Notation

C1.g, C2..g The first and second principal plane sections of the gear tooth flank G C1.T, C2..T The first and the second principal plane sections of generation surface T of

the gear cutting tool E A characteristic line Eg, Fg, Gg Fundamental magnitudes of the first order of the gear tooth surface G ET, FT, GT Fundamental magnitudes of the first order of generating surface T of the

gear cutting tool Eu(𝜓,𝜃,𝜑) Operator of the Eulerian transformation G Gear tooth surface K Point of contact of the surfaces G and T (or a point within a line of contact of

the surfaces P and T) Lg, Mg, Ng Fundamental magnitudes of the second order of the gear tooth surface G LT, MT, NT Fundamental magnitudes of the second order of generating surface T of the

gear cutting tool Pln Pitch line in the gear machining mesh Rlx(𝜑y, Y) Operator of rolling over a plane (Y axis is the axis of rotation, X axis is the

axis of translation) Rlz(𝜑y, Y) Operator of rolling over a plane (Y axis is the axis of rotation, Z axis is the

axis of translation) Rly(𝜑x, X) Operator of rolling over a plane (X axis is the axis of rotation, Y axis is the

axis of translation) Rlz(𝜑x, X) Operator of rolling over a plane (X axis is the axis of rotation, Z axis is the

axis of translation) Rlx(𝜑z, Z) Operator of rolling over a plane (Z axis is the axis of rotation, X axis is the

axis of translation) Rly(𝜑z, Z) Operator of rolling over a plane (Z axis is the axis of rotation, Y axis is the

axis of translation) Rru(𝜑, Z) Operator of rolling of two coordinate systems Rs ( )A B Operator of the resultant coordinate system transformation, say from the

coordinate system A to the coordinate system B Rt(𝜑x, X) Operator of rotation through an angle 𝜑x about the X axis Rt(𝜑y, Y) Operator of rotation through an angle 𝜑y about the Y axis Rt(𝜑z, Z) Operator of rotation through an angle 𝜑z about the Z axis R1.g, R2..g The first and second principal radii of the work gear tooth flank G R1.T, R2..T The first and second principal radii of curvature of generating surface T of

the gear cutting tool Scx(𝜑x, px) Operator of screw motion about the X axis Scy(φy, py) Operator of screw motion about the Y axis

Scz(𝜑z, pz) Operator of screw motion about the Z axis Tr(ax, X) Operator of translation at a distance ax along the X axis Tr(ay, Y) Operator of translation at a distance ay along the Y axis Tr(az, Z) Operator of translation at a distance az along the Z axis Ug, Vg Curvilinear (Gaussian) coordinates of a point on the work gear tooth

flank G UT, VT Curvilinear (Gaussian) coordinates of a point of generating surface T of the

gear cutting tool UP, VP Tangent vectors to curvilinear coordinate lines on the work gear tooth

flank G UT, VT Tangent vectors to curvilinear coordinate lines on generating surface T of the

gear cutting tool VΣ Vector of the resultant motion of generating surface T of the gear cutting tool

in relation to tooth flank G of the work gear k1.g, k2..g The first and second principal curvatures of the work gear tooth flank G k1.T, k2..T The first and second principal curvatures of generating surface T of the gear

cutting tool ng Unit normal vector to the work gear tooth flank G nT Unit normal vector to generating surface T of the gear cutting tool rcnf Position vector of a point of the indicatrix of conformity CnfR (G/T) rg Position vector of a point of the work gear tooth flank G t1.g, t2..g Unit tangent vectors of principal directions on the work gear tooth flank G t1.T, t2..T Unit tangent vectors of principal directions on generating surface T of the

gear cutting tool ug, vg Unit tangent vectors to curvilinear coordinate lines on the work gear tooth

flank G uT, vT Unit tangent vectors to curvilinear coordinate lines on generating surface T

of the gear cutting tool xPyPzP Local Cartesian coordinate system having origin at the point of contact of the

surfaces G and T

𝛷1.g, 𝛷2..g The first and second fundamental forms of the gear tooth flank surface G 𝛷1.T , 𝛷2..T The first and second fundamental forms of generating surface T of the gear

cutting tool Σ Crossed-axis angle 𝜙n Normal profile angle of a gear cutting tool 𝜇 Angle of the surfaces G and T local relative orientation 𝜁c Setting angle of a gear finishing tool ωc Rotation of the gear cutting tool ωg Rotation of the work gear ωpl Instant rotation of the gear cutting tool in relation to the work gear

cnf Conformity max Maximum min Minimum opt Optimal g Gear c Cutting tool