*3.3. Simulation and Analysis of the Gripper*

ADMAS 2018 software was used to carry out an analysis of motion simulation, exploring the movement characteristics of the gripper. It would provide the theoretical basis for realizing fast and undamaged control algorithms. The end-effector clamping principle is that constrain part controls the opening and closing of three fingers. In the simulation, only the relevant parts of the gripper were studied. Cherry tomatoes are non-standard spheres. So, the ball was used instead of actual fruit in the simulation model. The physical properties of cherry tomatoes were taken as the parameters of the ball. The fruit-holding process was idealized in simulation (Figure 8).

**Figure 8.** The Adams simulation model of gripper.

First, the ball was deactivated to verify the rationality of the gripper design. The constraint part moved from the chassis to the end of the mechanical finger. Figure 9 shows how the open range of the finger ends varies with the distance of the constrain part. The open range of the finger ends were from 72.8 mm to 9.8 mm, respectively, which met the actual grasping demand of cherry tomato sizes.

**Figure 9.** The simulation result of distance of finger end. Note: C is where the constraint part touches the finger. D is the position at which the finger ends converge to the minimum.

The ball diameters were set to three sizes, 20 mm, 30 mm, and 40 mm, respectively, to explore the motion parameters of the constraint part. The balls were activated in the simulation. The distance was 24 mm from the constraint part to the chassis, and it was set to the beginning position. The constraint part and fingers did not touch each other under this parameter. The simulation results are shown in Table 2. When the finger ends connected the ball, the distances between the constraint part and the chassis were 66.9 mm, 54.9 mm, and 46.2 mm, respectively. The moving distances of constraint part were 22.2 mm, 30.9 mm, and 42.9 mm, respectively. It is shown that the movement distance of the constraint part was related to the diameter of the ball when gripping. The larger the fruit sizes, the smaller the movement distance. There was a negative correlation between fruit sizes and the movement distances of the constraint part.

**Table 2.** Parameters of constraint part movement on holding cherry tomatoes.


Note: *r* is the fruit size; *L*<sup>1</sup> is the beginning distance of the constraint part from the chassis; *L*<sup>2</sup> is the distance from the constraint part to the chassis when the finger ends touch the fruit; Δ*L* is the moving distance.

The target required a holding time of 1s. In this paper, the maximum moving distance Δ*L* was set to 50 mm, and 50 mm/s was the minimum velocity of the constraint part. Based on this, for the convenience of calculation and electrical control, this section discussed the holding force of the finger ends on the three fruit sizes at six speeds. The speeds were 60 mm/s, 70 mm/s, 80 mm/s, 90 mm/s, and 100 mm/s, respectively.

From the mechanical structure of the gripper, it is easy to know that the gripping force of the finger ends on the fruit increases continuously from the touching to the gradual clamping process. Therefore, this work only needs to explore the maximum gripping force amplitude of contact moment between the fingers and the fruit. The simulation step of contact moment was adjusted to 10,000. The definition of the maximum gripping force amplitude of contact moment is:

$$F\_{\overline{s}} = \max[F\_{\Delta t}] \tag{13}$$

where Δ*t* is the time of contact moment, Δ*t* = 0.001 s; *F*Δ*<sup>t</sup>* is the gripping force of contact moment, N; [*F*Δ*t*] is the gripping force set of contact moment; *max*[*F*Δ*t*] is the maximum gripping force amplitude of contact moment. The simulation results are shown in Figure 10 and Table 3.

**Figure 10.** The simulation results: (**a**) the relationship between speed and time; (**b**) the relationship between speed and *Fs*


**Table 3.** Results of motivation simulation.

At the same speed, the holding time increased with the decrease in fruit size. Due to gripping small-size fruit, the moving distance of constraint part was long. Under the same fruit size, the larger the speed of constraint part was, the shorter the holding time was. The holding time of three kinds of cherry tomatoes was less than 1 s, which reached the expected target. At the same speed, *Fs* increased with fruit sizes. The minimum values of *Fs* were 0.2074 N, 0.9792 N, and 1.4509 N at the speed of 50 mm/s, respectively. At the same fruit size, *Fs* increased with the speed of the constraint part. When the constraint part speed was 0.1 m/s, *Fs* reached 10.1627 N [22,29] with 40 mm, which produced a risk of damaging the cherry tomatoes.

The indicators of time and gripping force should be considered to ensure a fast and undamaged grab. When the speed of the restrained part is 0.08 m/s, the comprehensive simulation results show that the clamping time were 0.5381 s, 0.3872 s, and 0.2761 s, respectively, and the maximum gripping force were 0.9717 N, 3.5077 N, and 4.0003 N, respectively, for three fruit sizes. This speed meets the requirement of fast and undamaged when picking. Therefore, 0.08 m/s can be used to the actual speed of the constrain part, then the program and algorithm can be designed.
