Modified Design of a Precision Planter For a Robotic Assistant Farmer

F
sm
 
F
y
 
F
B
 
L
1
L
2

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69 
There are different types of wires used to make springs. Hot Drawn (HD) wires are 
commonly used. For HD wire, the following properties are given in Table 3-5. 
Table 3- 5- Properties of HD spring wire, for d
s
>3 mm[21] 
Name 
Parameter 
Value 
Shear Modulus of Elasticity 
G 
78.6 GPa 
Modulus of Elasticity 
E 
196.5 GPa 
Wire ultimate tensile strength 
constant 
A 
1783 MPa.mm
m 
Wire ultimate tensile strength 
constant 
M 
0.190 
In table 3-3, G is the Shear module of elasticity, E is the module of elasticity. The 
Ultimate tensile strength, S
ut
, and Yield shear strength, S
sy
, are defined as follows [21], 
(Eq. 3-35) 
Choosing d
s
=8.5 mm and C=5.5, which result in D
s
=46.75 mm, 
(Eq. 3-36) 
To find other parameters of the spring Eq. 3-36 can be used. 
(Eq. 3-37) 

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70 
N
a
is the number of the active coils of the spring. For the ground and squared ends, the 
total number of coils and the free length can be found, using Eq. 3-37 and 3-38. 
(Eq. 3-38) 
(Eq. 3-39) 
In Eq. 3-37 and 3-38, N
t 
is the total number of coils, and p is the pitch of the spring. So 
Using Eq. 3-38 the pitch can be found too. 
(Eq. 3-40) 
Now to check for safety factor and strength of the spring, the shear stress in the coil needs 
to be calculated, using Eq. 3-41. 
(Eq. 3-41) 
In this equation, K
B
is the correction factor and can be calculated using Eq. 3-42. 
(Eq. 3-42) 
So if an assumption is made that the spring experience its maximum deformation as is expected, 
the maximum spring force on the spring will be
(Eq. 3-43) 
The shear stress in the coil will be, τ=497.6 MPa and the safety factor can be calculated 
as, 
(Eq. 3-44) 
which is greater than one. 

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71 
So the dimensions and properties of the main spring as designed are shown in table 3-6. 
Table 3- 6- Dimensions and properties of the main spring 
Material 
Hard drawn spring wire 
D 
8.5 
D 
46.75 mm 
C 
5.5 
P 
12 mm 
S
0
177 mm 
N
t
15.3 
End type 
Ground and Squared 
B) Press wheel spring design 
The same process can be used to design the spring that is used for press wheel. The only 
difference is that an extension spring is being used for press wheel, instead of compression 
spring. The main difference in the detail design of an extension spring is that the maximum stress 
always happens at the hook, not in the coil. The other difference is the pre-load or pre-tension 
that can be made in an extension spring while winding it. Pre-load will change the Eq. 3-33 to, 
(Eq. 3-45) 
As it is shown in section 3-3-2, with the optimized settings, the spring force can be 
recalculated, using Eq. 3-26 to get F
s
=837 N. 

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72 
If the displacement for the wheel is assumed to be ±100 mm in vertical direction, the 
displacement of the spring can simply be calculated, using the dimensions of figure 3-15. So 
ΔS= 
=27.78 mm. 
Assuming a spring index of C=5.5 for the spring, Eq. 3-46 can be used to find the range 
of preferred torsional stress caused by initial tension [21]. 
(
)
(Eq. 3-46) 
So 15.2 ksi< τ
i 
< 22.4 ksi. Then choosing, τ
i
= 20 ksi= 137.9 MPa and using Eq. 3-47, to
find the initial force in the spring, F
i
,
(Eq. 3-47) 
Choosing a spring wire with 7 mm diameter will result in D
s
=Cd= 38.5 mm. Thus, 
F
i
=482.4 N. 
Using Eq. 3-45, the spring constant of k
ex
= 12.8 N/mm can be found. 
Figure 3- 18- Parameters of the extension spring 

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73 
As mentioned earlier, the maximum stress usually happens at the hook of the extension 
spring, at point A or B in figure 3-18. Eq. 3-48 and 3-49 can be used to calculate the stress due to 
bending and tension at A, and torsional stress at B. 
[
] 
(Eq. 3-48) 
(Eq. 3-49) 
In which K
A
and K
B
are correction factors that can be found using Eq. 3-50 and 3-51, 
respectively. 
,
(Eq. 3-50) 
,
(Eq. 3-51) 
And r
1
and r
2
are the radiuses, as shown in Figure 3-18. Assuming 2r
1
=D
s
and r
2
= 10 mm, 
Eq. 3-50 and 3-51 can be used to find K
A
= 1.16 and K
B
=1.4. It is known that maximum 
displacement for the spring will result in maximum force and stress. Eq. 3-45 can be used to find 
F
max
= 1191.6 N. Then K
A
and K
B
and F
max
can be replaced into Eq. 3-48 and 3-49, to find
σ
A 
=818.8 MPa and τ
B
=478.1 MPa. 
Using the same material that was used for main spring (Hard Drawn spring wire), table 3-
3 and Eq. 3-35 can be used to find the properties of the wire. The strength of the spring wire in 
different modes can be found in Table 3-7. 
So, the safety factors of the spring at A and B can be sound. 
(Eq. 3-52) 
(Eq. 3-53) 

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74 
Table 3- 7- Strength properties of the extension spring wire for d=6 mm.[21] 
Parameter 
Equation 
Value 
S
ut
1231.9 MPa 
S
sy
554.4 MPa 
S
y
923.9 MPa 
Using the dimensions of the planter, where the spring must be installed, length and other 
dimensions of the spring can be found. The extension spring must be installed between two 
points that are 279.8 mm away from each other in working condition. So the free length of the 
spring will be 279.8 - 27.8 = 252 mm. Then Eq. 3-54 can be used to find the number of body 
coils of the spring. 
(Eq. 3-54) 
The number of body coils of the spring is N
b
=26. 
Finally the dimensions and properties of the extension spring, designed for press wheel 
can be found in table 3-8. 
Table 3- 8- Dimensions and properties of the press wheel spring 
Material 
Hard drawn spring wire 
D 
7 mm 
D 
38.5 mm 
C 
5.5 
L
0
252 mm 
F
i
482.4 N 
N
b
26 
Hook type 
Regular circular hook 

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75