By M. Z. Kolovsky, A. N. Evgrafov, Yu. A. Semenov, A. V. Slousch (auth.)
This e-book relies on a lecture direction added through the authors over a interval of a long time to the scholars in mechanics on the St. Petersburg country Technical college (the former Leningrad Polytechnic Institute). the fabric differs from a number of conventional textual content books on conception of Machines and Mechanisms via a extra profound elaboration of the equipment of structural, geometric, kinematic and dynamic research of mechanisms and machines, consisting in either the advance of recognized tools and the production of recent ones that bear in mind the wishes of modem desktop construction and the opportunity of modem desktops. The structural research of mechanisms relies on a brand new definition of structural workforce which makes it attainable to think about closed buildings that can not be lowered to linkages of Assur teams. The tools of geometric research are tailored to the research of planar and spatial mechanisms with closed constitution and a number of other levels of movability. huge cognizance is dedicated to the issues of con figuration multiplicity of a mechanism with given enter coordinates in addition to to the issues of distinguishing and elimination singular positions, that's of serious value for the layout of robotic platforms. those difficulties also are mirrored within the description of the equipment of kinematic research hired for the investi gation of either open ("tree"-type) constructions and closed mechanisms.
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Additional info for Advanced Theory of Mechanisms and Machines
We define in a unique way the position of its links by angles ql - q3, 1P2, 1P3, 1P6, 1P7. As mentioned earlier, the angles 1P2' 1P3' 1P6' 1P7 are additional coordinates. 3 Derivation of Equations of Geometric Analysis for Closed ... 53 3 x Fig. 10. Planar mechanism of movability three It is convenient to compose the equations of geometrical analysis on the basis of structural groups. Such an approach allows for the whole system of equations to be divided into several independent groups of equations of lower order, which can successively be solved for each group, following the sequence of their attachment to the frame.
This case will be considered separately. A Fig. 3. Mechanism of movability three of a planar platform In general, position functions can not be determined in simple analytical forms and the problem is to elaborate an algorithm for the calculation of output coordinates from input coordinates with the help of a computer. Because of geometric constraints, position functions exist only in a certain limited range of input coordinates. The determination of this area is also part of the direct problem of geometric analysis.
7) Let us consider some examples for determining the number w. For the planar mechanism of a horizontal forging machine (Fig. 28a) we have N = 9, P = S = 13. Hence, w = 1. For the spatial mechanism of a platform (Fig. 28b) we have N = 7, P = 9, S = 15, therefore, W = 3. 7) is correct only if there are no excessive constraints and no redundant degrees of movability in the mechanism structure. Their presence would violate the "normal" relations between the number of links, the number of constraints in kinematic pairs of a mechanism and the number of degrees of movability.
Advanced Theory of Mechanisms and Machines by M. Z. Kolovsky, A. N. Evgrafov, Yu. A. Semenov, A. V. Slousch (auth.)