ISSN 1068-798X, Russian Engineering Research, 2017, Vol. 37, No. 7, pp. 568–573. © Allerton Press, Inc., 2017.
Original Russian Text © B.M. Bazrov, 2017, published in Vestnik Mashinostroeniya, 2017, No. 4, pp. 5–10.
Theoretical and Practical Aspects of Basing in Manufacturing
B. M. Bazrov
Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Moscow, Russia
Abstract—The fundamental principles of basing theory are analyzed and refined. They are applied to the
design of products, equipment, and manufacturing systems.
Keywords: product, structure, basing, base, parts, reference point, manufacturing
In the basing of parts and assemblies, research
interest has focused recently on the use of implicit
bases, complex surfaces, or some combination of
explicit and implicit bases, as we see in [1–3], for
example. This indicates the need for further develop-
ment of basing theory.
Balakshin’s fundamental work on basing theory 
was used in the development of State Standard GOST
21495–76 . It outlines the basic principles of the
theory, which have since remained unchanged.
Some principles and definitions of this theory were
critiqued in [1–3]. Note, however, that it remains rel-
evant today, although it undoubtedly requires refine-
ment. We address some improvements in the present
Basing theory rests on the mechanical principle
that an absolutely solid body in space has six degrees of
freedom: three linear motions; and three rotations.
Accordingly, if an absolutely solid body is to be ren-
dered immobile, it must be deprived of all six degrees
Then the position of an absolutely solid body of any
shape in the right coordinate system ZYX (Fig. 1a) will
be determined by the position of three points (a, b, c)
that do not lie on a straight line. The spatial position of
each point is determined by three independent coordi-
nates: for example, aa', aa'', aa''' for point a; bb', bb'',
bb''' for point b; and cc', cc'', cc''' for point c. Here a
coordinate is understood to mean a relationship
depriving the body of one degree of freedom. The nine
relations just specified deprive the body of the follow-
ing degrees of freedom:
—the coordinates aa', aa'', aa''' eliminate three
motions (along the Z, Y, and X axes);
—the coordinates bb', bb'', bb''' eliminate rotation
around the Y and X axes and motions along the Z axis;
—the coordinates cc', cc'', cc''' eliminate rotation
around the Z and X axes and motions along the Y
According to Fig. 1, the coordinates bb''', cc'', cc'''
deprive the body of degrees of freedom that have
already been eliminated. Therefore, we need only
specify six relationships (independent coordinates) in
order to deprive the body of all its degrees of freedom.
The coordinates of one of the three points in the
body impose constraints on its motion along the three
axes; two coordinates of the second point eliminate
two rotations around the first point; the coordinate of
the third point eliminates rotation around the line
connecting the first and second points.
These six coordinates belong to the following coor-
dinate planes of the right coordinate system: each
coordinate of the first point belongs to a different
coordinate plane; one coordinate of the second point
belongs to the first plane and the other to the second
plane; and the coordinate of the third point belongs to
the first coordinate plane.
Fig. 1. Position of an absolutely solid body of any shape in
the right coordinate system XYZ.