Elements of Dynamic; An Introduction to the Study of Motion And Rest in Solid And Fluid Bodies

Cover Elements of Dynamic; An Introduction to the Study of Motion And Rest in Solid And Fluid Bodies
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Any path described by a point in a plane moving with three-bar motion may also be described in two other ways by three-bar motion. Suppose (second figure) that ah, hk, hb are the three bars, o the moving point which is rigidly connected with hh by the triangle ohJc. Then the theorem is that the path of o may TRIPLE GENERATION.
149 also be described by means of the bars ag, gfjc, or the bars hd, de, ec. The triangles hko, gof, ode are similar to one another, and the figures ahog, hdok, cfoe are
...parallelo- grams.
The theorem has been put by Prof. Cayley into the following elegant form. Take any triangle abc (first figure) and through any point o within it draw lines hf, eh, gd parallel to the sides. Let the triangles hko, gof, ode be supposed rigid and jointed together at o, and let the other lines in the figure represent bars forming three jointed parallelograms. Then however the system is moved about in its plane (e.g. into the configuration of the second figure) the triangle abc will be always of the same shape.


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