Solve Example 20.5 by fixing x, y, z axes to rod BD so that Ω = ω₁ + ω₂. In this case the collar appears only to move radially outward along BD; hence Ω_xyz = 0.

Solve Example 20.5

The pendulum shown in Fig. 20-13 consists of two rods; AB is pin supported at A and swings only in the Y-Z plane, whereas a bearing at B allows the attached rod BD to spin about rod AB. At a given instant, the rods have the angular motions shown. Also, a collar C, located 0.2 m from B, has a velocity of 3 m/s and an acceleration of 2 m/s² along the rod. Determine the velocity and acceleration of the collar at this instant.

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Z, z, z', z" A ₁ = 1.5 rad/s² X, x₁ = 4 rad/s x' w₂ = 5 rad/s 350 4 0.5 m 0.2 m ₂ = 6 rad/s² Fig.20-13 C "Y, y' 3 m/s 2 m/s² D y, y"