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.




and
. The k th basis vector of
can be represented by the following column matrix in
for k ∈ {1, 2, 3}.
and
,
can be expressed as follows:

picks up the k th column of the matrix, by which it is postmultiplied. Thus, in Eq. (3.28),
happens to be the k th column of
. Therefore,
can be expressed column by column as shown below.

, Eq. (3.30)leads to the following equation when it is transposed on both sides.
picks up the k th row of the matrix, by which it is premultiplied. Thus, in Eq. (3.31),
happens to be the k th row of
. Therefore, as an alternative to Eq. (3.29),
can also be expressed row by row as shown below.
requires the column matrix expressions of the basis vectors of
in
, whereas the row‐by‐row expression of the same
requires the row matrix expressions of the basis vectors of
in
.
, represent the members an orthonormal vector triad, i.e.
. This fact poses six independent scalar constraint equations on the nine elements of
. The independent constraint equations can be expressed as follows for i ∈ {1, 2, 3} and j ∈ {1, 2, 3}: