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Five-axis CNC machining centers have become quite common today. The kinematics of most of the machines are based on a
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rectangular Cartesian coordinate system. This paper classifies the possible conceptual designs and actual existing implementations
based on the theoretically possible combinations of the degrees of freedom. Some useful quantitative parameters, such as the
workspace utilization factor, machine tool space efficiency, orientation space index and orientation angle index are defined. The
advantages and disadvantages of each concept are analyzed. Criteria for selection and design of a machine configuration are given.
New concepts based on the Stewart platform have been introduced recently in industry and are also briefly discussed. 2002
Elsevier Science Ltd. All rights reserved.7385
Keywords: Five-axis; Machine tool; Kinematic chain; Workspace; CNC; Rotary axis1. Introduction
The main design specifications of a machine tool can
be deduced from the following principles:
The kinematics should provide sufficient flexibility in
orientation and position of tool and part.
Orientation and positioning with the highest poss-
ible speed.
Orientation and positioning with the highest poss-
ible accuracy.
Fast change of tool and workpiece.
Save for the environment.
Highest possible material removal rate.
The number of axes of a machine tool normally refers
to the number of degrees of freedom or the number of
independent controllable motions on the machine slides.
The ISO axes nomenclature recommends the use of a
right-handed coordinate system, with the tool axis corre-
sponding to the Z-axis. A three-axis milling machine has
three linear slides X, Y and Z which can be positioned
everywhere within the travel limit of each slide. The tool
axis direction stays fixed during machining. This limitsthe flexibility of the tool orientation relative to the work-
piece and results in a number of different set ups. To
increase the flexibility in possible tool workpiece orien-
tations, without need of re-setup, more degrees of free-
dom must be added. For a conventional three linear axes
machine this can be achieved by providing rotational
slides. Fig. 1 gives an example of a five-axis milling
machine.2. Kinematic chain diagram
To analyze the machine it is very useful to make a
kinematic diagram of the machine. From this kinematic
(chain) diagram two groups of axes can immediately be
distinguished: the workpiece carrying axes and the tool
carrying axes. Fig. 2 gives the kinematic diagram of the
five-axis machine in Fig. 1. As can be seen the work-
piece is carried by four axes and the tool only by one
axis.
The five-axis machine is similar to two cooperating
robots, one robot carrying the workpiece and one robot
carrying the tool.
Five degrees of freedom are the minimum required to
obtain maximum flexibility in tool workpiece orien-
tation, this means that the tool and workpiece can be
oriented relative to each other under any angle. The
minimum required number of axes can also be under-
stood from a rigid body kinematics point of view. To
orient two rigid bodies in space relative to each other 6
degrees of freedom are needed for each body (tool and
workpiece) or 12 degrees. However any common trans-
lation and rotation which does not change the relative
orientation is permitted reducing the number of degrees
by 6. The distance between the bodies is prescribed by
the toolpath and allows elimination of an additional
degree of freedom, resulting in a minimum requirement
of 5 degrees.
3. Literature review
One of the earliest (1970) and still very useful intro-
ductions to five-axis milling was given by Baughman [1]