Five-axis CNC machining centers have become quite common today. The kinematics of most of the machines are based on a

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-

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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] 五轴铣削机床英文文献和中文翻译:http://www.lwfree.cn/fanyi/20170419/5329.html