the iron hangers that support the crops. The torque provided by the DC motor reducer assembly must exceed the moment exerted by the plant's weight when the hanger rack is in the horizontal position, as this is the most unfavorable condition. The torque can be calculated using the following expression:  
\[T_{motor}=d\cdot load \tag{2}\]  
Thus, the torque of the motor (\(T_{motor}\)) in N\(\cdot\)m is obtained from the product of the distance (\(d\)) in m and the load (\(load\)) supported by the tool in N. Based on the torque required to roll or unroll the hangers, it is possible to determine the necessary motor power for efficient operation. The power of motor (\(P_{motor}\)) in W is calculated using the torque of the motor (\(T_{motor}\)) in N\(\cdot\)m, the angular velocity (\(\omega_{motor}\)) in rad/s, and the mechanical efficiency of the motor (\(\eta\)).