Mechanism and Kinematic Relation of a CNC Hob-
bing Machine
A 6-axis CNC hobbing machine can be used to manufacture
different types of gears owing to the movement of its axes with
multi-degree of freedom. The generation process of gears by
applying a CNC hobbing machine is quite complex. Figure 1
presents a schematic drawing of a 6-axis CNC hobbing machine,
where axes X, Y and Z are the radial axis, the tangential axis,
and the axial axis, respectively; axes A, B and C are the hob
swivel axis, the hob spindle axis and the work table axis, respec-
tively. However, in today's CNC hobbing machines, axes A and
Y are for set-up only and rotational ratio between axes B and C
is a constant. Some machines allow an interrelationship between
axes X and Z; therefore, today's CNC hobbing machines are 3-
axis machines. The proposed 6-axis hobbing machine may be
built in the future. Figure 2 illustrates the kinematic relationship
among those axes. Coordinate system St,{Xh, K;, , Z/,) is attached
to the hob cutter while coordinate system Sp(Xp, Yp, Zp) is
attached to the work piece which is cut by the hob cutter.
Coordinate system Sf(Xf, Yf, Z/) is the fixed coordinate system
attached to the machine housing and coordinate system Sr(Xr,
Yr, Zr) is the reference coordinate system, cj),, and 4>p are rotatio
angles of the hob cutter and gear blank, respectively; and F is
the setting angle of hob cutter. Also, kinematic relation between
different coordinate systems can be obtained by applying coor-
dinate transformation matrix equations. The transformation ma-
trix [My] transforms the coordinates from coordinate system
Sj(Xj, Yj, Zj) to Si{X,, Fj, Zj). Based on the relationship in
Fig. 2, matrices [M,*], [M/-r], and [M,,/] can be represented as
follows:
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