For the material selection, the strength, machinability, ductility and hardness for each component of the machine were given prior consideration. The boom, mast, the base plate of the machine will be subjected to high load, hence mild steel (low carbon steel: EN3B) material was chosen because of its hardness and strength. Also, cold rolled steel (AISI 1020) was used for the hydraulic cylinders because weight saving and durability is a major consign so as to reduce fatigue on the farmer during movement of the machine to the farm.

The physical model was created using SolidWorks CAD, based on the calculated dimensions from the design analysis. Figure 3 represents the physical model of this harvester, the major components are the boom, mast, hydraulic cylinder, cutting system and the base. Some of the components were designed to be telescopic in operation such that the segments of these component slides over each other, making it possible for the whole component to be longer or shorter during operation.

Boom:

This is the steel arm and a recognizable part of the machine responsible for lifting the cutting system to the height of the palm fruit. It was designed to be telescopic and consist of three hollow square tube segments fitted one inside the other. The three segments are segment 1 (B1), segment 2 (B2) and segment 3 (B3). The dimensions selected for the square tube Segments 1, 2 and 3 are 50 × 50 × 3 mm, 40 × 40 × 3 mm and 30 × 30 × 3 mm successively. The boom was designed to be telescopic so as to occupy less space for easy storage when the machine is collapsed.

Mast

It is also telescopic and consists of two cylindrical steel hollow pipe materials fitted one inside the other. The two segments are the top (M1) and the base (M2) segments. A top segment round tube of 70 mm diameter with 3 mm thickness was selected. The top segment has a fulcrum at its top end for which serve as a bracket for the boom, as well as a welded bracket on it for hydraulic cylinder 2 sitting (mount). The base segment (M₂) round tube has a diameter of 100 mm and 3 mm thickness. Provision was also made on the base segment where the steering bar was fixed to allow for steering the boom during cutting operation. The oil tank and the hydraulic pump were equally mounted on the base segment of the mast. There is also a welded bracket on the base segment for hydraulic cylinder 3 for its sliding operation.

Hydraulic cylinders

These are the mechanical actuators that gives linear back and forth movement to the boom and the mast. It consists of a cylinder barrel, a piston which is connected to a piston rod. The machine has three hydraulic cylinders: hydraulic cylinder I extend or retracts the boom, hydraulic cylinder 2 is for the boom inclination while hydraulic cylinder 3 is for extension and retraction of the mast. The hydraulic cylinders operate with the aid of hydraulic fluid which is pressurized by a hydraulic pump. These cylinders on the mast and boom are all screwed to brackets which are welded to the segments, thereby making it easier to detach these cylinders from its segment when necessary.

Cutting system

The harvesting(cutting) process of the fruit bunch is done by a fast, rotational motion of a circular saw blade attached to the boom. The rotary saw cutting was employed because it is fast in cutting and the tool changing procedure is easier [27]. A 210 mm diameter steel combination blade was used because it is suitable for cutting thick branches. For this design, a cutting system with minimum weight was considered to prevent failure of the boom, a battery powered system was used because of ease to recharge, lighter weight and distance to electric power supply to the farm.

The base

The other components of this machine are supported by the base. This machine base was designed to provide stability of the harvester during operation. It has a provision where the battery is kept, it also has a handle and caster wheels for easy movement of the machine.

The design analysis covers development of mathematical models for components of this machine. The areas are:

Boom Length

When this machine is in operation, the length of the boom required to meet the target tree height can be determined mathematically using Pythagoras theorem, since it can be represented with lines as shown in Figure 4.

The boom length (c) was determined with the given Equation (1)

c 2 = a 2 + b 2

c = a 2 + b 2 (1)

where, k is the Mast height, b is the horizontal distance between the tree and the machine, a is the height of the tree top above the mast and a + k is the Boom height (Fruit bunch height) [28].

Maximum Boom Angle

From Figure 4, the maximum boom angle (θ_A) of the machine can be determined using mathematical trigonometry as shown in Equation (2),

sin θ A = a c

Therefore,

θ A = sin − 1 ( a c ) (2)

Stroke Length of hydraulic cylinder 2

The inclination cylinder of the machine can be represented with a diagram as shown in Figure 5.

