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Table 3 Parameters for the design of a multifunctional robotic end-effector

From: A bio-inspired approach for the design of a multifunctional robotic end-effector customized for automated maintenance of a reconfigurable vibrating screen

Notation Description
F g Gripping force of the multifunctional robotic end-effector
M Mass of the object to be grasped by the multifunctional robotic end-effector
g Acceleration due to gravity
μ μ = coefficient of static friction between the object to be gripped and the multifunctional robotic end-effector = 
FS Factor of safety = 1.5
ω = ω 1 and ω 2 Relative angular speed of the worm and gear of the multifunctional robotic end-effector
n Rotational speed of the worm of the multifunctional robotic end-effector
V Linear speed of the worm of the multifunctional robotic end-effector
r Radius of the worm of the multifunctional robotic end-effector
P Power dissipated by the multifunctional robotic end-effector in carrying out a RVS machine maintenance task
N 1 and N 2 Rotational speed of the worm and gear of a multifunctional robotic end-effector
T 1 and T 2 Number of teeth in the worm and gear of a multifunctional robotic end-effector = 
i Worm–gear ratio
C Assumed centre distance of the worm–gear of the multifunctional robotic end-effector
d 1 and d 2 Diameters of the worm and gear of the multifunctional robotic end-effector
P 2 Circular pitch of the gear
m Module
P a Axial pitch of the worm
L Lead of the worm
N tw Number of the teeth on the worm
λ and Ψ Lead angle and helix angle
L w Axial length of the worm
L screw Total length of the lead screw
V 1 and V 2 Linear speed of the worm and gear of the multifunctional robotic end-effector
r 1 and r 2 Radius of the worm and gear of the multifunctional robotic end-effector
V s Sliding velocity
F 1t, F 2t, F n and F d Tangential forces, normal force and total force acting on the worm
F a and F r Thrust or axial force and radial force
\({\o}_{\text{n}}\) Pressure angle
F b Bending fatigue strength of the worm–gear of the end-effector
F w The maximum allowable value of dynamic load under surface fatigue condition
σ b Permissible bending stress in bending fatigue for worm–gear material
b Face width
Kw Material and geometry factor of the worm–gear
Y Modified Lewis form factor obtained from a worm–gear catalogue
ƞ Efficiency of the worm–gear module
f Coefficient of friction acting on the worm–gear module
H g Heat dissipation of the worm–gear
A Surface area
C The distance between the shafts of the duplex worm wheel of end-effector
C H Heat transfer coefficient
T o Lubricating oil temperature of the worm–gear
T a Ambient air temperature
σ a and σ max Nominal and maximum bending stresses acting on the bolt socket module of the robotic end-effector
τ a and τ max Nominal and maximum torsional stresses acting on the bolt socket module of the robotic end-effector
Mc Turning effect on the M-20 bolt
T Torque on the bolt
I Inertia of the object
d Diameter of the bolt socket module
K t and K ts Theoretical stress concentration factors
\(m_{{{\text{cyl-rod}}\;{\text{at}}\; 0\;{\text{str}}}}\) Mass of the cylinder rod at zeroth stroke
\(m_{\text{cyl-rod}}\) Mass of the cylinder rod
\(m_{\text{cyl-rod/mmstroke}}\) Mass of the cylinder rod per mm of stroke
\(m_{\text{ext}}\) External mass = mass of the screen panel pin on the RVS machine
\(F_{\text{fr-ext}}\) External frictional force in N
\(F_{\text{ham}}\) Hammering force
\(F_{\text{un-pin}}\) Unpinning force
\(F_{\text{x,ext}}\) External force
\(U_{\text{m}}\) and \(V_{\text{m}}\) Initial and final linear speed of the electric motor powering the electric cylinder actuator
a Acceleration of the electric motor
s Travel distance of the piston of the electric cylinder actuator