By M. Z. Kolovsky, A. N. Evgrafov, Yu. A. Semenov, A. V. Slousch (auth.)

This ebook relies on a lecture direction brought by means of the authors over a interval of decades to the scholars in mechanics on the St. Petersburg nation Technical college (the former Leningrad Polytechnic Institute). the fabric differs from a variety 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 famous equipment and the construction of recent ones that keep in mind the wishes of modem laptop development and the potential for modem pcs. The structural research of mechanisms relies on a brand new definition of structural team 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 several other levels of movability. huge awareness 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 removal singular positions, that is of significant value for the layout of robotic structures. 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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In accordance with the rules introduced above, four coordinate systems 0sxsYszs, (s = 1,2,3,4) are attached to the robot links. We also indicate their initial positions O. x •Y • z. as well as the input s s s s coordinates qs determining the relative positions of links. First, let us compose the matrices of the invariant direction cosines 50 2 Geometric Analysis of Mechanisms Fig. 8. Euler angles o1 o 0] 0 (s = 1,2,3), 1 Then, with these matrices, we find Zo, Z 1*, Z 1, Z2* Z 2, Z 3*, Z 3 Fig. 9.

5. 39a ); of a micromanipulator for electronic microscopes (Fig. 40a) and do the structural analysis. Answer: w = 1, 3, 6. 6 Construct the structural diagram of the winding machine (Fig. 41a) if generalized actuating forces are applied to links a) 1,2,3 , b) 1,11,3 . 9 Problems 35 Answer: a) Fig. 41b; b) Fig. lAIc 1. 7. Construct the structural diagram of the planar manipulator depicted in Fig. IA2a and do the structural inversion. a) b) c) d) Fig. 35. Kinematic chains 36 1 Structure of Machines and Mechansims a) b) c) Fig.

Let the axis 0 sX s be directed along the line of translational motion of link s relative to link (s -1). z s s s s•. Obviously, the translational motion of link s does not change the orientation of the axes. Therefore, we have As-I ,s = As-I,s' = As-I ,s(O) = const. 19) From Fig. 20) 48 2 Geometric Analysis of Mechanisms Next, the equations of geometric analysis will be derived that will allow us to determine the coordinates of link s of the kinematic chain, shown in Fig. 5, and the Cartesian coordinates of some point M.