From Figure 5, the length of hydraulic cylinder 2 in its instroke position with its mount (V) was first determined with the given Equation (3):

V 2 = h 2 + L 2

V = h 2 + L 2 (3)

where, L (≈L₂)—the distance between the welded bracket on boom segment 1 and the mast fulcrum, h—the distance between the welded bracket of top mast to the mast fulcrum,

When the cylinder extends to the maximum boom angle, we have the diagram in Figure 6.

From Figure 6, the total inclination height (Z) was then determined using trigonometry (Cosine rule) as show in Equation (5).

Z 2 = h 2 + L 2 − 2 ⋅ h ⋅ L ⋅ cos ( 90 + θ A )

Z = h 2 + L 2 − 2 ⋅ h ⋅ L ⋅ cos ( 90 + θ A ) (5)

Also, the outstroke length of cylinder 2 (J) was determined using Equation (6)

Z = V + J

J = Z − V (6)

Also, applying Sine rule, cylinder 2 minimum inclination angles (θ_B & θ_V) for top and bottom reached was determined as shown in Equations (7) and (8)

Z sin ( 90 + θ A ) = h sin θ B = L sin θ V

θ B = sin − 1 h sin ( 90 + θ A ) Z (7)

θ V = sin − 1 L sin ( 90 + θ A ) Z (8)

Force of hydraulic cylinder 2(F_C2)

The force of cylinder 2 required to elevate the boom to the maximum angle (F_C2) was determined using the free body diagram of the boom and cylinder 2 at its maximum outstroke position as shown in Figure 7.

According to Newton’s second law of motion for a linear mechanical system, the sum of external forces (f) acting on a rigid body is equal to the product of the mass (m) and acceleration (a) of the rigid body.

∑ F External = m a (8)

D’ Alembert’s law also relates the sum of all forces acting on the object as shown in Equation (9):

∑ F A L L = 0 (9)

Applying these two laws, the equations of motion for the system are as follow

∑ F A L L = 0

W B 1 cos θ A + W C 1 cos θ A + W B 2 cos θ A + W B 3 cos θ A + W E M cos θ A   − F R A − F C 2 cos ( 90 − θ A ) = 0

Taking Moment about point A, we have Equation (10) as shown

∑ M A = 0

W B 1 L 1 cos θ A + W C 1 L 3 cos θ A + W B 2 L 4 cos θ A + W B 3 L 5 cos θ A   + W E M L 6 cos θ A − F C 2 L 2 cos ( 90 − θ B ) = 0

F C 2 = ( L 1 W 1 + L 3 W C 1 + L 4 W B 2 + L 5 W B 3 + L 6 W E M ) cos θ A / cos ( 90 − θ B ) (10)

Where, W_B1—Weight of the boom 1; W_c1—Weight of hydraulic cylinder1; W_B2—Weight of boom section 2; W_B3—Weight of boom section 3; W_EM—Weight of the electric motor (cutter).

Force of hydraulic cylinder 1 (F_C1)

The force of the hydraulic cylinder 1 (F_C1) required to extend the boom was determined from the free body diagram Figure 8.

Resolving the forces, summation of forces about the horizontal i.e. ∑ F H = 0

F C 1 = W B 2 sin θ A + W B 3 sin θ A + W E M sin θ A (11)

Force of Hydraulic Cylinder 3(F_C3)

From the free body diagram of Figure 9, the force of hydraulic cylinder 3 (F_C3) required was determined from Equation (12).

Summation of forces about the vertical i.e. ∑ F V = 0

F C 3 = W M 1 + W C A + W B 1 + W C 1 + W C 2 + W B 2 + W B 3 + W E M (12)

where, W_CA—Weight of hydraulic cylinder 2 mount, W_M1—Weight of top segment of the mast,

W_C2—Weight of hydraulic cylinder 2, F_C3—Force of hydraulic cylinder 3 to lift the sections [29].

Hydraulic Pump Pressure for the System

Since the three hydraulic cylinders (1-3) will be working successively during operation, the hydraulic pump pressure specification required for the system will be based on the hydraulic cylinder with the maximum force (F_max) required for its outstroke, this is in assumption that the area of the piston for each hydraulic cylinders are equal.

The pressure of the hydraulic pump is determined with the given Equation (13)

P = F max A = 4 F max π D p 2 (13)

where, F_max—Maximum hydraulic cylinder force; A—Area of hydraulic cylinder piston; D_p—diameter of piston [30].

