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Bishop, Robert H. - The Mechatronics Handbook [CRC Press 2002] Part 3

Tham khảo tài liệu 'bishop, robert h. - the mechatronics handbook [crc press 2002] part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Point mass at radius r 2 J mr Cylindrical shell about axis c- c inner radius r J mr2 Rod or bar about centroid mứ 12 If outer radius is R and not a thin shell J 2 m R2 r 2 d Short bar about pivot J m d 2 4l2 12 Slender bar case d 0 c Cylinder about axis c-c radius r 12 J 2 mr FIGURE 9.13 Mass moments of inertia for some common bodies. and associated mass moments of inertia are given in Fig. 9.13. General rigid bodies are discussed in section Inertia Properties. There are several useful concepts and theorems related to the properties of rigid bodies that can be helpful at this point. First if the mass moment of inertia is known about an axis through its center of mass IG then Steiner s theorem parallel axis theorem relates this moment of inertia to that about another axis a distance d away by I IG md where m is the mass of the body. It is also possible to build a moment of inertia for composite bodies in those situations where the individual motion of each body is negligible. A useful concept is the radius of gyration k which is the radius of an imaginary cylinder of infinitely small wall thickness having the same mass m and the same mass moment of inertia I as a body in question and given by k JlIm . The radius of gyration can be used to find an equivalent mass for a rolling body say using meq Ilk . Coupling Mechanisms Numerous types of devices serve as couplers or power transforming mechanisms with the most common being levers gear trains scotch yokes block and tackle and chain hoists. Ideally these devices and their analogs in other energy domains are power conserving and it is useful to represent them using a 2-port model. In such a model element the power in is equal to the power out or in terms of effort-flow pairs e1f1 e2 f2. It turns out that there are two types of basic devices that can be represented this way based on the relationship between the power variables on the two ports. For either type a relationship between two of the variables can usually be .