By L. Huang
This up-to-date moment version broadens the reason of rotational kinematics and dynamics — an important point of inflexible physique movement in three-d area and an issue of a lot better complexity than linear movement. It expands therapy of vector and matrix, and contains 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 gains up to date remedies of recommendations in all chapters and case studies.
The textbook keeps its comprehensiveness in insurance and compactness in measurement, which make it simply obtainable to the readers from multidisciplinary parts who are looking to grab the foremost strategies of inflexible physique mechanics that are often scattered in a number of volumes of conventional textbooks. Theoretical innovations are defined via examples taken from throughout engineering disciplines and hyperlinks to purposes and extra complex classes (e.g. commercial robotics) are provided.
Ideal for college students and practitioners, this publication offers readers with a transparent route to realizing inflexible physique mechanics and its importance in different sub-fields of mechanical engineering and comparable areas.
Read Online or Download A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering PDF
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Additional info for A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering
Or /Â=2 : Comparing it to q D erOÂ=2 , the similarity between their forms is obvious. q/ and a rotation, and this relation will become clearer in the following discussion. 2/, the group of special unitary matrices of order 2. 2/ (k D 1; 2; 3). 0; ! x /, where ! q/ plays a similar role to that of q in qq in describing a rotation. So far, various types of representations of rotation have been discussed. Which one should be used depends on applications. For example, the Euler angle is usually chosen to formulate dynamic models of rigid bodies, whereas the equivalent/effective axis and angle or quaternion are preferred in a body’s posture measurement or calibration.
13b, the position vector itself rotates from the original position (C0 ) to the current position (C) with respect to a fixed frame (fAg). The rotation angle Â is the same as that of the angle between the fixed frame and the frame in which the position vector is attached in the passive representation. yˆ A yˆB yˆ A C C xˆ B OA OB (a ) C xˆ A OA xˆ A (b) Fig. 13 (a) Passive representation of position vector; (b) active representation of position vector 50 2 Orientation and Position Representation Fig.
8, starting from the frame fAg, the frame fCg is produced by two rotations around the axes ArO1 and BrO2 respectively. The rotational angles are Â1 and Â2 respectively. Note that the rotation axes are observed and described in the current frame, which is to be rotated to the next frame. In other words, each rotation is relative to the current frame. For clarity of presentation, the frame produced from the rotation in a current frame is not drawn together with the latter. 3 Orientation 41 zˆA A B rˆ1 zˆB zˆc 2 yˆA 1 yˆ c yˆ B rˆ2 OC (OB , O A ) OB (O A ) OA xˆA xˆ c xˆ B Fig.