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.
Equations (1.63)and (1.59)imply that
is exponentiated as follows:

The ssm operation is applied as shown below on the products
and
.

is a rotation matrix , i.e. an orthonormal matrix with
.
It happens that
is a singular matrix and its rank is two. That is,


, the matrix version of Eq. (1.70)can be written as
. Therefore, the frame indicating superscript ( a ) is concealed for the sake of brevity. By expanding the product
according to Eq. (1.61) Eq. 1.71can be written again as follows:


, consider the following equation, from which
is to be found for given
and
.
cannot be found uniquely from Eq. (1.74). However, it can be found with the following expression that contains an arbitrary parameter λ .
is the part of
that is orthogonal to
. So, it can be expressed as
and
are orthogonal,
. Therefore, Eq. (1.77) gives γ as