By L. Huang
This up-to-date moment variation broadens the reason of rotational kinematics and dynamics — crucial element of inflexible physique movement in third-dimensional house and a subject matter of a lot larger complexity than linear movement. It expands therapy of vector and matrix, and comprises quaternion operations to explain and study inflexible physique movement that are present in robotic keep an eye on, trajectory making plans, 3D imaginative and prescient method calibration, and hand-eye coordination of robots in meeting paintings, and so forth. It positive factors up to date remedies of suggestions in all chapters and case studies.
The textbook keeps its comprehensiveness in insurance and compactness in dimension, which make it simply available to the readers from multidisciplinary components who are looking to snatch the most important suggestions of inflexible physique mechanics that are frequently scattered in a number of volumes of conventional textbooks. Theoretical recommendations are defined via examples taken from throughout engineering disciplines and hyperlinks to purposes and extra complex classes (e.g. business robotics) are provided.
Ideal for college kids and practitioners, this e-book offers readers with a transparent route to realizing inflexible physique mechanics and its value in different sub-fields of mechanical engineering and comparable areas.
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Extra resources for A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering
4. 10 shows one type of sequence of rotations in which the body of the frame fBg represented by the axes xO 000 O 000 O000 B, y B , and z B is produced from frame fAg by rotations 0 around the axes zOA (angle ˛), yO B (angle ˇ), and xO 00B (angle ) consecutively. The Euler angles ˛, ˇ, and are called Z Y X Euler angles, corresponding to the yaw, pitch, and roll angles usually used in practice. From the definition of basic rotation matrices and the formula to derive the orientation of a body from successive rotations in Sect.
As shown in Fig. 9, the frame fCg is also produced by two rotations from the frame fAg, but the two rotational axes, A rO1 and ArO2 , are fixed in the frame fAg. 23) which means that the rotation matrix for the frame (fCg) reached by two successive rotations relative to the same (fixed) frame is the premultiplication of the rotation matrices for each rotation in the sequence. 23) lies in the difference in the frames relative to which the rotations occur. This is very important in orientation representation.
Cp is observed and described in the frame fCg. • When the description and observation frames are clear from the context, their names can be omitted from the notation. – C Remark. • The above notations are defined using the position vector as an example, but they can be used to represent any other types of vectors. , or a, it represents a linear velocity, an angular velocity, or a linear acceleration respectively. The following example is presented to show the application of the notation defined above.