Oil tank capacity (V_T)

The volume of hydraulic oil required for the machine operation (i.e. the hydraulic oil tank capacity) was determined from the given Equation (14):

V T = π D P 2 4 L S 1 + π D P 2 4 L S 2 + π D P 2 4 L s 3

V T = π D P 2 4 ( L S 1 + L S 2 + L S 3 ) (14)

where, D_P—diameter of piston of hydraulic cylinder, L_S1—Stroke length of hydraulic cylinder 1,

L_S2—Stroke length of hydraulic cylinder 2,L_S3—Stroke length of hydraulic cylinder 3,

Furthermore, given that the length and width of the tank is assumed, the height required for the fabrication of the tank was determined using Equation (15)

H T = V T L T W T (15)

where, L_T—Tank length, W_T—Tank width, H_T—tank height.

Thus, a good design requires the calculated volume of tank to be greater than the volume of oil

Base Weight of the Machine

The base weight (W_BA) that will balance the machine and prevent it from tipping over during operation was determined by applying E-crane equilibrium design principle. From Figure 10, we derived Equations (16)-(22) as:

X 1 = L 1 cos θ A (16)

X 3 = L 3 cos θ A (17)

X 4 = L 4 cos θ A (18)

X 5 = L 5 cos θ A (19)

X 6 = L 6 cos θ A (20)

X 7 = L 7 sin θ V (21)

X 8 = L 8 sin θ V (22)

From Basic crane design principle, we have Equations (23) and (24):

( W M 1 + W M 2 ) ( L B − ( X a + K a + y ) + W B A ( L B 2 − y ) = W B 1 X 1 + W C 1 X 3 + W B 2 X 4 + W B 3 X 5 + W E M X 6 + W C A X 7 + W C 2 X 8 + W R P O M (23)

where,

W R P O = W C 3 + W P + W O (24)

W_P—Weight of hydraulic pump, W_c3—Weight of hydraulic cylinder 3; W_O—Weight of oil filled tank, L_B—Length of the base, W_BA—Required base weight of the machine [31] [32].

Permissible Weight of the Cutting System

The safe weight of the electric cutting mechanism on the boom can be modeled as a force impacted on a cantilever beam at one end of it as shown in Figure 11.

As shown in Figure 12, the deflection of the boom due to the weight of the cutter was given in Equation (25)

y max = P C 3 3 ⋅ E ⋅ I (25)

where y_max—maximum deflection, P—maximum load, C—boom length, E—Young Modulus of Material (i.e. steel), I—Area moment of inertia of the boom.

For a boom which is a rectangular hollow cross sectional members, the area moment of inertia of each segment was determined using Equation (26)

I = ( W i 3 H i 12 − w i 3 h i 12 ) (26)

where, W_i—External width of segment; H_i—External height of segment; w_i—Internal width of segment, h_i—Internal height of segment, i—1, 2, 3.

For a design with minimal deflection, the area moment of Inertial with the highest value was selected [33].

Since dead load deflection seldom contribute to deflection, the allowable elastic deflection for the steel member (boom) is given in Equation (27) as shown

y all = C 360 (27)

where, y_all—Allowable deflection. [34]

For a satisfactory deflection criterion, maximum deflection must be equal or less than the allowable deflection (i.e. y_max ≤ y_all), therefore the maximum weight (load) of the electric motor (cutter) for an allowable deflection which is the design load as derived was determined with the given Equation (28).

P s = 3 ⋅ E ⋅ I 360 C 2 (28)

where, P_s—Permissible (Design/allowable) weight of the cutting system.

Thus for a safe design of this machine, W_EM should be equal to or less than P_s (i.e. W_EM ≤ P_S) [35] [36] [37].

Power Requirement

The power (P_WR) requirement for the electric cutter of the machine was determined from Equation (29)

P W R = M a ⋅ R ⋅ g ( 2 π N ) 60 (29)

where, P_WR—Power of electric motor(watts), M_a—Mass of cutting blade(kg), R—radius of the cutting blade, N—Rotational speed in rev/minutes., g—acceleration due to gravity ≈ 9.81 m/s² [38].

In summary, the principal dimensional and mechanical parameters of the harvester are listed in Table 1 and Table 2.