By M. Z. Kolovsky, A. N. Evgrafov, Yu. A. Semenov, A. V. Slousch (auth.)
This booklet relies on a lecture path added through the authors over a interval of decades to the scholars in mechanics on the St. Petersburg nation Technical collage (the former Leningrad Polytechnic Institute). the cloth differs from various conventional textual content books on conception of Machines and Mechanisms via a extra profound elaboration of the tools of structural, geometric, kinematic and dynamic research of mechanisms and machines, consisting in either the improvement of famous tools and the production of latest ones that bear in mind the wishes of modem computer development and the potential for modem pcs. The structural research of mechanisms is predicated on a brand new definition of structural staff which makes it attainable to think about closed constructions that can not be lowered to linkages of Assur teams. The equipment of geometric research are tailored to the research of planar and spatial mechanisms with closed constitution and several other levels of movability. enormous consciousness 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 significant 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) buildings and closed mechanisms.
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Example text
29. Graph and structural diagram of a horizontal forging machine The solution of this problem can be acieved with the help of graphs introduced in Sect. 4. Let us consider examples illustrating the process of division of mechanisms into structural groups. Fig. 29a shows the graph of the mechanism of a horizontal forging machine (Fig. 28a). There are four independent loops in this graph: 0 - 1- 2 - 3 - 0, 0- 1- 2 - 4 - 5 - 6 - 0, 6 - 5 - 7 - 8 - 6, 0 - 6 - 8 - 9 - 0, which differ in at least one vertex or edge.
22) Four-dimensional column matrices of coordinates are (s-I) _ (s-l) (s-I) (s-l) l)T RM - x M 'YM ,zM ' , R(s) _ (s) (s) (s) l)T M - x M 'YM ,zM' . 24) . Let us point out some properties of this transformation matrix and the direction cosine matrix As-I,s figuring in it. The direction cosine matrix is an orthogonal matrix (the absolute value of its determinant is equal to unity). 20) the transformation matrix is a function of the input coordinate q s; its form depends on the type of kinematic pair.
In addition, the four-bar group of movability two is eliminated which complicates the analysis. Let us consider the mechanism with diagram presented in Fig. 19a; it consists of a one-bar group of movability one (link 1) and a four-bar Assur group. Replacing the input coordinate q by the coordinate