Numerical Simulation of Bending Stiffness Analysis for Spring Linkage Applied to In-Pipe Robot

Table 2

Character definition table.

Notation	Meaning
E	Material elastic modulus
G	Material shear modulus
H1, h2	The only two components of the outer diameter, corresponding to the mix and max deformation in each cross section
	Coordinate basis vectors of principle reference systems
	Coordinate basis vectors of general reference systems
Ix, Iy, Iz	Inertia moment around x-, y-, and z-axis
K	Spring compression stiffness
Kb	Spring bending stiffness
L	Spring wire length
l1	Screw pitch of robot module
l2	Screw pitch of spring
M	Acting moment
	General Descartes reference system
	Start point at bottom of spring
	Point along the axis of spring wire
	Principle coordinate system
	Local coordinate system
R	Spring wire radius
R	Spring nominal radius
S	Accumulated arc length
	Curvature vector
Α	Rotation angle about ζ-axis
Β	Rotation angle of the cross section around the tangential direction
Γ	Included angle
υ	Poisson ratio
Θ	Helix angle
θ 0	Initial value of θ