By L. Huang

This up to date moment variation broadens the reason of rotational kinematics and dynamics — an important element of inflexible physique movement in three-d area and a subject matter of a lot higher complexity than linear movement. It expands therapy 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 forth. It gains up-to-date remedies of ideas 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 components who are looking to snatch the foremost options of inflexible physique mechanics that are often scattered in a number of volumes of conventional textbooks. Theoretical thoughts are defined via examples taken from throughout engineering disciplines and hyperlinks to functions and extra complex classes (e.g. commercial robotics) are provided.
Ideal for college students and practitioners, this booklet offers readers with a transparent route to figuring out inflexible physique mechanics and its importance in several sub-fields of mechanical engineering and similar areas.

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In the context of engineering applications, the universal frame is always assumed to be fixed on Earth, and its axes are denoted by the special basis O vectors Oi, Oj, and k. Though the Cartesian coordinate frame is the most popular for studying rigid body motions, cylindrical or spherical coordinate frames are more convenient for describing circular motions. © Springer International Publishing Switzerland 2017 L. 1007/978-3-319-45041-4_2 27 28 2 Orientation and Position Representation {B} Fig.

There is a need to find a way to embed them in a neat and compact notation for the vector. Let p be the position vector of a point. Define C pA as the vector p observed in the frame fAg and described in the frame fCg (Fig. 4). This notation consists of three parts: • p: the name of the position vector, which is the center of the notation. • A: the name of the observation frame, which forms the right subscript of the vector name. It is separated from the vector name with a slash. • C: the name of the description frame, which is the left superscript of the vector name.

There is a one-to-one mapping between the Cartesian coordinates and the cylindrical coordinates of a point. xOA ; yOA zOA / of the point OA , the corresponding cylindrical coordinates are rD q x2OA C y2OA ; D tan 1 y OA ; xOA ¤ 0; x OA z D zOA : If xOA D 0 and yOA ¤ 0, then D ˙ 2 . If xOA D yOA D 0, then OA is located on the O Z-axis and is not defined. 3 shows a spherical frame fAg W OA eO  eO eO r in the universal coordinate frame fUg. 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.

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