M. Kemal Ozgoren - Kinematics of General Spatial Mechanical Systems
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- Название:Kinematics of General Spatial Mechanical Systems
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Kinematics of General Spatial Mechanical Systems: краткое содержание, описание и аннотация
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This all-time beneficial book:
Provides an easy-to-use systematic formulation method that is applicable to all sorts of spatial machanisms and manipulators Introduces a symbolic manipulation method, which is effective and straightforward to use, so that kinematic relationships can be simplified by using all the special geometric features of the system Offers an accessible format that uses a systematic and easy-to-conceive notation which has proven successful Presents content written by an author who is a renowned expert in the field Includes an accompanying website Written for academicians, students, engineers, computer scientists and any other people working in the area of spatial mechanisms and manipulators,
provides a clear notation, formulation, and a logical approach to the topic and offers a fresh presentation of challenging material.
in
rather than in
. By doing so, Eq. (3.166)can be written again as follows:
and
. Suppose they are related to each other by means of a function
so that
, the relationship described by Eq. (3.168)is characterized by various designations, which are explained below.
is called homogeneous if

is called linear if, for a scalar k and for all
,

is expressed as follows in terms of an m × n matrix
, which does not depend on
:
is called affine , if
is expressed as follows in terms of an m × n matrix
and an m × 1 matrix
, which are both independent of
.
is defined as the bias term . It may or may not be zero, i.e.
.
is both nonhomogeneous and nonlinear. However, a special affine relationship with
happens to be both homogeneous and linear.
and
consist of the coordinates of P in
and
. So, the following equation, which is the repetition of Eq. (3.167), constitutes an affine transformation between
and
, i.e. between the coordinates of P in
and
.