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 better complexity than linear movement. It expands therapy of vector and matrix, and comprises quaternion operations to explain and examine inflexible physique movement that are present in robotic keep watch over, trajectory making plans, 3D imaginative and prescient procedure calibration, and hand-eye coordination of robots in meeting paintings, and so on. It beneficial properties up-to-date remedies of recommendations in all chapters and case studies.
The textbook keeps its comprehensiveness in insurance and compactness in dimension, which make it simply obtainable to the readers from multidisciplinary components who are looking to take hold of the foremost thoughts 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 complicated classes (e.g. business robotics) are provided.
Ideal for college students and practitioners, this ebook presents readers with a transparent route to realizing inflexible physique mechanics and its importance in different sub-fields of mechanical engineering and comparable areas.
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Additional resources for A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering
The rotational angles are ˛, ˇ, and , called the roll(R), pitch (P), and yaw (Y) angles. For simplicity and clarity of presentation, the immediate frames appearing in the rotations are not shown. Following the rules to derive the rotation matrix for the orientation of successive rotations relative to a fixed frame in Sect. ˇ/Rz . 29) 44 2 Orientation and Position Representation Fig. 11 RPY angles zˆA yˆA xˆA Note that this is the same as the rotation matrix of Z Y X angles, which means that the same orientation will be reached either by three rotations (X Y Z) about the axes of a fixed frame or by three rotations in opposite order (Z Y X) about the axes of the moving frames.
A AT /x D 0: If A is a skew-symmetric matrix, AT D A, then xT Ax D 0. If for every x ¤ 0, xT Ax > 0, then A is said to be positive definite. It is negative definite if xT Ax < 0. It can be proved that the eigenvalues of a positive definite matrix are positive, and those of a negative definite matrix are negative. 23), Ä x Ax D Œx1 x2 T 5 2 2 2 Ä x1 x2 D 3x21 Ä 0: If x ¤ 0, then xT Ax < 0, and so A is negative definite. The matrix A has negative eigenvalues 6 and 2. 24) is an invertible matrix.
Its origin O is at the bottom of the rod O (OA ). Three fixed principal axes X, Y, and Z are along the basis vectors Oi, Oj, and k. • Body frame of the rod fAg W OA xO A yO A zOA . Its origin OA coincides with O, and zOA coincides with the axis Z. The yO A axis is the projection of the rod on the XOY plane. Its angle Â with the Y axis describes the angular displacement of the rod around the Z axis. The xO A axis is then determined by the right-hand rule. • Body frame of the box fBg W OB xO B yO B zOB .