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possible tool axis selection (1 out of 6 or 6 possibilities).
So theoretically there are 6×120=720 possible five-axis
machines with one tool carrying axis. The same analysis
can be done for all other combinations. With t the num-
ber of tool carrying axes and w the number of workpiece
carrying axes (w+t=5) the total number of combinations
is as follows.The value of this equation is always equal to 6! or
720 when w+t=5. Some of these 720 combinations will
be containing only two linear axis. If only five-axis
machines with three linear axes are considered, only
3×5!=360 combinations are still possible.
The set Gt of combinations is characterized by a fixed
value of t. This set is identical to the set Gw charac-
terized by a fixed value of w, w=5t. Using above defi-
nitions following subgroups of five-axis machines exist:
(i) Group G0/G5; (ii) Group G1/G4; (iii) Group
G2/G3; (iv) Group G3/G2; (v) Group G4/G1; (vi)
Group G5/G0.
4.1.1. G5/G0 machine
All axes carry the tool and the workpiece is fixed on
a fixed table. Fig. 4 shows a machine with all the five
axes carrying the tool. The kinematic chain is XBYAZ
(TRTRT). This machine was one of the earliest models
of five-axis machines to handle very heavy workpieces.
As there are many links in the tool carrying kinematic
chain, there can be a considerable error due to elastic
deformations and backlash in the slides.
4.1.2. G0/G5 machine
All axes carry the workpiece and the tool is fixed in
space. This construction is best used for very small
workpieces (see Section 6.3).4.1.3. G4/G1 machine
Four axes carry the tool and one axis carries the work-
piece. There are basically two possibilities, the work-
piece carrying axis can be R or T.
4.1.4. G1/G4 machine
One axis carries the tool and the other four axes carry
the workpiece. There are basically two possibilities, the
single axis kinematic chain can be R or T. Fig. 1 is an
example of such a machine, with the single tool carrying
axis T.
4.1.5. G3/G2 machine
Three axes carry the tool and two axes carry the work-
piece. There are basically three possibilities, the work-
piece carrying axes can be both linear (TT) both
rotational (RR) or mixed (TR). Fig. 5 gives an
example of a machine with the tool carried by two rotary
axes and one linear axis. This machine allows processing
of large workpieces but the construction of the toolside
is complicated. The most common configuration is the
workpiece carried by the two rotary axes such as the one
given in Figs. 3, 6 and 8.
4.1.6. G2/G3 machine
Two axes carry the tool and three axes carry the work-
piece. There are basically three possibilities, the tool car-
rying axis can be both linear (TT) both rotational (RR)
or mixed (TR). Fig. 7 shows the mixed construction. Fig.
8 shows two linear axes carrying the tool.
4.2. Classification based on the location of rotary
axes
The machines can be classified depending on the place
where the rotation axes are implemented.Only machines with two rotary axes and three linear
axes will be considered further. The possible configur-
ations are:
(a) rotation axes are implemented on tool spindle;
(b) rotation axes are implemented on machine table;
(c) combination of both.
The sequence of the axes in the tool or workpiece
carrying kinematic chain is not important if the axes are
of the same type R or T. In general, if there are N
T trans-
latory axes and N
R rotary axes in the workpiece carrying
kinematic chain and NT translatory axes and NR rotary
axes in the tool kinematic chain, then the numbers of