By L. Huang

ISBN-10: 3319450409

ISBN-13: 9783319450407

ISBN-10: 3319450417

ISBN-13: 9783319450414

This up to date moment version broadens the reason of rotational kinematics and dynamics — crucial point of inflexible physique movement in third-dimensional area and a subject of a lot larger complexity than linear movement. It expands remedy of vector and matrix, and comprises quaternion operations to explain and learn inflexible physique movement that are present in robotic keep an eye on, 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 strategies in all chapters and case studies.
The textbook keeps its comprehensiveness in assurance and compactness in dimension, which make it simply obtainable to the readers from multidisciplinary parts who are looking to seize the foremost options of inflexible physique mechanics that are frequently scattered in a number of volumes of conventional textbooks. Theoretical thoughts 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 kids and practitioners, this e-book offers readers with a transparent route to knowing inflexible physique mechanics and its value in different 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

Example text

1 as an example. If the observation frame is fAg, the vector is observed as the directional line OA OB . If the observation frame changes to fUg, the vector is observed as the directional line OOB . What happens if the observation frame is fBg? 2 Observation Frame, Description Frame, and Vector Notation 31 zˆ A Fig. 4 Position of a point in the body frame C A pC kˆ {U } Z iˆ O pC { A} yˆ A OA pOA xˆ A ˆj Y X degenerate, and is just a point, and a zero (null) vector is formed. For each directed line observed, its x, y, and z components along the axes of the description frame fAg are different from those along the axes of another description frame fUg, generating different vector expressions.

Q0 ˙ p0 /; ! q ˙! q0 p0 ! p ; q0! p C p0! q C! q q T! 28) Note quaternion multiplication uses both the vector inner (dot) and outer (cross) products. If p and q are pure quaternions, then qp D ! q ! p; q! q D ! q T! qq D q2 D ! q D k! 4 Quaternions 23 In matrix form, Ä Ä ! 0 p D q: ! 3 3 q q0 I C Œ q  p p0 I Œ! p  Obviously, pq ¤ qp, unless Œ! q ! p D 0 or ! q ! p D 0. This means that ! q and ! p are parallel to each other. q0 ; q/; qp D qp; qq D qq D q20 C ! q: q T! q/ D kqk D q p p p qq D qq D q20 C k!

The frame is defined by pOA D rOer ; eO r D sin  cos Oi C sin  sin eO  D cos  cos Oi C cos  sin eO D eO r eO  D sin Oi C cos Oj C cos  k; O Oj O sin  k; Oj; right-hand rule: The spherical coordinates include r, Â, and , where r is the radius of the sphere,  is called the colatitude angle, and is called the azimuth angle. Like a cylindrical coordinate frame, the axes of a spherical coordinate frame depend on its origin. The spherical coordinates and the Cartesian coordinates of the origin OA are related through q r D x2OA C y2OA C z2OA ; 30 2 Orientation and Position Representation Fig.

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A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering by L. Huang


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