By L. Huang
This up-to-date moment version broadens the reason of rotational kinematics and dynamics — crucial point of inflexible physique movement in 3-dimensional house and a subject of a lot larger complexity than linear movement. It expands therapy of vector and matrix, and contains quaternion operations to explain and research inflexible physique movement that are present in robotic regulate, trajectory making plans, 3D imaginative and prescient method calibration, and hand-eye coordination of robots in meeting paintings, and so on. It gains up-to-date remedies of suggestions in all chapters and case studies.
The textbook keeps its comprehensiveness in insurance and compactness in measurement, which make it simply available to the readers from multidisciplinary parts who are looking to take hold of the most important innovations of inflexible physique mechanics that are often scattered in a number of volumes of conventional textbooks. Theoretical recommendations are defined via examples taken from throughout engineering disciplines and hyperlinks to functions and extra complicated classes (e.g. business robotics) are provided.
Ideal for college students and practitioners, this booklet presents readers with a transparent route to knowing inflexible physique mechanics and its value in several sub-fields of mechanical engineering and comparable areas.
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Extra info for A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering
Note that R r . Â/. This is an ambiguity in the equivalent/effective axis–angle representation of rotation. Â/ corresponding to the equivalent/effective representation of rotation [Eq. 12)]. Applying Taylor expansions of the sine and cosine functions, sin Â D 1 X . 2k C 1/Š 1 X x2k ; . 2k/Š kD0 and considering that ŒOr 2k D . 1/kC1 ŒOr 2 ; ŒOr 2kC1 D . Â/ D 1 X ŒOr k D eŒOr kŠ kD0 Â : These are the exponential coordinates for the rotation specified by an axis (Or) and an angle (Â). 40 2 Orientation and Position Representation Since eŒOr Â D eŒ rO .
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.
Here fAg and fUg share the same origin, and xO A D Oj, yO A D kO and zOA D Oi. The origin of the frame fBg is on the Oj-axis at a distance a from OA , and O yO B D Oi and zOB D Oj. The point C is on the zOB -axis. xO B D k, The expressions for positions of OB and C are determined by the choice of observation frame and description frame. For the position of the point C, pC D Œb 0 0T ; observed in fBg and described in fBg; B pCB D Œ0 0 bT ; observed in fBg and described in fUg; pC D Œ0 a bT ; observed in fUg and described in fUg: Fig.